## Engineering Mathematics  ## Engineering Mathematics I

Engineering mathematics is a branch of applied mathematics, involving mathematical methods and techniques commonly used in engineering and industry. Like the fields of engineering physics and engineering geology, both fields can belong to the broader realm of engineering science. Engineering mathematics is an interdisciplinary subject, motivated by engineers’ consideration of practice, theory, and other considerations beyond their profession. Rank requirements and dealing with limitations to be able to play a role in your job.

### Modules Covered in the subject study material

Module-I

Partial differential equation of first order, Linear partial differential equation, Non-linear partial differential equation, Homogenous and non-homogeneous partial differential equation with constant co-efficient, Cauchy type, Monge’s method, Second order partial differential equation The vibrating string, the wave equation and its solution, the heat equation and its solution, Two dimensional wave equation and its solution, Laplace equation in polar, cylindrical and spherical coordinates, potential.

Module-II

Complex Analysis:
Analytic function, Cauchy-Riemann equations, Laplace equation, conformal mapping, Complex integration: Line integral in the complex plane, Cauchy’s integral theorem, Cauchy’s integral formula, Derivatives of analytic functions

Module –III
Power Series, Taylor’s series, Laurent’s series, Singularities and zeros, Residue integration method, evaluation of real integrals

#### Topics Covered

1.1 Formation of Partial Differential Equations

1.2 Linear partial differential equations of First Order

1.3 Non-Linear P.D.Es of the first order

1.3 Charpit’s Method

1.4 Homogenous partial differential Equations with constant coefficients

1.5 Non Homogenous partial differential Equations

1.6 Cauchy type Differential Equation

1.7 Monge’s Method

2.1 One Dimensional wave equation

2.2 D Alemberts Solution of the wave equation

2.3 Heat Equation

2.4 Two Dimensional wave equation

2.5 Laplacian in polar coordinates

2.6 Circular Membrane ( Use of Fourier-Bessel Series)

2.7 Laplace’s Equation in cylindrical and spherical coordinates

2.8 Solution of the Partial Differential equation by Laplace Transform.

3.1 Analytic function

3.2 Cauchy –Reiman equation & Laplace equation

3.3 Conformal mapping

3.4 Line integral in the complex plane

3.5 Cauchy’s integral theorem

3.6 Cauchy’s integral formula

3.7 Derivatives of analytic function

4.1 Power Series

4.2 Taylor series

4.3 Laurent Series

4.4 Singularities, Pole, and Residue

4.5 Residue Integral

4.6 Evaluation of real integral