DIFFERENTIAL AND DIFFERENCE EQUATIONS

Paper Code: 
MAT 302
Credits: 
3
Contact Hours: 
45.00
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

Paper Code

Paper Title

MAT 302

 

 

 

 

 

 

 

 

Differential and Difference Equations

 (Theory)

 

 

 

 

 

 

The students will be able to –

 

CO31: Students will be able to solve first order differential equations utilizing the standard techniques for separable, exact, linear, homogeneous, or Bernoulli cases.

CO32: Students will be able to find the complete solution of a non-homogeneous differential equation as a linear combination of the complementary function and a particular solution.

CO33: Students will be introduced to the complete solution of a homogeneous differential and difference equations with constant coefficients by the method of undetermined coefficients.

CO34: Students will be able to find the complete solution of a differential equation with constant coefficients by variation of parameters.

CO35: Students will have a working knowledge of basic application problems described by second order linear difference equations with constant coefficients.

 

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, 1998.
  • J. L. Bansal and H.S. Dhami, Differential Equations, JPH, 2012.
  • K.K. Gupta and D.C. Agarwal, Linear Difference Equation, Krishna Prakashan, 2004.
  • A.R. Forsyth, A Treatise on Differential Equations, Macmillan and Co. Ltd, London, 1997.
  • 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: 
2020-2021
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