MAN-002 (Mathematical Methods)

Welcome to webpage of Mathematical Methods (MAN-002) course.

Objective of this course is to provide knowledge of essential mathematical tools applied in solving ordinary and partial differential equations, initial and boundary value problems.

Contents of the Course:

• Ordinary Differential Equations: Solution of linear differential equations with constant coefficients. Euler-Cauchy equations, Solution of second order differential equations by changing dependent and independent variables. Method of variation of parameters, Introduction to series solution method.

• Partial Differential Equations: Formation of first and second order partial differential equations. Solution of first order partial differential equations: Lagrange`s equation, Four standard forms of non-linear first order equations .

• Laplace Transform: Laplace and inverse Laplace transform of some standard functions, Shifting theorems, Laplace transform of derivatives and integrals. Convolution theorem, Initial and final value theorem. Laplace transform of periodic functions, error functions, Heaviside unit step function and Dirac delta function. Applications of Laplace transform.

• Z - Transform: Z – transform and inverse Z-transform of elementary functions, Shifting theorems, Convolution theorem, Initial and final value theorem. Application of Z- transform to solve difference equations.

• Fourier series: Trigonometric Fourier series and its convergence. Fourier series of even and odd functions. Fourier half-range series. Parseval`s identity. Complex form of Fourier series.

• Fourier Transforms: Fourier integrals, Fourier sine and cosine integrals. Fourier transform, Fourier sine and cosine transforms and their elementary properties. Convolution theorem. Application of Fourier transforms to BVP.

References:

• Kreyszig, E., "Advanced Engineering Mathematics", Johan Wiley & Sons, 2011

• Jain, R. K. and Iyenger, S. R. K., "Advanced Engineering Mathematics", Narosa Publishing House, 2009

• Hildebrand F. B., "Methods of Applied Mathematics", Courier Dover Publications, 1992

• Sneddon, I. N., " Elements of Partial Differential Equations", McGraw-Hill Book Company, 1988

• Simmons, G. F. and Krantz, S. G., Differential Equations:Theory, Technique and Practice" , Tata McGraw-Hill Edition, 2007

• Amarnath, T., "An Elementary Course in Partial Differential Equations", Narosa Publishing House (II Edition), 2012

• 5. Rao, K. S., "Introduction to Partial Differential Equations", PHI Learning Pvt. Ltd. (II Edition), 2010