## Topics with syllabus and resources

1 Laplace Transform

1.01 Function of Bounded Variation

1.02 Linearity Property of Laplace Transform

2 Inverse Laplace Transform

2.01 Linearity Property

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2.02 Applications to Solve Initial and Boundary Value Problems Involving Ordinary Differential Equations with One Dependent Variable

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3 Complex Variables

3.01 Functions of Complex Variable

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3.02 Milne- Thomson Method

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3.03 Mapping

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4 Complex Integral

4.01 Line Integral of a Function

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4.02 Singularities and Poles

4.03 Taylor’S and Laurent’S Series Development (Without Proof)

4.04 Residue at Isolated Singularity and Its Evaluation

4.05 Residue Theorem

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5 Fourier Series

5.01 Orthogonal and Orthonormal Functions

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5.02 Dirichlet’s Theorem

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5.03 Complex Form of Fourier Series

6 Partial Differential Equations

6.01 Numerical Solution of Partial Differential Equations

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6.02 Partial Differential Equations

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6.03 Heat Equation

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6.04 Two and Three Dimensional Laplace Equations

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