V.L-1

V.L-2

V.L-3

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1.1

1.2

1.3

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1.1

1.2

1.3

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Fourier series of functions of 2π or any other period

1.1

1.2

1.3

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Dirichlet’s condition for convergence of Fourier series

1.1

1.2

1.3

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Fourier series of even and odd functions

1.1

1.2

1.3

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Half-range Fourier series

1.1

1.2

1.3

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V.L-2

V.L-3

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2.1

2.2

2.3

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Formation of partial differential equations

2.1 2.1.1

2.2

2.3

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Solution of first order linear and non-linear partial differential equations

2.1 2.1.1

2.2 

2.3 2.3.1

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Charpit’s method

2.1

2.2

2.3

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Solution of homogeneous and non-homogeneous linear PDEs of second and higher order by complementary function and particular integral method

2.1

2.2

2.3 2.3.1

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Classification of second order linear partial differential equations

2.1

2.2

2.3

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Method of separation of variables

2.1

2.2

2.3

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One-dimensional wave equation and heat equation

2.1

2.2 2.2.1

2.3 2.3.1

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V.L-2

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3.1  3.11

3.2

3.3

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Finite difference operators and their relations

3.1

3.2

3.3

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Newton’s forward difference interpolation

3.1

3.2

3.3

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Newton’s backward difference interpolation

3.1

3.2

3.3

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Lagrange’s interpolation method

3.1

3.2

3.3

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Inverse interpolation

3.1

3.2

3.3

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Newton’s divided difference method

3.1

3.2

3.3

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4.1

4.2

4.3

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Integration & Derivative Formula

4.1

4.2

4.3

Numerical Differentiation:

4.1

4.2

4.3

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Derivatives using forward difference formula

4.1

4.2

4.3

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Derivatives using backward difference formula

4.1

4.2

4.3 4.31

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Numerical Integration:

4.1

4.2

4.3

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Newton–Cotes quadrature formulae

4.1

4.2

4.3

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Trapezoidal rule

4.1

4.2

4.3

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Simpson’s 1/3 rules 

4.1

4.2

4.3

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Simpson’s 3/8 rules

4.1

4.2

4.3

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Gaussian integration

4.1

4.2

4.3

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5.1

5.2

5.3

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Picard’s method

5.1 5.11

5.2

5.3

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Euler’s method

5.1 5.11

5.2

5.3

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Runge–Kutta 2nd order method

5.1

5.2

5.3

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Runge–Kutta 4th order method

5.1

5.2

5.3

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V.L-1

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Laplace transform

6.1

6.2

6.3

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Inverse Laplace transform

6.1

6.2

6.3

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Linearity

6.1

6.2

6.3

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First shifting theorem (s-shifting)

6.1

6.2

6.3

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Transforms of derivatives 

6.1

6.2

6.3

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Transforms of integrals​

6.1

6.2

6.3

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Laplace transform of periodic functions​

6.1

6.2

6.3

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Short impulses, Dirac’s delta function

6.1

6.2

6.3

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Convolution​

6.1

6.2 6.2.1

6.3

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Integral equations

6.1

6.2

6.3

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Differentiation and integration of transforms

6.1

6.2 6.2.1

6.3

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ODEs with variable coefficients

6.1

6.2

6.3

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Systems of ODEs

6.1

6.2

6.3

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