Annexure ‘CD – 01’
FORMAT FOR COURSE CURRICULUM
Course Title: DIFFERENTIAL EQUATIONS AND COMPLEX ANALYSIS
L
T
P/S
SW/FW
3
0
0
0
Course Code: MATH122
TOTAL
CREDIT
UNITS
3
Credit Units: 3
Course Objectives: By the end of the semester, students will be able to analyze techniques to solve differential equations and complex analysis problems which can be
further applied to solve practical engineering problems in fluid dynamics, mechanics and modelling of simple electrical circuits etc.
Pre-requisites: Students must have knowledge of Differential Calculus, Integral Calculus, Partial Derivatives and Complex numbers.
Student Learning Outcomes:
Upon successful completion of this course, student will be able to
1) Analyze and solve first second and higher order ordinary differential equations using different analytical and numerical methods.
2) Differentiate between ordinary and partial differential equations.
3) Form and solve linear and non-linear partial differential equations using different methods.
4) Differentiate between homogeneous and non-homogeneous partial differential equations and solve these equations by finding complementary function
and particular integral.
5) Represent complex numbers and their functions in different forms.
6) Define and analyze limits and continuity of complex functions.
7) Apply concept of analyticity using Cauchy Riemann Equations and analyze harmonic function and its conjugate.
8) Evaluate complex contour integral by applying Cauchy Integral Theorem and Cauchy Integral Formula.
9) Represent complex numbers as Taylor and Laurent series.
10) Classify singularities and poles and find residue which will be further used to evaluate complex integral using Residue Theorem.
Course Contents/Syllabus:
Weightage (%)
Module I Ordinary Differential Equations
Descriptors/Topics
Solution of Ordinary Differential Equations of First Order: Method of Separation of Variables, Homogeneous and non
homogeneous equations, Linear Differential Equations & Bernoulli’s Equations, Exact Differential Equations Linear Differential
Equations of Higher Order, Complete Solution, Complementary Function, Particular Integrals, Solution of simultaneous ODE.
30%
Module II Partial Differential Equations
Descriptors/Topics
Formation of PDE, Equations solvable by direct integration, Linear equations of the first order, Non-linear equations of the first
order, Charpit’s method, Homogeneous linear equations with constant coefficients, Non homogeneous linear equations with
constant coefficients.
Module III Complex
Descriptors/Topics
30%
Analysis
De Moivre’s Theorem and Roots of Complex Numbers, Logarithmic Functions, Functions of a Complex Variables,
Limits, Continuity and Derivatives, Analytic Function, Cauchy-Riemann Equations (without proof), Harmonic
Function, Harmonic Conjugates, Complex Line Integral, Cauchy Integral Theorem (without proof), Cauchy Integral
Formula (without proof), Power Series, Taylor Series, Laurent Series, Zeroes and Singularities, Residues, Residue
Theorem (without proof) .
40%
Pedagogy for Course Delivery:





Reviewing relevant, previously-learned topics.
Presenting the new information by linking it to previous topics.
Providing learning guidance and assignments.
Providing time for practice, problem solving sessions and feedback.
Taking tests and quiz on regular basis.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term Examination
-
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
End Term Examination
Components (Drop down)
A
CT
S/V/Q
HA
EE
Weightage (%)
5
10
8
7
100
Text & References:

Engineering Mathematics by Erwin Kreyszig


Engineering Mathematics by B.S. Grewal.
Differential Equation by A.R.Forsyth.



Higher Engineering Mathematics by H.K. Dass.
Partial Differential Equations by I.N. Snedon
Complex Variables and Applications by Ruel Churchill