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Differential Equations [1]

Paper Code: 
24CMAT201
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: 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

24CMAT 201

 

 

 

Differential Equations

 (Theory)

 

 

 

 

 

 

CO12: Estimate the methods of finding solutions of differential equations of the first order but not the first degree.

CO13: Explain the various techniques for getting exact solutions to certain solvable first-order differential equations and linear differential equations of second order.

CO14: Solve basic application problems described by second order linear differential equations with variable coefficients.

CO15: Determine the solution of first order linear and nonlinear partial differential equations using Lagrange's method and Charpit’s method.

CO16: Explain how to solve second order linear partial differential equations with constant coefficients.

CO17: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, PowerPoint presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, Assigned tasks

 

 

Quiz, Individual and group tasks,

Open Book Test, Semester End Examination

 

 

 

 

 

Unit I: 
I
12.00
Differential equation of first order: 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
12.00
Linear differential equation with constant coefficients: Linear differential equation with constant coefficients, Complementary function and particular integral, Homogeneous linear differential equations with variable coefficients, Simultaneous differential equations. 
 
Unit III: 
III
12.00
Linear differential equation with  variable coefficients: 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.
 
Unit IV: 
IV
12.00
Partial differential equations of the first order: Partial differential equations of the first order, Lagrange’s linear equation, Charpit’s general method of solution 
 
Unit V: 
V
12.00
Partial differential equations with constant coefficients: Linear partial differential equations with constant coefficients: Homogeneous and non-Homogeneous linear with all cases.
 
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.
  • Ian.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.
e- RESOURCES

 

 

Academic Year: 
2024-2025 [9]

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Source URL: https://maths.iisuniv.ac.in/courses/subjects/differential-equations-5

Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/differential-equations-5
[2] http://mdudde.net/pdf/study_material_DDE/M.Sc.MAthematics/DIFFERENTIAL%20EQUATIONS.pdf
[3] https://nptel.ac.in/courses/111108081
[4] https://www.rand.org/content/dam/rand/pubs/reports/2006/R374.pdf
[5] https://downloads.hindawi.com/books/9789775945389.pdf
[6] https://www.journals.elsevier.com/journal-of-differential-equations
[7] https://www.sciencedirect.com/journal/journal-of-differential-equations
[8] https://www.hindawi.com/journals/ijde/about/ 
[9] https://maths.iisuniv.ac.in/academic-year/2024-2025