JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisites

Foundation course (No prerequisites).

Course Objectives:

To learn

• concepts & properties of Laplace Transforms
• solving differential equations using Laplace transform techniques
• evaluation of integrals using Beta and Gamma Functions
• evaluation of multiple integrals and applying them to compute the volume and areas of regions
• the physical quantities involved in engineering field related to the vector valued functions.
• the basic properties of vector valued functions and their applications to line, surface and volume integrals.

Course Outcomes:

After learning the contents of this course the student must be able to

• use Laplace transform techniques for solving DE’s
• evaluate integrals using Beta and Gamma functions
• evaluate the multiple integrals and can apply these concepts to find areas, volumes, moment of inertia etc of regions on a plane or in space
• evaluate the line, surface and volume integrals and converting them from one to another

UNIT - I

Laplace Transforms: Laplace transforms of standard functions, Shifting theorems, derivatives and integrals, properties- Unit step function, Dirac’s delta function, Periodic function, Inverse Laplace transforms, Convolution theorem (without proof). Applications: Solving ordinary differential equations (initial value problems) using Laplace transforms.

UNIT - II

Beta and Gamma Functions: Beta and Gamma functions, properties, relation between Beta and Gamma functions, evaluation of integrals using Beta and Gamma functions. Applications: Evaluation of integrals.

UNIT - III

Multiple Integrals: Double and triple integrals, Change of variables, Change of order of integration. Applications: Finding areas, volumes& Center of gravity (evaluation using Beta and Gamma functions).

UNIT - IV

Vector Differentiation: Scalar and vector point functions, Gradient, Divergence, Curl and their physical and geometrical interpretation, Laplacian operator, Vector identities.

UNIT - V

Vector Integration: Line Integral, Work done, Potential function, area, surface and volume integrals, Vector integral theorems: Greens, Stokes and Gauss divergence theorems (without proof) and related problems.

Text Books:

• 1. Advanced Engineering Mathematics by R K Jain & S R K Iyengar, Narosa Publishers
• 2. Engineering Mathematics by Srimanthapal and Subodh C. Bhunia, Oxford Publishers

References:

• 1. Advanced Engineering Mathematics by Peter V. O. Neil, Cengage Learning Publishers.
• 2. Advanced Engineering Mathematics by Lawrence Turyn, CRC Press