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Math-IIIA (Ordinary Differential Equations)

Course Code: MM 202  |  Credits: 3  |  Prerequisite: Calculus

Syllabus Details

  • Unit I:(First Order Equations) Order and degree of a differential equation; first order equations by the variables separable method; homogeneous equations of degree zero, non-homogeneous equations, exact equations, the integrating factor, linear equations and Bernoulli’s equation.
  • Unit II:(First Order Higher Degree Equations) Equations solvable for x, y and p; Clairaut’s form and singular solutions; Picard’s method of successive approximations and the statement of Picard’s theorem on existence and uniqueness for first order equations.
  • Unit III:(Higher Order Linear Equations) Higher order homogeneous linear equations with constant coefficients; second order homogeneous linear equations with variable coefficients; variation of parameters; 2 × 2 autonomous systems; power series solutions; the meaning of existence and uniqueness, with counterexamples.
  • Unit IV:(Laplace Transform) Definition and transforms of elementary functions; the effect of the transform on translation, scaling and convolution; the inverse transform and applications to ordinary differential equations.
  • Unit V:(Fourier Series) Fourier series of a periodic function and half range Fourier series.
  • Unit VI:(Sets, Relations and Functions) Sets, relations, equivalence, partially ordered relations, mathematical induction and elements of mathematical logic.

Course Learning Objective

  1. Explain the genesis of ordinary differential equations.
  2. Apply the techniques for exact solutions of solvable first order equations and of higher order linear equations.
  3. Apply Picard’s method of successive approximations, and the power series method for higher order linear equations, especially where no solution method is available.
  4. Explain the general solution of a linear differential equation of arbitrary order and apply methods to obtain it.
  5. Explain the Laplace transform and Fourier series and their applications.
  1. Kreyszig, Erwin. Advanced Engineering Mathematics. Wiley, 2011
  2. Simmons, George F. Differential Equations with Applications and Historical Notes. McGraw Hill, 1972
  3. Boyce, William E. and DiPrima, Richard C. Elementary Differential Equations. Wiley, 2012
  4. Murray, Daniel A. Introductory Course in Differential Equations. Orient, 2003
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