> [ bjbj 4.ΐΐ66yyyyyY\DCCCCCCCF~IzCyNCyyC...yyC.C..?AM~"A@CC0DY@\I.I0AIyA.CC.DI6 ?: LADOKE AKINTOLA UNIVERSITY OF TECHNOLOGY, OGBOMOSO.
DEPARTMENT OF PURE AND APPLIED MATHEMATICS
MATHEMATICS
FACULTY OF PURE AND APPLIED SCIENCES
STUDENT
HANDBOOK
LADOKE AKINTOLA UNIVERSITY OF TECHNOLOGY,
PMB 4000, OGBOMOSO
DEPARTMENT OF PURE AND APPLIED MATHEMATICS
FACULTY OF PURE AND APPLIED SCIENCES
STUDENTS
INFORMATION HANDBOOK
SEPTEMBER, 2012
TABLE OF CONTENTS
Front Cover ..i
Table of Contents.....ii
The Viusitors...iii
THE VISITORS
Executive Governor of Oyo State
SENATOR ISIAKA ABIOLA AJIMOBI
Executive Governor of Osun State
Mr. RAUF ADESOJI AREGBESOLA
LIST OF PRINCIPAL OFFICERS OF THE UNIVERISTY
CHANCELLOR
HON. ASIWAJU AHMED TINUBU
Ag. VICE CHANCELLOR
Prof. Adeniyi Sulaiman Gbadegesin
DEPUTY VICECHANCELLOR
Prof. T. A. Adebayo
THE UNIVERSITY REGISTRAR
MR. J. A. AGBOOLA
Ag. UNIVERSITY BURSAR
Mr. A. B. C. Olagunju
THE UNIVERSITY LIBERIAN
Mr. I. O. AJALA
STAFF LIST
Academic Staff
Ag. Head
Dr. S. O. Adewale
B. Tech, M. Tech, Ph.D, (Ogbomoso) Reader
Prof. (Mrs.) F. O. Akinpelu
B.Sc. (Zaria), M. Sc., Ph.D. (Ilorin) Professor
Prof. A. T. Oladipo
B. Sc., M. Sc., Ph.D (Ilorin) Professor
Dr. A. W. Ogunsola MAN, NMS
B. Tech. M. Tech. (Ogbomoso), Ph.D. (Ogbomoso) Reader
Dr. (Mrs.) T. O. Oluyo
B. Sc. (Ilorin), M. Tech., Ph.D. (Ogbomoso) Senior Lecturer
Dr. S. Oluyemi
B. Sc. (Lagos), M. Sc. (Ibadan), Ph.D. (Ogbomoso) Senior Lecturer
Dr. O. A. Ajala
B. Tech. M. Tech. Ph.D. (Ogbomoso) Senior Lecturer
Mr. O. A. Adepoju
B. Tech. M. Tech. (Ogbomoso) Lecturer II
Mr. S. Olaniyi
B. Tech. (Ogbomoso), M. Sc., (Ibadan) Assistant Lecturer
Administrative Staff
Mrs. E. O. Olaleye  Senior Confidential Secretary
Mrs. F. A. Asafa  Chief Data Management Officer
Mrs. C. O. Olaniyi  Clerical Officer
Mrs. R. T. Bhadmus  Senior Office Assistant
Other Departmental Officer
Examination Officers  Dr. T. O. Oluyo/Mr. R. A. Oderinu
Use of Computers Coordinator  Mr. R. A. Oderinu
LEVEL ADVISERS
100 Level  Dr. O. A. Ajala
200 Level  Dr. S. O. Adewale
300 Level  Dr. (Mrs.) T. O. Oluyo
400 Level  Mr. S. Olaniyi
500 Level  Mr. O. A. Adepoju
DEPARTMENTAL COMMITTEES
Board of Examiners
Dr. S. O. Adewale  Chairman
All Academic Staff from rank of Assistant Lecturer and above  Member
Mrs. E. O. Olaleye  Secretary
Board of Studies
Dr. S. O. Adewale  Chairman
All Academic Staff from rank of Assistant Lecturer and above  Member
Mrs. E. O. Olaleye  Secretary
BRIEF HISTORY OF THE DEPARTMENT
1. BRIEF HISTORY OF THE DEPARTMENT
The Department of Pure and applied Mathematics was established in 1990 with Professor R. O. Ayeni as the foundation Head of Department. Three programmes were approved to run in the department. These are B. Tech. Mathematics, B. Tech. Industrial Mathematics and B. Tech. Statistics.
The Department has graduated at least thirteen (13) sets of students with B. Tech Mathematics three (3) sets of students with B. Tech. Statistics. Moreover, Senate at one of its meetings in May, 2012 gave approval for the separation of the B. Tech Statistics programme from the department which led to the creation of a new Department of Statistics.
2. PHILOSOPHY
The philosophy that guides the programme is to train the students in order to produce Professional mathematicians who are able to apply mathematical techniques in the study of scientific and technological problem and are competent enough to undertake research activities in various branches of mathematics and Science in general. In line with the Universitys mission the training of the graduate will be geared towards producing quality graduate with great entrepreneural skills suitable for national development.
3. THE OBJECTIVES OF THE DEPARTMENT PROGRAMMES
The main objectives of the Department Programmes at the undergraduate level are:
To provide adequate instructions and training of professional Mathematicians who will be able to apply mathematical techniques in the study of scientific and technological problems and who will be competent enough to undertake research activities in various branches of mathematics; and
To give instructions and expert advice in mathematics to those who require them in some other disciplines in the various departments of the University.
4. DEGREES OFFERED
The department offers two programmes leading to the following degree
B. Tech (Maths) with restricted electives in Physical Sciences and Engineering (Industrial Mathematics).
B. Tech (Maths) with restricted electives in Biology (Biomathematics). Thirteen (13) sets of students had been graduated from the B. Tech (Maths) with restricted electives in Physical Sciences and Engineering. Many of these graduates are working in several sectors of the Nigerian economy and other countries. Some of them had obtained higher academic qualifications, including M. Sc and Ph.D Degrees.
5. MODES OF ADMISSION INTO B. TECH PROGRAMMES OF THE DEPARTMENT
Admissions can be sought
into 100 Level
direct into 200 Level
into any approved level by transfer
change from other programmes of the university to any of the programmes in the department
6. ADMISSION REQUIREMENTS
(i) To be eligible for admission by any mode, a candidate must possess at least five credit passes in the WAEC/NECO SSCE or the O/L GCE or any equivalent qualifications. The credit passes must include English Language, Biology, Chemistry, Mathematics and Physics.
(ii) To be eligible for admission into 100 Level, a candidate in addition to 5 (i) above must pass both the UTME and the University post UTME Examination or score a minimum of 250 marks in the University PreDegree final Examinations.
To be eligible for admission direct into 200 Level, a candidate must in addition to 5 (i) above, possess at least one of
A/L GCE or equivalent qualifications with passes in mathematics, Physics and any one of Biology and Chemistry
NCE (Maths/Stats) with minimum grade of B. and
OND (Statistics) with a minimum of Upper Credit Pass
To be eligible for transfer from another programme within the University to any of the programmes in the department, a candidate can do so through the University approved process, provided he/she meets the initial requirements for admission into the departments programme of his/her choice.
To be eligible for transfer from another university into any of the programmes in the department, a candidate must satisfy the university regulations governing this mode of admission into the university. Normally no such transfer is to be entertained above 200 Level.
7. MATRICULATION
All students entering the University for the first time will be required to matriculate at a formal ceremony to be presided over by the ViceChancellor which normally takes place after registration and having been certified that such candidates are qualified for the courses offered them on admission.
The Dean of each Faculty presents students from his/her Faculty for matriculation while the registrar administers the matriculation Oath. Students are made to solemnly undertake and swear to observe and respect the provisions of the Ladoke Akintola University of Technology, Ogbomoso, laws and status ordinances and regulations which are now in force or which may be brought into force in addition to not belonging to secrete cult.
8. DURATION OF B. TECH DEGREE PROGRAMME
Normally, the B. Tech Programmes are five year programmes
A student admitted through UTME or PreDegree is expected normally to spend a minimum of five (5) years and a maximum of seven and half (7) years
A student admitted through Direct entry is expected normally to spend a minimum of four (4) years and a maximum of six (6) years.
A student admitted though transfer is expected normally to spend a minimum of the number of years left for him/her to graduate and a maximum of one and half (1) of the number of years left. For example, a student transferred to 300 Level has three years left to graduate. Therefore he/she normally has a minimum of three (3) years and a maximum of four and half (4) years to graduate.
9. REGISTRATION FOR courses
All students of the department must register at the beginning of each semester for courses approved by the university authority. Normally a student is allowed to register for a minimum of twelve (12) units and a maximum of twentyfour (24) units per semester, unless otherwise stated in a situation where a final year student needs to exceed the maximum of twentyfour (24) units for him/her to be able to graduate, a formal application to that effect must be made in writing to the senate through the HOD and through the Dean for approval.
A student is free to borrow courses from other departments if he/she wishes to do so.
10. UNIT LOAD
A unit is fifteen onehour lecturer or tutorial or a series of fifteen threehour practical classes, or the combination of these types of instruction.
11. REGISTRATION PROCEDURE
11.1 New Students
The procedure for the registration of new students is as follows:
Obtaining the students preregistration forms. Filling it and returning it to the Admissions Officer with the require credentials.
Collecting the registration kit (green file) from the Admission officer
Presenting the originals of the required credential to the Admission Officer who will sign the preregistration forms and academic clearance after the credentials have been checked and verified and entry qualifications confirmed.
Proceeding to the Faculty Officer who will issue course registration forms and direct students to the appropriate Heads of Departments for guidance in selecting courses.
After selection of courses, filling course registration forms separately and completely with biro and obtaining the signature of Course and Level Adviser.
Submitting course registration forms to the Faculty officer for the signature of the Dean; and
Finally, asking the Faculty Officer for copy of the course registration form.
IMPORTANT: Note that registration is not complete until all payments are made and registration forms are submitted to appropriate places.
11.2 Returning Students
i. After the payments have been made, proceeds to the Faculty Officer and obtain
course registration forms.
ii. Consult with the appropriate Head of Department for guidance in selecting courses.
iii. After the selection of courses obtaining signature of Course and level Adviser
iv. Submitting course registration forms to the Faculty Officer for the signature of the Dean.
v. Finally, asking the Faculty Officer for copy of the course registration form.
NB: The online registration is in full operation now.
12. SEMESTER AND SESSION
The University runs a semester system.
A semester is normally a period of sixteen (16) weeks of instruction. The period of instruction is followed by a period of examinations.
A session consists of two consecutive semesters as determined by the University Senate (Harmattan & Rain).
13. REGULATIONS IN RESPECT OF CONDUCT OF EXAMINATIONS
14.1 REGULATIONS GOVERNING THE CONDUCT OF UNIVERSITY EXAMINATIONS
DEFINITION OF TERMS
University Examinations
University Examinations include semester.
Professional and other Examinations involving the participations of both the Department of Faculty and the examination office.
Continuous Assessment means course tests, tutorial and other graded assignments done within the Department/Faculty where the course is being taught.
Semester
A semester is onehalf of an academic year as determined by senate.
Session
A session consists of two semester otherwise referred to as an Academic year as determined by senate.
Course Unit/Credit
One credit/unit represents fifteen of lecture/tutorial or 45 hours practical work per semester.
Two units/credits represent thirty hours of lecture/tutorial or 90 hours of practical work per semester.
Three credits/units represent fortyfive hours of lecturer/tutorial or 135 hours of practical work per semester.
There are courses that purely theoretical or practical while some others are combination of both.
15 EXAMINATION OFFENCES AND SANCTIONS
1. Code of Conduct: Candidates shall
a. Not use or consult, during an examination, such books, papers, instruments or other materials or aids as are specifically permitted or provided by the Department in which the examination is being held.
b. Not introduce nor attempt to introduce into examination venue handbags, notes, instruments or other materials or aids that are not permitted.
c. Not enter any examination venue with any inscription on any part of the body e.g. palm, arm, thigh, etc, if such inscriptions bear any relevance to the examination.
d. Not pass or attempt to pass any information from one person to another during an examination.
e. Neither act in collusion with any other candidate(s) or person(s) or copy nor attempt to copy from another candidate, nor engaged in any similar activity.
f. Not disturb or distract any other candidate(s) during the examination
g. Not be allowed to leave an examination venue until after 75% of the time allocated for the particular paper has expired.
h. Not use other people to sit for any University Examination on their behalf.
Failure to observe any of the rules (a) to (h) above, shall prima constitute examination misconduct. The table below contains the various examination offences and the respective sections as approved by the senate.
S/NExamination OffenceSanction1.Involvement in leakages of examination questions and/or marking scheme:
Student(s) involved
Staff involved
Expulsion
Dismissal2.Illegal possession of answer script(s) by student
Blank answer script(s) Script(s) containing answersSuspension for two (2) Semesters
Expulsion3.Possession of unauthorized text(s) filled with more than one handwriting:
Student(s) involved
Staff complicity in multiple handwriting malpractices
Expulsion
Dismissal4.Possession of unauthorized text(s) and illustration(s) of any form that aid examinations malpracticeSuspension for 4 Semesters5.Impersonation (machinery) in writing examinations:
Student(s) involved
Staff complicity in impersonation malpractices
Impersonation in any form
Expulsion
Dismissal6.Student(s) Involvement in assault on personnel involved in InvigilationExpulsion/Dismissal of parties involved7.Assaults on personnel involved in invigilation
Harassment and/or battery of personnel involved in InvigilationSuspension for 4 Semesters
Expulsion8.Harassment of costudents for noncooperation in examination malpractices
Battery of costudents for noncooperation in examination malpracticesSuspension for 2 Semesters
Expulsion9.Falsification of identity, such as names, matriculation number, etc, by a studentSuspension for 4 Semesters10.GraftingSuspension for 2 Semesters11.Exchanging of scripts or information during examination failure to submit examination answer scriptSuspension for 4 semesters
2. Procedure for Investigating Alleged Examination Misconduct:
(a) At the discretion of the Chief invigilator, a candidate may be required to leave the examination venue when his/her conduct is judged to be disturbing or likely to disturb the examination. The Chief Invigilator shall report immediately any such action taken to the Dean through the Faculty Examination Coordinator after the completion of the examination by the candidates.
(b) Any candidates suspected of any examination irregularity shall be required to sine and submit to the Chief Invigilator a written statement in the Examination Hall Failure to make a written statement shall be regarded as an admission of the charge against such a candidate.
(c) The dean shall, within 48 hours of receipt of a report, set up a panel of not less than three (3) academic staff to investigate the report. Recommendation shall be made available within two (2) weeks through the Deputy Registrar (Academic) to the Registrar who shall on the basis of the recommendations, determine whether or not the matter should receive the attention of the Students Disciplinary Committee.
(d) The Student Disciplinary Committee shall within weeks of receiving such a report, investigate and recommend penalty in cases of proven misconduct to the ViceChancellor in accordance with section 17 of the University Act.
16. THE COURSE GRADING SYSTEM
SCORE% LETTER GRADEPOINT
039 F 0
4044 E 1
4549 D 2
5059 C 3
6069 B 4
70100 A 5
17. GRADING POINT, GRADE POINT AVERAGE AND CUMULATIVE GRADEPOINT AVERAGE.
17.1 GRADE POINT (GP)
If a student has a score of 61% in a course that has 3 units, then the students letter grade is B and the corresponding point is 4. Therefore the students grade point (GP) for that course is 3 x 4 = 12.
GP = number of units X corresponding point.
17.2 The grade point average (GPA) is the average of grade points for the semester. If a students for the Harmattan Semester are as follows:
(1) (2) (3) (4) (5) (6)
Course Units Score%Letter Grade Point GP
MTH 201 3 60 B 4 12
MTH 203 2 54 C 3 6
MTH 207 3 64 B 4 12
MTH 211 3 80 A 5 15
STA 207 4 60 B 4 16
BCH 201 3 50 C 3 9
CSE 201 3 65 B 4 12
GNS 209 2 71 A 5 10
23 92
The entries under (6) are the products of corresponding entries under (2) and (5)
For example the 15 for MTH 211 is obtained from 3 x 5
The sum of the units is 23
The sum of the GPs is 92
Therefore the average of the GPs is
92
GPA = = 4
23
NOTE that GPA is computed per semester
17.3 Cumulative Grade Point Average (CGPA)
The cumulative grade point average (CGPA) is the grade point average of all the course taken to date.
Example: Suppose a student in year 2 who is a direct admission student has the following cumulative records:
HARMATTAN RAIN SEMESTER
Course Units Grade GP COURSE Units Grade GP
MTH 201 3 B 12 MTH 202 3 C 9
MTH 203 2 C 6 MTH 206 2 B 8
MTH 207 3 B 12 MTH 208 3 C 9
MTH 211 3 A 15 MTH 212 4 B 16
STA 207 4 B 16 MTH 210 2 B 8
BCH 201 3 C 9 STA 208 4 B 16
CSE 201 3 B 12 CSE 202 2 B 8
CSE 204 2 C 8
GNS 209 2 A 10 GNS 202 2 C 6
23 92 24 98
GPA = 92 = 4 GPA = 88 = 3.667
23 24
CGPA = GPA = 4 CGPA = 92 + 88 = 180 = 3.89
23 + 24 47
18. GOODSTANDING, PROBATION AND WITHDRAWAL
(i) Good standing: At the end of semester a student is said to be in good standing if his/her cumulative grade point average (CGPA) is at least 1.0
(ii) Probation: A student shall be on probation for the duration of the semester following a semester at the end of which he/she is found not to be in good standing
(iii) Withdrawal: A student shall be advised to withdraw from the programme if at the end of the probational semester he/she still has a CGPA less than 1.0
19. GRADUATION REQUIREMENTS
To qualify for the award of the degree of the programme admitted into, a student must be found worthy in learning if he/she satisfies the following conditions.
Passed all the University required courses
Passed all the Department required courses
Satisfied residential requirements in terms of duration of studentship with respect to mode entry.
20. CLASSIFICATION OF DEGREE
The degree awarded by the University are classified according to CGPA as follows:
CGPA RANGECLASS OF DEGREE4.50 5.00
3.50 4.49
2.40 3.49
1.50 2.39
1.00 1.49First Class Honours
Second Class Upper Honours
Second Class Lower Honours
Third Class Honours
Pass
21. LEVEL ADVISORS
The level advisors are to assist/advise students on choice of courses. They should also provide academic guidance and counseling to the students, particularly the weak ones. Students are encouraged to interact adequately with their level advisers, who also double as their level academic record keepers.
22. PROGRAMMES OF INSTRUCTION
To be awarded a B.Tech Degree of the University a student must pass all of the following courses or parts of the specified on the programme.
22.1 UNIVERSITY REQUIREMENTS
The University requires each student of the Department to offer and pass the following courses in order to qualify for an award of a degree of the University
22.2 DEPARTMENTAL REQUIREMENTS
Departmental Requirement for B. Tech (Maths) Restricted electives in physical Sciences and Engineering.
100 LEVELS
Course Code Course Title L T P Units
BIO 101 General Biology I 3 0 0 3
BIO 102 General Biology II 3 0 0 3
BIO 103 Experimental Biology I 0 0 3 1
BIO 104 Experimental Biology II 0 0 3 1
CHM 101 General Chemistry I 3 1 0 4
CHM 102 General Chemistry II 3 1 0 4
CHM 191 Experimental Chemistry I 0 0 3 1
CHM 192 Experimental Chemistry II 0 0 3 1
PHY 101 General Physics I 3 1 0 4
PHY 102 General Physics II 3 1 0 4
PHY 191 Experimental Physics I A 0 0 3 1
PHY 192 Experimental Physics I B 0 0 3 1
MTH 101 Elementary Mathematics I 4 1 0 5
MTH 102 Elementary Mathematics II 4 1 0 5
GNS 101 Use of English I 2 0 0 2
GNS 102 Use of English II 2 0 0 2
FAA 101 Fundamental Drawing 1 0 3 2
GNS 104 Science & Technology in Africa 2 0 0 2
CSE 100 Introduction to Computing 1 1 1 1
LIB 101 Use of Library 1 0 0 0
200 LEVELS
Course Code Course Title L T P Units
MTH 201 Mathematical Method I 2 1 0 2
MTH 203 Linear Algebra I 1 1 0 2
MTH 207 Real Analysis I 1 1 0 2
MTH 211 Introductory Applied Mathematics 2 1 0 3
STA 207 Statistics for Physical Science
and Engineering 3 1 0 4
CHM 231 Basic Physical Chemistry 3 1 0 4
GNS 209 Citizenship Education
MTH 202 Elementary Differential Equation I 2 1 0 3
MTH 206 Linear Algebra II 1 1 0 2
MTH 208 Introduction to Numerical Analysis 2 1 0 3
MTH 212 Mathematical Method II 3 1 0 4
MTH 210 History of Mathematics 1 1 0 2
STA 208 Probability II 3 1 0 4
300 LEVEL
Course Code Course Title L T P Units
MTH 301 Abstract Algebra I 2 1 0 3
MTH 303 Elementary Differential Equations 2 1 0 3
MTH 305 Vector and Tensor Analysis 2 1 0 3
MTH 307 Sets, Logic and Algebra 2 1 0 3
MTH 309 Electromagnetism 2 1 0 3
CSE 301 Computer Programming 2 1 0 3
MTH 304 Metric space Topology 2 1 0 3
MTH 306 Real Analysis II 2 1 0 3
MTH 308 Computer Analysis I 2 1 0 3
MTH 310 Dynamics of a Rigid Body 2 1 0 3
STA 302 Probability III 3 1 0 4
CSE 310 Numerical Computation II 2 1 0 3
400 LEVEL
Course Code Course Title L T P Units
MTH 401 Complex Analysis II 2 1 0 3
MTH 403 Abstract Algebra II 2 1 0 3
MTH 405 Introduction to Mathematical
Modeling 2 1 0 3
MTH 407 Lebesque Measured and Integration 2 1 0 3
MTH 409 Fluid Dynamics I 2 1 0 2
MTH 411 Theory of Algorithms & Application 2 0 3 3
CSE 311 Theory Computation 2 1 0 3
500 LEVEL
Course Code Course Title L T P Units
MTH 501 Intro, to Operation Research 2 1 0 3
MTH 503 Partial Differential Equations 2 1 0 3
MTH 507 Functional Analysis 2 1 0 3
MTH 509 Fluid Dynamics II 2 1 0 3
MTH 511 Mathematical Methods III 3 0 0 3
MTH 512 Analytical Dynamics 2 1 0 3
MTH 513 Elasticity 3 0 0 3
MTH 514 System Theory 2 0 3 3
MTH 517 Quantum Mechanics 3 0 0 3
MTH 502 General Topology 2 1 0 3
MTH 504 Ordinary Differential Equations 2 1 0 3
MTH 508 Measure Theory 3 1 0 4
STA 504 NonParametric Method 3 1 0 4
STA 506 Operation Research II 3 1 0 4
STA 508 Laboratory for Operation Research 0 0 2 2
MTH 509 Project 0 0 0 6
DESCRIPTION OF MATHEMATICS COURSES
MTH 101 Elementary Mathematics I (4 1 0) 5 Units
Set Theory: Set, Union, Intersection, Empty set and universal set, complement of a set, subset, finite and infinite set, Venn diagram, Mapping and Functions. Operations with Real Numbers. The real number R and its extension to the set of complex number C Equation involving one variable. The Reminder Theorem and the Factor Theorem. Equation is two variables, inequalities, partial fractions, surds indices and logarithms.
Theory of Quadratic Functions and Equations. The quadratic function and the relation between the roots of a quadratic equation and the coefficients.
Sequences and Series: Finite sequences and series, the arithmetic sequences and series, the finite and infinite geometric sequences and series.
The Binomial Theorem: Elementary examples in the use of induction, permutation and combination and their applications. The Binomial Theorem for a positive integral index. The use of the expansion (1 + x), where n is fractional or negative: simple approximations. Matrices: Definition of m x n matrices: addition of matrices, matrix multiplication and inversion. Determinant of a matrix, application simple linear equations, consistency and linear dependence.
MTH 102 ELEMENTARY MATHEMATICS 11 (41 0) 5 UNITS
Trigonometry: Circular measure, small angles, definition and properties of si ne, cosine, tangent, etc Formulae for Sin(A + B), Cos(A + B) Sin A/2, Tan A/2. Etc Sine and Cosine formulae, factor formulae, inverse trigonometric function, functions, General solution of trigonometric equations such as a Cos + bSin = C.
Calculus: Differentiation of algebraic of algebraic, exponential, trigonometric, product and quotient functions, applications of differentiation to curve sketching, etc. Maxima and minima. Definite and indefinite integrals with application to areas and volumes. Simple techniques of integration such as Integration by parts etc. Simple first order ordinary differential equation.
Coordinate Geometry: Coordinates, Equations of lines, circles ellipse, hyperbola and parabola.
Statistics: Finite sample spaces, definition of probability of finite sample spaces and examples. Probability as proportion of areas, conditional probability of events. Independence, tree diagrams, variables and cumulative frequency distributions mean, median, variable and covariance conditional expectation and linear correlation, using scatter diagram.
MTH 201 MATHEMATICAL METHOD: 21 0 (3 UNITS)
Prerequisite MTH 102
Sequence and series : Limits, continuity, Differentiability, Implicit functions, sequences, series, test for convergence, sequences and series of function.
Numerical Methods: Introduction of iterative methods, Newtons method applied to finding roots. Trapezium and Simson 1 as rules of integration.
Differential Equations: Introduction equation of first order and first degree, separable equations, homogeneous equation, exact equations linear equation, Bernoullis and Riccati equations. Application to mechanics and electronic Orthogonal and oblique trajectories. Second order equations with constant coefficients. General theory of nth order linear equations. Laplace transform, solution of initial value problem by Laplace transform method. Simple treatment of partial equations in two independent variables.
MTH 202 ELEMENTARY DIFFERENTIAL EQUATIONS I: 210 (3 UNITS)
First order ordinary differential equations. Existence and uniqueness. Second order ordinary differential equations with constant coefficient. General theory of order linear equations. Lap lace transforms, solution of partial differential equations in two independent variables. Applications of O.D.E. and P.D.E to physical, life and social sciences.
MTH 203 LINEAR ALGEBRA 1;1 1(2 UNITS)
Prerequisite MTH101, 102
Vector space over the real field. Subspace, linear independence. Basis and dimension. Linear transformation and their representation by matrices. Algebra matrices.
MTH 207 REAL ANALYSIS 1: 2 1 0 (3UNITS)
Prerequisite MTH101
Bound of real numbers, sequence and series convergence, converge of sequence numbers. Monotone sequence, the theory of nested intervals. Cauchy sequences, test of convergence of series.
Absolute and conditional convergence of series, and rearrangements.
Completeness of real and incompleteness of rationale.
Continuity and differentiability of functions. Rolles mean and value theorem for differentiable functions. Taylors series.
STA 207 STATISTICS PHYSICAL SCIENCES AND ENGINEERING 310
(4 UNITS)
Measures of location and dispersion in simple and grouped data exponentials. Element of probability and probability distribution. Estimation and tests of hypotheses concerning the parameters of distributions. Regression, correlation and analyjsis of various contingency table. Nonparametric inference.
MTH 208 INTRODUCTION TO NUMERICAL ANALYSIS: 210 (3 UNITS)
Prerequisite MTH 101
Solution of algebraic and transcendental equations. Curve fitting. Error analysis. Interpolation and approximation. Zeros of nonlinear equations is one variable. Systems of linear equations. Numerical differentiation an integration. Initial value problems of ordinary differential equations.
MTH 210 HISTORY OF MATHEMATICS: 110 (2 UNITS)
Topics in the History of Mathematics with emphasis on the development of modern Mathematics.
MTH 211 INTRODUCTORY APPLIED MATHEMATICS : 2 1 0 (3UNITS)
Vectors, geometry and dynamics
Geometric representation of vectors in 1 3 dimension, components, direction cosines. Addition, Scalar, multiplication of vectors, linear independence. Scalar and vector products
MTH 212 MATHEMATICAL METHODS II 3 1 0 ( 4 UNITS)
Use of the Neyman Pearson lemma Hypotheses testing, the power of a test. Point and internal estimation. (Testing and estimation of large sample situations) binomial, Poisson, normal contingency tables, Goodness of fit tests.
HARMATTAN SEMESTER
MTH 301 ABSTRACT ALGEBRA I: (3 UNITS) 210
Prerequisite MTH 101, 203
Group: Definition, examples including permutation groups. Subgroups, coset. Lagranges theorem and applications. Cyclic groups. Rings: definition examples including Z, Zn rings of polynomials and matrices. Integral domains, fields. Polynomial rings, factorization. Euclidean algorithm for polynomials H.C.F. an L.C.M of polynomials.
MTH 303 ELEMENTARY DIFFERENTIALEQUATIONS II: (3 UNITS)
Series solution of second order linear equations. Bessel, Legendre and pypergeometric equations and functions. Gamma Beta functions Sturnliouvelle problems.Orthogonal polynomials and functions. Fourier, Bessel and Fourier Legendre Series. Fourier transformation. Solution of Laplace, wave and heat equations by Fourer method.
MTH 305 VECTOR AND TENSOR ANALYSIS: (3 UNITS)
Prerequistie MTH 201,212
Vector algebra. Vector, dot and crossProducts. Equation of curves and surfaces. Vector differentaiation and applications. Gradient, divergence and curl. Vector integrate, line surface and volume integrals.Greens Stokes and divergence theorems. Tensor products of vector space. Tensor algebra. Symmetry. Gartesan tensors
MTH 307 SETS, LOGIC AND ALGERA: (3 UNITS)
Prerequisite MTH 101
Introduction to the language and concepts of modern Mathematics. Topic include; Basic set theory mappings, relations, equivalence and other relations, Cartesian products. Binary logic, methods of proof. Binary operations. Algebraic structures, semigroups, rings, integral domains fields. Homoeomaphics. Number systems; properties of integers, rationals, real and complex numbers.
MTH 309 ELECTROMAGNETISM: (3 UNITS)
Maxwells field equations. Electromagnetic waves and Electromagnetic theory of lights. plane detromagnetic waves in nonconducting media, reflection and refraction at place boundry. Waves guides and resonant cavities. Simple radiating systems. The LorentzEinstein transformation. Energuides and momentum. Electromagnetic 4vectors. Transformation of (E.H) fields. The Lorentz force.
RAIN SEMESTER
MTH 304 METRIC SPACE4 TOPOLOGY: (3 UNITS 210)
Sets matrices, and examples open spheres (or balls). Open sets and neighborhoods. Closed sets. Interior exterior, frontier, limits points and closure of set. Dense subsets and separable space. Convergence in metric spare homomorphism. Continuity and compactness, Prerequisite MTH 202
MTH 306 REAL ANALYSIS II: (3 UNITS: 210)
Riemann integral of functions r) R: continuous monopositive functions. Functions of bounded variation. The Riemann still jets integral. Point wise and uniform convergence of sequences and series of function R) R. Effects on limits (sums) when the functions are continuous differentiable or Riemann
Prerequisite MTH 207
MTH 308 COMPLEX ANALYSIS 1 (3 UNITS: 210)
Functions of a complex variable. Limits and continuity of functions of a complex variable. Derivation of the CauchyRiemann equations. Cauchys theorems and its main consequences. Convergence of sequences and series of functions of a complex variable. Power series. Taylor series.
Prerequisite MTH 203, 207
MTH 310 DYNAMICS OF A RIGID BODY: (3 UINTS: 210)
General motions of a rigid body as a translation plus a rotation. Moment, and products of inertia in three dimensions. Parallel and perpendicular axes theorems. Principal axes, Angular momentum, kinetic energy of rigid body. Impulsive motion. Examples involving one and twodimensional motion of simple system. Moving rates of reference; rotating and translating frames of reference. Coriolis force. Motion near the Earths surface. The Foucaults pendulum. Eulers dynamical equations for motion of a rigid body with one point fixed. The symmetrical top. Procession.
MTH 401 COMPLEX ANALYSIS II. (3 UNITS: 210)
Corequisite MTH 307
Laurent expansions. Isolated singularities and residues. Residue theorem Calculus of residue, and application to evaluation of integrals and to summation of series. Maximum Modulus principles. Argument principal. Rouches therem. The fundamental theorem of algebra. Principle of analytic continuation. Multiple valued functions and Riemann surfaces. Dirichlet and Newman problems. Maximum principle.
Prerequisite MTH 202.
MTH 403 ABSTRACT ALGEBRA II: (3 UNITS: 210)
Normal subgroups and quotient groups. Monomorphic isomorphism theorem. Cayleys theorems. Direct products. Groups of small order. Group acting on sets. Sylow theorems. Ideal and quotient rings. P.I.D. 8, U.F.DS Euclids rings. Irreducibility, Field extensions, degree of an extension, minimum polynomial. Algebraic and transcendental extensions. Straightedge and compass constructions.
Prerequisite MTH 207, MTH 307
MTH 405 INTRODUCTION TO MATHEMATICAL MODELLING: (3UNITS: 210)
Methodology of model building: Identification, formulation and solution of problems, causeeffect diagrams. Equation types. Algebraic, ordinary differential equations. Application of mathematical models to pluprical, biological, social and behavioral sciences.
MTH 407 LEBESGUE MEASURE AND INTEGRALS (3 UNITS: 210)
Lebesque measure, measureable and non measureable sets, Measurable function, Lebsque integral: Integration of nonnegative functions, the general integral converged theorems.
Prerequisite MTH 207, MTH 307
MTH 409 FLUJID DYNAMICS: I (3 UNITS: 210)
Real and Ideal fluids. Differentiation following the motion of fluid particles. Equations of motion and continuity for incompressible invisoid fluids. Velocity potentials and Stokes Stream functions. Bernoulli equation with application to flow along curved paths. Kinetic energy. Sources, sinks, doubles in 2 and 3 dimensions, limiting streamlines. Images and rigid planes.
Prerequisite MTH 202
MTH 501 INTRODUCTION TO OPERATION RESEARCH: (3 UNITS: 210)
Phases of operation Research Study. Classification of operation Research models, linear; Dynamic and integer programming. Decision Theory. Inventory Models, Critical Path Analysis and project Controls.
MTH 502 GENERAL TOPOLOGY (3 UNITS: 210)
Topological spaces, definition, open and closed sets neighborhoods. Coarser, and finer topologies. Basis and subbases. Separates axioms,. Compactness, local compactness, connectedness. Continuous functions, homeomorphones, topological invariants, spaces of continuous functions: Point wise and uniform convergence.
Prerequisite MTH 301.
MTH 503 PARTIAL DIFFERENTIAL EQUATIONS (UNITS: 210)
Initial value problems for hyperbolic and parabolic equation. Characteristic surfaces. Domain of dependence. Wave phenomena. Elliptic equation, Harmonic function. Greens function.
MTH 504 ORDINARY DIFFERENTIAL EQUATION1: (3 UNITS: 210)
Existence of solutions. Uniqueness of solutions. Method of successive approximations. Continuation of solutions. Systems of differential equations. The order equation. Extension of the idea of a solution, maximum and minimum solutions. Elementary differential inequalities. Dependence of solutions on initial. Conditions and parameters. Variation of solutions with respect to initial conditions and parameters.
Prerequisite MTH 201, 202 , 203, 305.
MTH 507 FUNCTIONAL ANALYSIS (3 UNITS: 210)
Normed Linear Spaces: Definition and Examples. Convex sets. Norms. Holders Minkowskis inequalities. RieszFisher theorem. Linear operations on finite dimensional spaces. Linear functionalism, space. Banach spaces, examples. Quotient spaces: Inner product spaces Topological linear spaces.
Hilbert spaces, examples. Linear operators in Hilbert spaces. Joint operators. Hermitian operators. Orthogonality; orthogonal complement and projections in Hilberts spaces.
Prerequisite MTH 314 and MTH 403
MTH 508 MEASURE THEORY (4 UNITS: 310)
Abstract Integration. Settheoretic notations and terminology. The concepts of measurability. Simple functions. Elementary properties of measures. Integration of positive functions. Integration of complex functions. The role played by sets measure zero. Convex functions and inequalities. Lpspaces Approximation by continuous functions.
MTH 509 FLUID DYNAMICS II 3 UNITS: (210)
Navierstokes equations, Equation of energy. Simple exact solutions. Dynamic similarity, slow flows: stokes and OSeen flows. Laminar boundary layer theory. Thinkness, skin friction and heat transfer. Blasius solution for flat plate and similar solutions. Laminar boundary layer separation, small disturbance theory. Normal and oblique shock waves.
MTH 511 MATHEMATICAL METHODS (3 UNITS: 210)
Calculus of variation: Lagranges functional and associated density. Necessary condition for a weak relative extremum. Hamiltons principles Lagranges equations and geodesic problems. The Du BoisRaymond equation and corner conditions. Variable endpoints and related theorems. Sufficient conditions for a minimum. Isoperimetric problems. Variation integral transforms. Laplace, Fourier and Hankel transforms. Complex variable methods convolution.
Prerequisite MTH 207, MTH 307
MTH 512 ANALYTICAL DYNAMICS II (3 UNITS 210)
Lagranges equation for nonholonomic systems. Langrangian multipliers. Variational Principles. Calculus of variation. Hamiltons principle, Lagranges equation from Hamilttons principle. Canonicals transformations. Normal models of Variations. Hamilton Jacabi equations.
MTH 513 ELASTICITY (3 UNITS 210)
Particle gravitational field: Curvilinear coordinates, integrals. Covariant differentiation. Christofel symbol and matrix tensor. The constant gravitational field Rotation.
MTH 514 SYSTEMS THEORY (3 UNITS 210)
Lyapunov theorems. Solution of Lyapunov statibility equation ATP ? PA Q = Controllability and observability. Theorem on existence of solution of linear systems of differential operations with constant coefficients.
MTH 517 QUANTUM MECHANICS (3 UNITS 210)
Perticleware duality. Quantum poatulates. Schroedinger equation of motion. Potential steps and wells in I dimensia. Heisenberg formulation. Classical limit of Quantum mechanics. Computer brackets linear harmonic oscillator. Angular momentum 3d square well potential. The hydrogen atom collision in 3d.
Approximation methods for stationery problems.
34_`amŵʰʞ}n^QA4ht*5CJOJQJaJht*ht*5CJOJQJaJht*5CJ(OJQJaJ(h=cht*5CJ(OJQJaJ(ht*5CJ`OJQJ^JaJ`h?5CJ`OJQJ^JaJ`#h4h45CJ`OJQJ^JaJ`#h4h?5CJ`OJQJ^JaJ` h45h=ch=c5CJ`OJQJaJ` h=c5 h?5h=ch?5CJ OJQJaJ h=ch?65CJ(OJQJaJ(h=ch?5CJ(OJQJaJ(4_`am$a$gdt*$a$gd4$a$gd=cB D M N d e t u  }
:
F
оПucTH<*"he:hz456CJOJQJaJhz4CJOJQJaJh~CJOJQJaJh~5>*CJOJQJaJ"h~h~5>*CJOJQJaJh~h~5CJOJQJaJh~5CJ0OJQJaJ0ht*5CJ0OJQJaJ0h~h~5CJ0OJQJaJ0ht*5CJ4OJQJ^JaJ4#ht*ht*5CJ4OJQJ^JaJ4ht*5CJ`OJQJ^JaJ`ht*ht*5CJ OJQJaJ ht*ht*5CJOJQJaJ B C D N d e u v w x y z {  }
gd~$a$gd4$a$gdt*
!
"
#
$
%
&
'
(
)
*
+
,

.
/
0
1
2
3
4
5
6
7
8
9
:
gd~:
G
g
1STlgdz4$a$gdz4F
G
f
g
n
%&0²²ᢒuhVDVDV"h$hz456CJOJQJaJ"h$h$56CJOJQJaJh$5CJOJQJaJh$hN5CJ OJQJaJ hz45CJ OJQJaJ h$hz45CJ OJQJaJ h$h$5CJ OJQJaJ he:hN5CJOJQJaJhz45CJOJQJaJ"he:hz456CJOJQJaJhe:hz45CJOJQJaJhz456CJOJQJaJ01RST_`jklοޑΑtg[OChNCJOJQJaJh~CJOJQJaJhz4CJOJQJaJhw5CJOJQJaJh$h$5CJOJQJaJh$5CJOJQJaJhz45CJOJQJaJh$56CJOJQJaJ"h$h$56CJOJQJaJhe:hz4CJOJQJaJhe:hz45CJOJQJaJhe:h$5CJOJQJaJ"h$hz456CJOJQJaJ
,6HvwgdN$a$gdNgd~$a$gdz4+
@
J
R
\
f
g
=GĸrrrrrhN16CJOJQJaJhN1hN16CJOJQJaJhN1CJOJQJaJhN6CJOJQJaJhNhN6CJOJQJaJhNCJOJQJaJhN56CJOJQJaJ"hNhN56CJOJQJaJhNCJOJQJaJhNhNCJOJQJaJ,
.
g
h
%\]o8mgdNOlUVXgh˼˰zm]PzD4hh5CJOJQJaJhCJOJQJaJh,S5CJOJQJaJhh,S5CJOJQJaJh5CJOJQJaJh,SCJOJQJaJh^+5>*CJOJQJaJh^+CJOJQJaJhX<hX<CJOJQJaJhX<CJOJQJaJhN5>*CJOJQJaJhX<5>*CJOJQJaJhN1CJOJQJaJh,CJOJQJaJh,6CJOJQJaJ"UVWXgh+,O6[gd:,gd,S$a$gd,SgdN,3?D[\]tʾʾʾʲwj]P]Dh@CCJOJQJaJh:,5CJOJQJaJh@C5CJOJQJaJh:,5CJOJQJaJh:,h:,5CJOJQJaJh:,h:,CJOJQJaJhh:,CJOJQJaJh:,>*CJOJQJaJh:,CJOJQJaJh+CJOJQJaJhCJOJQJaJhhCJOJQJaJh>*CJOJQJaJh5CJOJQJaJ[\]^_`abcdefghijklmnopqrst$a$gd:,gd,S56DEIJyz$dh^a$gd#$
&Fdha$gd#gdeg7gdeYdhgd#$dh^`a$gd#gd:,59EIMy{µ{h{h{X{E2$h\S!h\S!CJOJQJaJmHsH$he:h2CCJOJQJaJmHsHh2CCJOJQJaJmHsH$h2Ch2CCJOJQJaJmHsH$h2Ch\S!CJOJQJaJmHsHh\S!CJOJQJaJhwCJOJQJaJhwhwCJOJQJaJhw5CJOJQJaJheg75CJOJQJaJheg7CJOJQJaJheY5CJOJQJaJheYCJOJQJaJhBCJOJQJaJ +@IJ [!\!µthh\O@\4\h[CJOJQJaJh,h,CJOJQJaJh,5CJOJQJaJh,CJOJQJaJh4`aCJOJQJaJh9Eh9ECJOJQJaJh9E5CJOJQJaJh9ECJOJQJaJh#CJOJQJaJh#5CJOJQJaJh2C5CJOJQJaJh2Ch2CCJOJQJaJh\S!CJOJQJaJ$h\S!h\S!CJOJQJaJmHsHh2CCJOJQJaJmHsHK ;J`f$
&Fdha$gd,$
&Fdha$gd,$0dh^`0a$gd,
$dha$gd,$
&Fdha$gd9E$0dh^`0a$gd9E0dh^`0gd]$
&Fdha$gd9Egdeg7 8 \!i"z"#Y%Z%%%P&&W(s(*$dh^a$gdr
$dha$gdr$
&Fdha$gd8u
$dha$gd8u$dh^a$gd8u$dh^a$gdxj
$dha$gd[$
&Fdha$gd,$
&Fdha$gd,\!l"y"z"%%H%X%]%%J&O&P&&&&W'V(W(Z(s(***+ζym`mTGTh*S5CJOJQJaJh*SCJOJQJaJhr5CJOJQJaJhrCJOJQJaJhhICJOJQJaJhgCJOJQJaJh+XCJOJQJaJh8u5CJOJQJaJh8uCJOJQJaJheFCJOJQJaJhCJOJQJaJhxjCJOJQJaJh[5CJOJQJaJhxj5CJOJQJaJh[CJOJQJaJ***+++,,,\..V//.0G000$0dh^`0a$gdM{
$dha$gdM{$
&Fdha$gd(C
$dha$gd(C$dh^a$gd*S
$dha$gd*S$dh^a$gdr+++++//40H01112J2N2d2~33333334#4*444¶tgXKh4u>*CJOJQJaJhhCJOJQJaJh>*CJOJQJaJhh5CJOJQJaJh5CJOJQJaJhCJOJQJaJh195CJOJQJaJh19CJOJQJaJhCJOJQJaJhY
dCJOJQJaJhM{CJOJQJaJhM{5CJOJQJaJh(C5CJOJQJaJh(CCJOJQJaJ01b112J2c2233334$4N44$dh^a$gd$
&Fdha$gd$0dh^`0a$gd
$dha$gd$dh^a$gd19
$dha$gd$0dh^`0a$gdM{44+5,5b5j5n555666/606j66677778
89v9w9<<<
=峤ppddXLdh?CJOJQJaJh
CJOJQJaJh,CJOJQJaJhp&hp&CJOJQJaJhp&5CJOJQJaJhp&CJOJQJaJh5jCJOJQJaJhlhlCJOJQJaJhl>*CJOJQJaJhlCJOJQJaJh4u>*CJOJQJaJh]CJOJQJaJh4uCJOJQJaJh4uh4uCJOJQJaJ4b5k55560666j77788w9::;$p0dh^p`0a$gdp&
$dha$gdp&$dh^a$gdl$
&Fdha$gdl$dh^a$gd4u$dh^a$gd4u$
&Fdha$gd4u;g;;2<
=="=+=$dh$Ifa$gdl$dh$Ifa$gdl
$dha$gd,$p0dh^p`0a$gdp&
==!="=*=+=,=.=/=v=w=====F>G>>>v?w?x?y?#@$@@@@@@@@%A&A0AɺɺɺɳɳɤɳxixiZixihh,CJOJQJaJhhCJOJQJaJhhOCJOJQJaJhhI\WhhI\WCJOJQJaJhhbhhbCJOJQJaJhhDhh?CJOJQJaJhhDCJOJQJaJhh?hhD5CJOJQJaJhh?5CJOJQJaJ"+=,=/=w=======q^^^^^^^^$Ifgdblkd$$IflFvR&
t0&644
layt =====><>F>q^^^^^^$Ifgdblkd$$IflFvR&
t0&644
laytF>G>J>>>>>>>>q^^^^^^^^$IfgdblkdR$$IflFvR&
t0&644
layt >>>]?x?q^^^$Ifgdblkd$$IflFvR&
t0&644
laytx?y?????
@@@@#@q[[[[[[[[[$$Ifa$gdlkd$$IflFvR&
t0&644
layt
#@$@'@o@@q[[[$$Ifa$gdlkdM$$IflFvR&
t0&644
layt@@@@@A&A0Aq^^^^^^$Ifgd=lkd$$IflFvR&
t0&644
layt0A1A4A~AAAAq^^^^^$Ifgd=lkd$$IflFvR&
t0&644
layt0A1A4A>A~AAAAA@BZB[B\BBBBCC C
CCCICJCZHŶ}qeXK?hKCJOJQJaJhM&5CJOJQJaJhK5CJOJQJaJhM&CJOJQJaJhI:CJOJQJaJh5CJOJQJaJhh.CJOJQJaJhh:hhophh:CJOJQJaJhhopCJOJQJaJhhhh=CJOJQJaJhh,CJOJQJaJhhCJOJQJaJhhOAAA@B[Bq^^^$Ifgd=lkdH$$IflFvR&
t0&644
layt[B\B`BiBBq^^^$Ifgd=lkd$$IflFvR&
t0&644
laytBBBBCq^^^$Ifgd=lkd$$IflFvR&
t0&644
laytC C
CCJCDExGqfWWDDD$p0dh^p`0a$gdK$dh`a$gdM&
$dha$gdkdC$$IflFvR&
t0&644
laytxGZHxHHHHHHII.IxII]JJK5KdK}KKK$0dh^`0a$gdq$dh^a$gdGG$0dh^`0a$gd 1a
$dha$gd"^$p0dh^p`0a$gdKZH^HwHxHHHHHHHHHHHHHHIII%II.I2IyI~III,JSJ\J]JJKKwwkkk_hqCJOJQJaJhc%CJOJQJaJh 1a5CJOJQJaJh 1aCJOJQJaJhI:CJOJQJaJh5PCJOJQJaJh^B]CJOJQJaJh:}CJOJQJaJh:}5CJOJQJaJhg5CJOJQJaJh"^5CJOJQJaJhp"5CJOJQJaJh"^CJOJQJaJ"KKWKXKbKcKLL0L?L@LALM&M'M)M.M/M5M9M:M=M@MAMKMhMiMnM²虍ҙrcTcha,hq/CJOJQJaJha,h)/CJOJQJaJha,hI:CJOJQJaJh)/CJOJQJaJh
anCJOJQJaJhSICJOJQJaJh&015CJOJQJaJh?h&015CJOJQJaJh?h?5CJOJQJaJ*jh*XCJOJQJUaJmHnHuh?CJOJQJaJh&01CJOJQJaJKKKKL0LALLLLM'M.M:M@MAMhMiMMMgNNNdh^gd)/gd)/$^a$gd
an$0^`0a$gd
an$0dh^`0a$gdqnMMMMgNNNNNNNNNNNNNNNNOOOOO O$O/O0O?OAOEOPOQOUOaOdOoOpOuOOOOOOOOOOOOOOOOOO³³³³³³³³ha,h)/>*CJOJQJaJha,hVCJOJQJaJha,hiTCJOJQJaJha,hI:CJOJQJaJha,h)/CJOJQJaJha,h)/5CJOJQJaJ8NNNO5OUOuOOOOOOPDPEPPPPP[QRRRRR0^`0gd)/0dh^`0gd)/dhgd)/gd)/OOOOOOOOOPP$P&PAPEPGPdPePPPPPPPPPP[Q\Q^Q`QiQRRRRT4TTȸȸؓظؓةةظظsظظssظظha,h)/>*CJOJQJaJha,ha,5CJOJQJaJ*jh*XCJOJQJUaJmHnHuha,hVCJOJQJaJha,h)/5CJOJQJaJha,hV5CJOJQJaJha,h)/CJOJQJaJ0jh*Xh*XCJOJQJUaJmHnHu&R^SSST4T5TTTTT$Ifgd/66lgd)/
&F dhgd)/dh^gd)/
TTTYUZU[UoUVVTWlWX+XXXXX"Y/YCYYYYYYYYYYYYZZZeZzZZZZZZZZZ[[[[[[[[\\\&\ʺʺʺʺʺʡʡʡʡʡʡʡʡʡʕʡʕʕʕʕʕʕʕʺh"KCJOJQJaJha,CJOJQJaJha,5CJOJQJaJha,h)/5CJOJQJaJha,h)/CJOJQJaJhh)/CJOJQJaJhh)/hh)/5CJOJQJaJ6TTTTTTTTTTTUU"Uqqqqqqqqqqqq$Ifgd/66l{kd$$Ifl0X
t0644
laXyt
"U#U>U?USUTUYUZU[UnUoUqlllgd)/{kd$$Ifl0X
t0644
laXyt$Ifgd/66l
oUVVVVNWOWlW
XX+XXXXXXXYCYnYY
$dha$gd)/gda,$^a$gd)/$dh^a$gd)/$^a$gd)/$a$gd)/$dh^a$gd)/YYYZ>ZeZZZZ[=[c[[[[
\\\\E\n\\\\]1]]]$a$gd"K$a$gd)/
$dha$gd)/&\'\7\8\E\\\]]^^{^^^^^^^^
__;_<___*`+`V`W`{```````````aaa.aaaaabb!b"b*b,b6b=bRbTb`bӮӮӮӮӢӮӺh=5CJOJQJaJh=CJOJQJaJh,MCJOJQJaJh,M5CJOJQJaJh.#CJOJQJaJha,h)/CJOJQJaJha,h)/5CJOJQJaJh.#5CJOJQJaJ:]]]]]^6^`^^^^^^^_D_p____`3`_``````a6agd)/$a$gd)/6a]araaab*b+b6b`bbbbc>cfccccc+dNdxddddd
$gd)/^`gd)/gd)/`bbbbbbb5c6c]c^cccddddde"eii'jnnn$r%r&rcrssssstttvvvɼuhe:h5CJOJQJaJhe:hc0CJOJQJaJhe:hc05CJOJQJaJhc0CJOJQJaJh)/CJOJQJaJh_5CJOJQJaJha,h)/5CJOJQJaJh~CJOJQJaJh=CJOJQJaJha,h)/CJOJQJaJ(deNefg"hii'jfklFmnnnnop%r&rcrssst$a$gd)/
$dha$gdc0$a$gdc0
$dha$gd)/gd)/tttttuu!vvvvvxSxjxyyyzzXzwz{a{
$dha$gdc0$a$gdc0
$dha$gd$a$gd$a$gd)/
$dha$gd)/vxSxyyyzzXz{a{CDWc}k}}}}$~kl"܂[]ŵҚzk_k_k_RzkRzkzkRzk_h;5CJOJQJaJh;CJOJQJaJhe:h;CJOJQJaJhe:h;5CJOJQJaJh>!h>!5CJOJQJaJhc0CJOJQJaJha,h)/CJOJQJaJha,h)/5CJOJQJaJhc05CJOJQJaJhe:hc0CJOJQJaJhe:hc05CJOJQJaJhe:hCJOJQJaJ a{DW}}$~kl":܂\]^_`n
$dha$gdnG$a$gd;
$dha$gdc0]`mn(T#34<.ƓǓȓɓIJ56p23`TΛKkUҝҞƹƹƹƹƬՠƠƬƬƬƠhe:hnGCJOJQJaJh;CJOJQJaJhnG5CJOJQJaJh;5CJOJQJaJhe:h;CJOJQJaJh;h;CJOJQJaJhe:h;5CJOJQJaJhnGCJOJQJaJ6(Tm#:Ɍ34.$a$gd;
$dha$gdnGǓȓɓ0IJ56p23`2TΛUD$a$gdnG$a$gd;
$dha$gdnGҞCDcˠ̠}}xޣߣ
ɼɔwk[NB6B6hXCJOJQJaJh/66CJOJQJaJh65CJOJQJaJh/66h65CJOJQJaJh6CJOJQJaJh&5CJOJQJaJh6h&5CJOJQJaJh.5CJOJQJaJh.CJOJQJaJh.h.CJOJQJaJh05CJOJQJaJh.h.5CJOJQJaJh;CJOJQJaJhe:h;CJOJQJaJh0CJOJQJaJDc̠}}ߣgd)/$a$gd)/
$dha$gdnG
$dha$gd0
ôha,h)/CJOJQJaJha,h)/5CJOJQJaJha,h;CJOJQJaJh.h6CJOJQJaJh/66hXCJOJQJaJ21h:p?6/ =!"#$%$$If!vh555#v#v#v:Vl
t0&6555yt$$If!vh555#v#v#v:Vl
t0&6555yt$$If!vh555#v#v#v:Vl
t0&6555yt$$If!vh555#v#v#v:Vl
t0&6555yt$$If!vh555#v#v#v:Vl
t0&6555yt$$If!vh555#v#v#v:Vl
t0&6555yt$$If!vh555#v#v#v:Vl
t0&6555yt$$If!vh555#v#v#v:Vl
t0&6555yt$$If!vh555#v#v#v:Vl
t0&6555yt$$If!vh555#v#v#v:Vl
t0&6555yt$$If!vh555#v#v#v:Vl
t0&6555yt$$If!vh555#v#v#v:Vl
t0&6555yt$$IfX!vh5 5#v #v:Vl
t065 5aXyt$$IfX!vh5 5#v #v:Vl
t065 5aXytj 666666666vvvvvvvvv666666>6666666666666666666666666666666666666666666666666hH6666666666666666666666666666666666666666666666666666666666666666662 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p8XV~ OJ PJ QJ _HmH nH sH tH @`@?6NormalCJ_HaJmH sH tH DA D
Default Paragraph FontRi@R0Table Normal4
l4a(k (
0No List@@@:, List Paragraph ^m$j`j?
Table Grid7:V0PK![Content_Types].xmlj0Eжr(Iw},j4 wPt#bΙ{UTU^hd}㨫)*1P' ^W0)T9<l#$yi};~@(Hu*Dנz/0ǰ$X3aZ,D0j~3߶b~i>3\`?/[G\!Rk.sԻ..a濭?PK!֧6_rels/.relsj0}Q%v/C/}(h"O
= C?hv=Ʌ%[xp{۵_Pѣ<1H0ORBdJE4b$q_6LR7`0̞O,En7Lib/SeеPK!kytheme/theme/themeManager.xmlM
@}w7c(EbˮCAǠҟ7՛K
Y,
e.,H,lxɴIsQ}#Ր ֵ+!,^$j=GW)E+&
8PK!Ptheme/theme/theme1.xmlYOo6w toc'vuرMniP@I}úama[إ4:lЯGRX^6؊>$!)O^rC$y@/yH*)UDb`}"qۋJחX^)I`nEp)liV[]1M<OP6r=zgbIguSebORD۫qu gZo~ٺlAplxpT0+[}`jzAV2Fi@qv֬5\ʜ̭NleXdsjcs7f
W+Ն7`gȘJjh(KD
dXiJ؇(x$(:;˹!I_TS1?E??ZBΪmU/?~xY'y5g&/ɋ>GMGeD3Vq%'#q$8K)fw9:ĵ
x}rxwr:\TZaG*y8IjbRcXŻǿI
u3KGnD1NIBs
RuK>V.EL+M2#'fi~Vvl{u8zH
*:(W☕
~JTe\O*tHGHY}KNP*ݾ˦TѼ9/#A7qZ$*c?qUnwN%Oi4=3ڗP
1Pm\\9Mؓ2aD];Yt\[x]}Wr]g
eW
)6rCSj
id DЇAΜIqbJ#x꺃6k#ASh&ʌt(Q%p%m&]caSl=X\P1Mh9MVdDAaVB[݈fJíP8քAV^f
Hn"d>znǊ ة>b&2vKyϼD:,AGm\nziÙ.uχYC6OMf3or$5NHT[XF64T,ќM0E)`#5XY`פ;%1U٥m;R>QDDcpU'&LE/pm%]8firS4d7y\`JnίIR3U~7+#mqBiDi*L69mY&iHE=(K&N!V.KeLDĕ{D vEꦚdeNƟe(MN9ߜR6&3(a/DUz<{ˊYȳV)9Z[4^n5!J?Q3eBoCMm<.vpIYfZY_p[=alY}Nc͙ŋ4vfavl'SA8*u{ߟ0%M07%<ҍPK!
ѐ'theme/theme/_rels/themeManager.xml.relsM
0wooӺ&݈Э5
6?$Q
,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}$b{P8g/]QAsم(#L[PK![Content_Types].xmlPK!֧6+_rels/.relsPK!kytheme/theme/themeManager.xmlPK!Ptheme/theme/theme1.xmlPK!
ѐ' theme/theme/_rels/themeManager.xml.relsPK]
. F
0\!+4
=0AZHKnMOT&\`bv]Ҟ
SUYZ\^`cdgiknw}~
:
[*04;+==F>>x?#@@0AA[BBCxGKNRT"UoUY]]6adta{DTVWX[]_abefhjlmopqrstuvxyz{\(
#AA@(
6
6
6
6
6
6
6
6
6
6
6
B
S ?`
DD.EGGGGGHEHFH
?tu!(#tpt
ySt^8tN(t tvPtat""t !P "t7>?GHR@GZ^$y~gnCHx
!MT6 = A
H
HRd
m
TYQRCDaj?HH(I(m+v+==BBCCOCHHDJMJcJnJJJLMM!M6M=MKMRMNNCOLOQPVP{YY__rbtbTcXc[c`cghhhQnXnoolsrsttkvyvvvvv\wbwwwww
xxyxxxxxxyy/z9z[zhzzz9{F{{{{{~"~<D5@V^U^Ç̇4<݉ČҌ`fƐː)/ӑܑinȔ͗ܗ<G,6ęؙ̙͙ǚњԚ3 00lqkq))N,,=>EEGGGHNHHHHH:L^L+PPUUVVXXZ Z/Z4Z]]]^
^p^r^^^&_(__``aabbd#d$dldnddddeefgghh*i_iii$jjjjk{kkkkl%l'lElGl[l]llllAmsmmmmmm n!nOnpnnnnn4o5oiojooooopp+pjpppppp
q)qDqRqTqqqrwrrrsVsYsasssssCttuuumuuuu$vUvVvvvww+w,wjwtwzwwwwwwxx/x0xNxxxxxxx:yzy{yyyzzz[zizjzzzzzzz2{3{8{{{{{{{{
()Hn;}<}^}_}}.~M~8@TtuOP]^l<KLlmӂ:MNrsރ߃BCfgȄɄ߄45UVhiyzх@AjkɆapq.DE}~ĉŉ7FȊԊ !vwً͋8@Wk~Ԍߌ0H֍"#4pŎƎ[\
"'FNŐƐېܐ(ґӑ1ْڒ1z͓%&=v45Tȕ;<op֖Cڗܗ
RToq*,PRҚԚ68]ޛߛ
333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 &
tΕy[
^lz4d\S!xnZ*6oM4к^fMW5tZ;Ĕ@?@z0^`0o(()^`. L^ `L.^`.x^x`.HL^H`L.^`.^`.L^`L.0^`0o(.^`. L^ `L.^`.x^x`.HL^H`L.^`.^`.L^`L.0^`0o(()^`. L^ `L.^`.x^x`.HL^H`L.^`.^`.L^`L.0^`0o(()^`. L^ `L.^`.x^x`.HL^H`L.^`.^`.L^`L.0^`0o(()^`. L^ `L.^`.x^x`.HL^H`L.^`.^`.L^`L.^`o(() ^ `.L^`L.x^x`.H^H`.L^`L.^`.^`.L^`L.0^`0o(()^`. L^ `L.^`.x^x`.HL^H`L.^`.^`.L^`L.0^`0o(()^`. L^ `L.^`.x^x`.HL^H`L.^`.^`.L^`L.0^`0o(()^`. L^ `L.^`.x^x`.HL^H`L.^`.^`.L^`L. MW5@?&
SM4;y[
nZ*4d jJ Zl & P Z+ & Z, : 1) xyw0q
+19~,Sp&;B\S!p".#M&,,:,P,a,.c0&01p&3z4/66?6eg7I:X<jA@CeFnGN5PiTVI\W*X^B]"^L(a 1a4`aY
d
anUjyM{.:}9E=,8uO=cb?,MXGG_>!5j"K6""$4?*S??]+XJt*2Clg,~#:^+4uDhpc%k}weY
)/opgSIhI=[Kr(Cxjq/wN12&w@P@UnknownG*Ax Times New Roman5Symbol3.*Cx ArialO&Albertus Extra Bold?.Arial BlackG&Albertus MediumC.Eras Bold ITC7 Aharoni9&Albertus7.@ CalibriACambria Math"qh LфOLфO!20ΛΛ2HP $Pp&32!
xxMathematics Dept. laMathematics Dept. la0 Oh+'08
px
(0Mathematics Dept. laNormalMathematics Dept. la2Microsoft Office Word@F#@W~@W~Lф՜.+,0hp
OΛTitle
!"#$%&'()*+,./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~Root Entry FM~Data
1Table(JWordDocument
4.SummaryInformation(DocumentSummaryInformation8MsoDataStoreM~M~LECAG==2M~M~Item
PropertiesUCompObj
y
F'Microsoft Office Word 972003 Document
MSWordDocWord.Document.89q