KAU
KING ABDULAZIZ UNIVERSITY
ACADEMIC ASSESSMENT UNIT
COURSE PORTFOLIO
FACULTY OF SCIENCE
MATHEMATICS DEPARTMENT
COURSE NAME:
COURSE NUMBER:
SEMESTER/YEAR:
DATE:
M
A
T
2nd semester
H
3
0
2009/2010
20/2/2010
5
ACADEMIC ASSESSMENT UNIT
PART II
COURSE SYLLABUS
ACADEMIC ASSESSMENT UNIT
Instructor Information
Name of the instructor: Wafaa Alhasan AlBarakati
Building: 7
Office location: Room: 158-C
Office hours:
Sat
Sun
Mon
Time
11-12 10-12
1-2
Tue
11-12
1-2
Wed
Tue
9:3011
Wed
Contact number(s): 6952959, 6400000 (26406)
E-mail address(s): [email protected]
[email protected]
Course Information
Course name: Differential Equations II
Course number: 305
Course meeting times:
Sat
Sun
Time
9:3011
Mon
Building: 7
Place: Room: 2154-C
Course website address:
Course prerequisites and requirements:
Course name
Ordinary Differential
Equation (I)
Course number
204
Description of the course: - Series solutions about an ordinary point and a
singular point, the method of Frobenius, solution
about the point at infinity, some special equations with
variable coefficients.
- Gamma and Beata functions, Bessel and
hypergeometric functions, orthogonal polynomials
and general properties, Legender, Hermit and
Laguerre polynomials.
Course Objectives
 To improve the students logical thinking and skills in solving differential equations problems.
 To introduce the series solutions method for solving ordinary differential equations.
 To introduce the basic concepts of special functions and orthogonal polynomials.
ACADEMIC ASSESSMENT UNIT
Learning Resources
Main text book: Title: Special Functions for Scientists and Engineers
Author: W. W. Bell
Publisher: D. Van Nostrand company LTD, 1968.
Subsidiary Books:
Fundamentals of Differential equations and boundary Value Problems,
R. K. Nagle, E. B. Saff and A. D. Snider,
Addison-Wesley
-
A. L. Rabenstein, Introduction to Ordinary Differential Equations,
Academic Press.
D. Rainville and P. E. Bedient. Elementary Differential Equations,
MacMillan Publishing Co., Inc., New York, (1995).
S. L. Ross, Introduction to ordinary differential equations, John
Wiley& Sons, Inc. New York (1998).
T. Myint-U, Ordinary differential equations, North-Holland, Inc.,
(1978).
D. G. Zill, A First Course in Differential Equations, PWS. Kent
Pub. Com., (1993).
W. E. Boyce and R. C. Diprima, Elementary Differential
Equations and Boundary value problems, John Wiley and sons,
Inc., (1997).
The computer usage: The students are encourage to drew graphs with the help of a computer.
Software needed: Scientific workplace, MATLAB, Mathematica, Maple
Course Requirements and Grading
1st Exam
20 marks
20 marks
Student assessment: 2nd Exam
HomeWork 10 marks
Project
10 marks
Final
40 marks
ACADEMIC ASSESSMENT UNIT
Expectations from students: 1. Attendance the class
2. Class interaction and cooperation
3. Good behavior
4. Attendance the exams.
Student responsibilities to the course: She should be well versed in the pre-requisites of
the course and should be willing and able to
complement her knowledge through independent
study.
Expectations for each assignment and project: 1.Handing in the homework within a week
2.Handing in the project within the specified
date
1. Student who are absent for more than 25%
Important rules of academic conduct: of the lectures WILL NOT be able to take the
final exam and she will get DN.
2. No late attendance, it is considered absence.
3. Exams dates are unchangeable.
4. No REPLACEMENT exams.
5. Following the KAAU exam regulations is a
MUST, failing to know it is the student
responsibility.
6. The student has the right to review her exam
paper and learn from her mistakes
ACADEMIC ASSESSMENT UNIT
Course Schedule Model
(meeting three times a week)
Week
#
Lecture
NO.
Topic
Exercises
What is Due?
Download Book 
1
Introduction (Nagle and Saff reference)
 Ordinary and Singular points
Regular & Irregular singular points
2


1
3
2
4
5
Indicial Equation
Convergence of solutions
Chapter 1
1.1 Method of Frobenius
1.2 Example 1
1.2 Example 2
1.2 Example 3
1.2 Example 4
1.2 Example 5
6
Chapter 2
2.1 Definitions
2.2 Properties of the beta and gamma
functions. (proofs of Th. 2.1- Th. 2.5)
7
2.2 Properties of the beta and gamma
functions. (proofs of Th. 2.6 - Th. 2.8 Th. 2.8))
8
2.2 Properties of the beta and gamma
functions. (proofs of Th. 2.10 - corollary)
2.3 Definition of the gamma function for
negative values of the argument (proof of
Th. 2.11 – Th. 2.12 without proof)
3
4

Problems
page21
1 ( i – ix)
ACADEMIC ASSESSMENT UNIT
Week
#
Lecture
NO.
9
5
10
Chapter 3
3.1 Legendre's equation and its solutions.
3.2 Generating function for the L.P.
(proof of Th. 3.1)
12
3.3 Further expressions for the L.P. (proof
of Th. 3.2)
3.4 Explicit expressions for special values
of the L.P. (Proofs of Th. 3.4 (i ,ii, iii, iv))
13
7
14
15
8
Problems page
40
1(i –
ii),2,4(i,ii,iv), 6
3.4 Th. 3.4 (v,vi)
3.5 Orthogonality Properties of the L.P.
(proof of Th. 3.5 case l not equal to m)
Theorem 3.6 without proof
Corollary without proof
3.5 Orthogonality Properties of the L.P.
(proof of Th. 3.5 case l equal to m)
3.7 Recurrence Relations (proof of Th.
3.8 (ii-iii))
3.7 Recurrence Relations (proof of Th.
3.8 (iv-viii))
3.8 Associated Legendre Functions (Th.
3.9 without proof- corollary without
proof- proof of Th. 3.10- Th. 3.11
16
3.13 Examples 1, 2 and 4
17
Chapter 4
4.1 Bessel's Equation and its solutions
18
4.1 (Proof of Th. 4.1, Discuss Th. 4.2)
4.2 Generating Function for B.F. (Proof
of Th. 4.5)
19
4.4 Recurrence Relations (Proof of Th.
4.8)
4.14 Orthogonormality of the B.F. (Proof
of Th. 4.23 case i not equal to j)
9
Exercises
2.4 Examples (1-2)
11
6
10
Topic
Problems page
90
1,2
Extra problem
sheet
What is Due?
Beginning date for
Project
"Hypergeometric
Functions"
ACADEMIC ASSESSMENT UNIT
Week
#
Lecture
NO.
Topic
20
4.14 Orthogonormality of the B.F. (Proof
of Th. 4.23 case i equal to j)
4.16 Example 1, 2, 5, and 6
21
Chapter 5
5.1 Hermite's Equation and its solution
22
5.2 Generating Function (proof of Th.
5.1)
5.3 Other expressions for the H.P. (proof
of Th. 5.2)
11
23
Exercises
What is Due?
Problems page
154
1, Extra
problem sheet
5.4 Explicit Expressions for H.P. (Proof of
Th. 5.4)
12
24
25
13
26
5.5 Orthogonality properties of H.P.
(Proof of Th. 5.5)
5.6 Recurrence relations (Proof of Th.
5.6)
Examples page 164 (1-3)
Chapter 6
6.1 Laguerre's Equation and its solution
6.2 Generating Function (proof of Th. 6.1)
6.3 Alternative expression for the L.P.
(Proof of Th. 6.2)
28
6.4 Explicit expressions of L.P. (proof of
Th. 6.3)
6.5 Orthogonality properties of L.P.
(proof of Th. 6.4)
Recurrence relations for the Laguerre
polynomials (Th. 6.5 )
Discussions of project "Hypergeometric
Functions"
29
Discussions of project " Hypergeometric
Functions""
27
14
Problems page
166 (1)
Extra problem
sheet
Extra problem
sheet
Due date for the
project
"Hypergeometric
Functions"
ACADEMIC ASSESSMENT UNIT
PART III
COURSE RELATED MATERIAL
Contains all the materials considered essential to teaching the
course, includes:
Quizzes, lab quizzes, mid-terms, and final exams and their solution set
Paper or transparency copies of lecture notes/ handouts (optional)
Practical Session Manual (if one exists)
Handouts for project/term paper assignments
(use the following template for Quizzes, lab quizzes, mid-terms, and final exams and their
solution set)
ACADEMIC ASSESSMENT UNIT
King Abdul Aziz University
Faculty of Science
Mathematics Department
Math 408 - Exam 1
2 Semester 2005/2006
Date: (28/1/1426)
Time allowed: (1.5 hr)
nd
8 marks
Q1 (Insert question one here)
8 marks
Q2 (Insert question two here)
8 marks
Q3 (Insert question three here)
8 marks
Q4 (Insert question four here)
8 marks
Q5 (Insert question five here)
Total
25
ACADEMIC ASSESSMENT UNIT
PART IV
EXAMPLES OF STUDENT LEARNING
Examples of student work. (Included good, average, and poor
examples)
Graded work, i.e. exams, homework, quizzes
Students' lab books or other workbooks
Students' papers, essays, and other creative work
Final grade roster and grade distribution
Examples of instructor’s written feedback of student’s work, (optional)
Scores on standardized or other tests, before and after instruction,
(optional)
Course evaluation, self evaluation or students comments (optional)
ACADEMIC ASSESSMENT UNIT
PART V
INSTRUCTOR REFLECTION (optional)
ACADEMIC ASSESSMENT UNIT
Part V. Instructor Reflections on the Course
 Instructor feedback and reflections
 Propose future improvement and enhancement
 Evaluate student competency and reflect on their course evaluation for improvements
to the course
 Conceptual map of relationships among the content, objective, and assessment
 Recent trends and new approaches to teach the course.
ACADEMIC ASSESSMENT UNIT
COURSE PORTFOLIO
CHECKLIST

TITLE PAGE

COURSE SYLLABUS

COURSE RELATED MATERIAL

EXAMPLES OF EXTENT OF STUDENT LEARNING

INSTRUCTOR REFLECTION ON THE COURSE