ENGINEERING MATHEMATICS III [SH 501]
Course Objective:
To round out the students’ preparation for more sophisticated applications with an introduction to linear algebra, Fourier series, Laplace Transforms, integral transformation theorems and linear programming.
 Determinants and Matrices (11 hours)
 Determinant and its properties
 Solution of system of linear equations
 Algebra of matrices
 Complex matrices
 Rank of matrices
 System of linear equations
 Vector spaces
 Linear transformations
 Eigen value and Eigen vectors
 The CayleyHamilton theorem and its uses
 Diagonalization of matrices and its applications
 Line, Surface and Volume Integrals (12 hours)
 Line integrals
 Evaluation of line integrals
 Line integrals independent of path
 Surfaces and surface integrals
 Green’s theorem in the plane and its applications
 Stoke’s theorem (without proof) and its applications
 Volume integrals; Divergence theorem of Gauss (without proof) and its applications
 Laplace Transform (8 hours)
 Definitions and properties of Laplace Transform
 Derivations of basic formulae of Laplace Transform
 Inverse Laplace Transform: Definition and standard formulae of inverse Laplace Transform
 Theorems on Laplace transform and its inverse
 Convolution and related problems
 Applications of Laplace Transform to ordinary differential equations
 Fourier Series (5 hours)
 Fourier Series
 Periodic functions
 Odd and even functions
 Fourier series for arbitrary range
 Half range Fourier series
 Linear Programming (9 hours)
 System of Linear Inequalities in two variables
 Linear Programming in two dimensions: A Geometrical Approach
 A Geometric introduction to the Simplex method
 The Simplex method: Maximization with Problem constraints of the form “≤”
 The Dual: Maximization with Problem Constraints of the form “≥”
 Maximization and Minimization with mixed Constraints. The two phase method (An alternative to the Big M Method)
References:
 S. K. Mishra, G. B. Joshi, V. Parajuli, "Advance Engineering Mathematics", Athrai Publication.
 E. Kreszig, "Advance Engineering Mathematics", Willey, New York.
 M.M Gutterman and Z.N.Nitecki, "Differential Equation, a First Course", Saunders, New York.
Evaluation Scheme
The questions will cover all the chapters of the syllabus. The evaluation scheme will be as indicated in the table below:
Unit 
Chapter 
Topics 
Marks 
1 
1 
1.1 to 1.8 
16 
2 
1 
1.9 to 1.11 
16 
2 
2.1 to 2.4 
3 
2 
2.5 to 2.7 
16 
3 
3.1 to 3.2 
4 
3 
3.3 to 3.6 
16 
4 
4.1 to 4.3 
5 
4 
4.4 to 4.5 
16 
5 
All 
Total 
80 
*Note: There may be minor deviation in marks distribution
