**ENGINEERING MATHEMATICS-II**

**15MAT21**

**Course objectives:**

To enable students to apply the knowledge of Mathematics in various engineering fields by making them to learn the following

- Ordinary differential equations
- Partial differential equations
- Double and triple integration
- Laplace transform

**Module – I**

Linear differential equations with constant coefficients: Solutions of second and higher order differential equations – inverse differential operator method, method of undetermined coefficients and method of variation of parameters.

**Module – 2**

Differential equations 2:

Linear differential equations with variable coefficients: Solution of Cauchy’s and Legendre’s linear differential equations.

Nonlinear differential equations – Equations solvable for p, equations solvable for y, equations solvable for x, general and singular solutions, Clairauit’s equations and equations reducible to Clairauit’s form.

**Module – 3**

Partial Differential equations: Formulation of Partial differential equations by elimination of arbitrary constants/functions, solution of non-homogeneous Partial differential equations by direct integration, solution of homogeneous Partial differential equations involving derivative with respect to one independent variable only.

Derivation of one dimensional heat and wave equations and their solutions by variable separable method.

**Module – 4**

Integral Calculus: Double and triple integrals: Evaluation of double and triple integrals. Evaluation of double integrals by changing the order of integration and by changing into polar co-ordinates. Application of double and triple integrals to find area and volume.

Beta and Gamma functions: definitions, Relation between beta and gamma functions and simple problems.

**Module – 5**

Laplace Transform Definition and Laplace transforms of elementary functions. Laplace transforms of e^atf(t), t^nf(t) and f(t)/(t) (without proof) , periodic functions and unit-step function- problems Inverse Laplace Transform Inverse Laplace Transform – problems, Convolution theorem to find the inverse Laplace transforms(without proof) and problems, solution of linear differential equations using Laplace Transforms.**Course outcomes: **

On completion of this course, students are able to,

- solve differential equations of electrical circuits, forced oscillation of mass spring and elementary heat transfer.

- solve partial differential equations fluid mechanics, electromagnetic theory and heat transfer.

- Evaluate double and triple integrals to find area , volume, mass and moment of inertia of plane and solid region.

- Use curl and divergence of a vector valued functions in various applications of electricity, magnetism and fluid flows.

- Use Laplace transforms to determine general or complete solutions to linear ODE

**Text Books:**

1. B. S. Grewal,” Higher Engineering Mathematics”, Khanna publishers,

42nd edition, 2013.

2. Kreyszig, “Advanced Engineering Mathematics ” – Wiley, 2013**Reference Books:**

· B.V.Ramana “Higher Engineering M athematics” Tata Mc Graw-Hill, 2006

· N P Bali and Manish Goyal, “A text book of Engineering mathematics” ,Laxmi publications, latest edition.

H. K Dass and Er. Rajnish Verma ,”Higher Engineerig Mathematics”,

S. Chand publishing,1st edition, 2011.