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 Cayley-Hamilton 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
|