Engineering Mathematics III

Course Title: Engineering Mathematics III

Course No: SH 231

Nature of the Course: THEORY

Semester: 3

Full Marks: 100

Pass Marks: 45

Credit Hours: 3

Course Description

This course provides a comprehensive study of advanced mathematical concepts essential for engineering applications. It covers matrix algebra, determinants, systems of linear equations, vector spaces, eigenvalues and eigenvectors, linear programming, Fourier series, infinite series, and vector calculus. Emphasis is placed on mathematical techniques for solving engineering problems involving optimization, function approximation, and multivariable analysis. The course also introduces line, surface, and volume integrals, along with Green’s, Gauss’s, and Stokes’ theorems, enabling students to apply mathematical methods in various engineering and scientific domains.

Course Objectives

The basic objective of the course is to provide a sound knowledge of determinant, matrix algebra, derivative and antiderivative of vector valued function (Line, surface and volume integrals), infinite series, Fourier series and linear programming. After learning the course one may enhance the fundamental concepts on Mathematics and able to study the further courses of the subject which are more applicable in Engineering.

Course Contents

1. Matrix and Determinant

10 hrs

1.1. Review of matrix and determinant with their properties

1.2. System of linear equations with their solution by Gauss elimination method

1.3. Rank of a matrix, consistency and inconsistency of a system of linear equations

1.4. Concept of vector space, subspace, linearly dependent and independent vectors, basis of a vector space, linear transformation

1.5. Eigenvalues and Eigenvectors, Cayley-Hamilton Theorem(without proof) and its use to find an inverse of a matrix, diagonalization of a matrix, determination of a modal matrix

2. Linear Programming

6 hrs

2.1. Review of graphical method for a system of linear inequalities

2.2. Concept of simplex method and its use to find optimal solution. Concept of duality and dual simplex method, Big-M method

3. Fourier Series

5 hrs

3.1. Periodic function, even and odd function, trigonometric function

3.2. Fourier series of a function with period 2π and arbitrary period 2L

3.3. Fourier sine and cosine series of the half range function

4. Infinite Series

8 hrs

4.1. Concept of sequence and series and their convergence

4.2. P-test, Ratio test, Root test, Integral test, Leibnitz test and absolute convergence, Interval and radius of convergence of power series, Taylor and Maclaurin series expansion( no need to prove) of functions

5. Vector Calculus

16 hrs

5.1. Concept of scalar and vector point functions, differentiation and integration of vectors, directional derivative, tangent vector to a curve

5.2. Gradient, Divergence and Curl with their properties

5.3. Path, simply connected region, line of integration, evolution of line integral, surface integral and volume integrals

5.4. Application of Greens, Gauss divergence and Stokes Theorems

Reference Books

1.E. Kreyszig, Advanced Engineering mathematics, Wiley- Eastern, Publication.
2.N. P. Bali, Dr. Manish Goyal, A text book of engineering mathematics, Laxmi Publication (P). LTD.
3.Thomas George B. and Finney. Ross L., Calculus and Analytical Geometry, Pearson Education

Notes:

This syllabus follows the official BE Comp curriculum of Far Western University. In case of any doubt or revision, the university's published syllabus shall be considered authorative.

Mathematics III