JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-requisites

Mathematical Knowledge at pre-university level

Course Objectives

To learn

• Methods of solving the differential equations of first and higher order.
• Concept, properties of Laplace transforms
• Solving ordinary differential equations using Laplace transforms techniques.
• The physical quantities involved in engineering field related to 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 paper the student must be able to
• Identify whether the given differential equation of first order is exact or not
• Solve higher differential equation and apply the concept of differential equation to real world problems.
• Use the Laplace transforms techniques for solving ODE’s.
• Evaluate the line, surface and volume integrals and converting them from one to another

UNIT - I: First Order ODE

Exact differential equations, Equations reducible to exact differential equations, linear and Bernoulli’s equations, Orthogonal Trajectories (only in Cartesian Coordinates). Applications: Newton’s law of cooling, Law of natural growth and decay.

UNIT - II: Ordinary Differential Equations of Higher Order

Second order linear differential equations with constant coefficients: Non-Homogeneous terms of the type , sin , cos , polynomials in , ( ) and ( ), method of variation of parameters, Equations reducible to linear ODE with constant coefficients: Legendre’s equation, Cauchy-Euler equation. Applications: Electric Circuits

UNIT - III: Laplace transforms

Laplace Transforms: Laplace Transform of standard functions, First shifting theorem, Second shifting theorem, Unit step function, Dirac delta function, Laplace transforms of functions when they are multiplied and divided by ‘t’, Laplace transforms of derivatives and integrals of function, Evaluation of integrals by Laplace transforms, Laplace transform of periodic functions, Inverse Laplace transform by different methods, convolution theorem (without proof). Applications: solving Initial value problems by Laplace Transform method.

UNIT - IV: Vector Differentiation

Vector point functions and scalar point functions, Gradient, Divergence and Curl, Directional derivatives, Tangent plane and normal line, Vector Identities, Scalar potential functions, Solenoidal and Irrotational vectors.

UNIT - V: Vector Integration

Line, Surface and Volume Integrals, Theorems of Green, Gauss and Stokes (without proofs) and their applications.

TEXT BOOKS:

• 1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 36th Edition, 2010
• 2. R.K. Jain and S.R.K. Iyengar, Advanced Engineering Mathematics, Narosa Publications, 5th Edition, 2016.

REFERENCE BOOKS:

• 1. Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, 2006.
• 2. G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, 9th Edition, Pearson, Reprint, 2002.
• 3. H. K. Dass and Er. Rajnish Verma, Higher Engineering Mathematics, S Chand and Company Limited, New Delhi.
• 4. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications, Reprint, 2008.