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#### Topics

1 Laplace Transform

1.01 Function of Bounded Variation

1.02 Linearity Property of Laplace Transform

2 Inverse Laplace Transform

2.01 Linearity Property

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

3 Complex Variables

3.01 Functions of Complex Variable

3.02 Milne- Thomson Method

3.03 Mapping

4 Complex Integral

4.01 Line Integral of a Function

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

5 Fourier Series

5.01 Orthogonal and Orthonormal Functions

5.02 Dirichlet’s Theorem

5.03 Complex Form of Fourier Series

6 Partial Differential Equations

6.01 Numerical Solution of Partial Differential Equations

6.02 Partial Differential Equations

6.03 Heat Equation

6.04 Two and Three Dimensional Laplace Equations

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Question paper for Applied Mathematics 3 2013 - 2014 Semester 3 (SE Second Year) by University of Mumbai for the courses BE Mechanical Engineering, BE Civil Engineering, BE Automobile Engineering, BE Production Engineering.