|
Week
|
Topics
|
Study Metarials
|
|
1
|
Classification of differential equations: Open solution, closed solution, initial value problems, existence and uniqueness of solution
|
K1-Chapter-1
|
|
2
|
First order ordinary differential equations: Separable differential equations, exact differential equations
|
K1-Chapter-2
|
|
3
|
Integral factor and reducible equations, first order linear differential equations, Bernoulli differential equations
|
K1-Chapter-2
|
|
4
|
First order homogeneous equations, special transformations. Riccati equation, applications of first order differential equations
|
K1-Chapter-2
|
|
5
|
Theory of higher order homogeneous linear differential equations, linear dependence and independence, nonhomogeneous linear differential equations
|
K1-Chapter-3
|
|
6
|
Reduction of order. Homogeneous linear equations with constant coefficients
|
K2-Chapter-3
|
|
7
|
Solution of non-homogeneous differential equations: Indefinite coefficients method, method of changing parameters
|
K2-Chapter-4
|
|
8
|
Cauchy Euler differential equations, Laplace transforms: Definition and properties of Laplace transform
|
K2-Chapter-4
|
|
9
|
Inverse Laplace transforms. Solution of initial value problems by Laplace transform method
|
K2-Chapter-4
|
|
10
|
Series solutions of differential equations: Power series solutions: Solution around ordinary point
|
K2-Chapter-5
|
|
11
|
Systems of linear differential equations: Differential operators, operator method and Laplace transform method
|
K3-Chapter-3
|
|
12
|
Fourier series for periodic functions
|
K3-Chapter-3
|
|
13
|
Fourier cosine and sine series-I
|
K3-Chapter-4
|
|
14
|
Fourier cosine and sine series-II
|
K3-Chapter-4
|