ENGINEERING MATHEMATICS

Course Code: GYMAT101

Course Name: ENGINEERING MATHEMATICS

Course Prerequisite: Basic knowledge in single variable calculus and matrix operations.

Course Objectives:

1. To provide a comprehensive understanding and basic techniques of matrix theory to
analyze linear systems.
2. To offer advanced knowledge and practical skills in solving second-order ordinary
differential equations, applying Laplace transforms, and understanding Fourier series,
enabling students to analyze and model dynamic systems encountered in engineering
disciplines effectively.

Course Outcomes:

At the end of the course students should be able to:

CO1: Solve systems of linear equations and diagonalize matrices.
CO2: Solve homogeneous and non-homogeneous linear differential equation with constant coefficients.
CO3: Compute Laplace transform and apply it to solve ODEs arising in engineering.
CO4: Determine the Taylor series and evaluate Fourier series expansion for different periodic functions.

Syllabus

Module 1-Linear systems of equations: Gauss elimination, Row echelon form, Linear Independence:
rank of a matrix, Solutions of linear systems: Existence, Uniqueness (without proof), The matrix
Eigen Value Problem, Determining Eigen values and Eigen vector, Diagonalization of matrices

Module2- Homogeneous linear ODEs of second order, Superposition principle, General solution,
Homogeneous linear ODEs of second order with constant coefficients (Method to find general
solution, solution of linear Initial Value Problem). Non homogenous ODEs (with constant
coefficients) – General solution, Particular solution by the method of undetermined coefficients), Initial
value Problem for Non-Homogeneous Second order linear ODE(with constant coefficients),
Solution by variation of parameters (Second Order).
Module 3- Laplace Transform, Inverse Laplace Transform, Linearity property, First shifting theorem,
Transform of derivatives, Solution of Initial value problems by Laplace transform (Second order
linear ODE with constant coefficients with initial conditions at t=0 only), Unit step function, Second
shifting theorem, Dirac delta function and its transform (Initial value problems involving unit step function and Dirac delta function are excluded), Convolution theorem (without proof) and its
application to finding inverse Laplace transform of products of functions.

Module 4- Taylor series representation (without proof, assuming the possibility of power series
expansion in appropriate domains), Maclaurin series representation, Fourier series, Euler formulas,
Convergence of Fourier series (Dirichlet’s conditions), Fourier series of 2π periodic functions, Fourier
series of 2l periodic functions, Half range sine series expansion, Half range cosine series expansion.

Course References:

1. Erwin Kreyszig, “Advanced Engineering Mathematics”, Wiley, 10th edition, 2016

 2. H. Anton, I. Biven S.Davis, “Calculus”, Wiley, 10th edition, 2015.

3. Maurice D. Weir, Joel Hass, Christopher Heil, Przemyslaw Bogacki, Thomas’ Calculus,
Pearson, 15th edition, 2023