Differential and Difference Equations

Paper Code: 
CMAT 313
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Differentiate the different types of Differential Equations and apply the appropriate analytical technique for finding the solution of first order and selected higher order ordinary differential equations.
  2. Evaluate first order differential equations including separable, homogeneous, exact, and linear.

Course Outcomes (COs):

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

CMAT 313

 

 

 

 

 

Differential and Difference Equations

 (Theory)

 

 

 

 

 

 

The students will be able to –

 

CO48: Distinguish between linear, nonlinear, partial and ordinary differential
equations.
CO49: Learn various techniques of getting exact solutions of certain solvable first order
differential equations and linear differential equations of second order.
CO50: Solve basic application problems described by second order linear
differential equations with constant coefficients.
CO51: Learn about solution of first order linear partial differential equations using
Lagrange's method.
CO52: Know how to solve second order linear partial differential equations with constant
coefficients.

CO53: Obtain an approximate set of solution function values to a second order
boundary value problem using a finite difference equation

Approach in teaching:

 

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Giving tasks

 

 

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
I
9.00
Linear differential equation of first order first degree and irreducible forms, Exact differential equation and equation which can be made exact using I.F. First order higher degree differential equations solvable for x, y, p, Clairaut’s form.
 
Unit II: 
II
9.00
Linear differential equation with constant coefficients, Complimentary function and particular integral, Homogeneous linear differential equations with variable coefficients, Simultaneous differential equations. 
 
Unit III: 
III
9.00
Linear differential equation of second order: Linear independence of solutions, Solution by transformation of the equations by changing the dependent and independent variable, Factorization of operators, Method of variation of parameters, Method of undetermined coefficients.
 
Unit IV: 
IV
9.00
Partial differential equations of the first order, Lagrange’s linear equation, Charpit’s general method of solution, Homogeneous linear partial differential equations with constant coefficients, Equations reducible to equations with constant coefficients.
 
Unit V: 
V
9.00
Difference equation: Definition and order of difference equation, first and higher order homogeneous linear difference equations, Difference equation reducible to homogenous form, Non-homogeneous linear difference equation, Complementary functions, Particular integrals.
 
Essential Readings: 
  • Zafar Ahsan, Differential Equations & Their Applications, PHI, New Delhi, 2004.
  • J. L. Bansal and H.S. Dhami, Differential Equations, JPH, 2012.
  • K.K. Gupta and D.C. Agarwal, Linear Difference Equation, Krishna Prakashan, 2004.
 
References: 
  • A.R. Forsyth, A Treatise on Differential Equations, Macmillan and Co. Ltd, London, 2005.
  • Frank Ayres, Theory and Problems of Differential Equations, TMH, 2002.
  • D. A. Murray, Introductory Course on Differential Equations, Orient Longman, 2004.
  • I. N. Sneddon, Elements of Partial Differential Equations, TMH, 2001.
  • Walter G. Kelley and Allan C. Peterson, Difference Equation: An Introduction with Applications, Academic Press London, 2001.
  • Saber Elaydi, An Introduction to Difference Equation, Springer, 2005.
 
Academic Year: 
2022-2023
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