Course Title: Ordinary Differential Equations
Course code:
4. SUGGESTED LESSION PLAN (THEORY)
Uni
t
Unit Title
Teaching
Hours
I
4
First Order Differential Equations
Exact equations and Integrating factors
Solution by Substitution, Bernoulli’s Equations
Linear and Non Linear model: Growth and decay, Newton’ law of
cooling, Mixing, Population model
II
Higher order differential equations
Preliminary Theory- Linear equations, Reduction of order
Homogeneous Linear Equations with constant coefficients
Method of undetermined coefficients for non homogeneous equation
Variation of parameters
Cauchy – Euler Equation
Solving system of Linear Equations, Nonlinear Differential equations
Modeling with Higher order differential equations
III Series solutions of linear equations
Power Series
Power series solution
Solution near regular singular point
Special functions
Total
1
1
2
14
2
2
2
1
1
2
4
6
1
1
2
2
24
5. ASSESSMENT SCHEME (Including Rationale)
Final Examination Plan
Unit
Unit Title
Distribution of Theory Marks
Cognitive level
R
I
II
First Order Differential Equations
Higher order linear differential
equations
III
Series solutions of second order
linear equations
Total
(Bloom’s taxonomy)
U An Ap
E
2
6
3
6
3
6
4
18
2
4
4
8
10
13
13
30
Sy
Total
Marks
12
40
4
18
4
00
70
Legends: R = Remember; U = Understand; Ap = Apply; An = Analysis; E = Evaluation, Sy = Synthesis, as per
(Bloom’s revised taxonomy)
1
Course Title: Ordinary Differential Equations
Course code:
6. SUGGESTED LEARNING RESOURCES
A. List of Books:
S.
Title of Books
No.
1
Elementary Differential Equation
and Boundary value problems
2
Differential Equations
3
Advanced Engineering
Mathematics Fourth edition
4
Advanced Engineering
Mathematics
B.
Learning Websites
1
MIT Open Course Ware
Author
Publication
William E. Boyce,
Richard C. Di Prime
Dennis G. Zill
Dennis G. Zill,
Warren S Wright
E. Kreyszig
Wiley-India
Cengage Publication
Jones and Bartlett
Wiley-India
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/
2
NPTEL Differential Equations
Lecture Series on Differential Equations by Dr.P.N.Agrawal, Department of Mathematics, IIT
Roorkee.
C.
List of Software (preferably open source)
(1)
D.
MATLAB
(2)
Scilab
List of Major Equipment with broad specifications
Computer Systems
2