Course

Linear Algebra: Vector Algebra, Matrices, System of Linear Equations and Solutions, Vector Space, Eigenvalue and Eigenvectors, Matrix Decomposition Techniques. Application Problems.

Vector Calculus: Differential Calculus – Dot product, Cross product, Derivatives, Scalar field, Divergence and Curl of Vector field. Integral Calculus – Line integral, Surface integrals, Divergence theorem, Stokes theorem, Application Problems.

Numerical Analysis: Numerical Solution of Differential Equations, Numerical Integration, Splines, Interpolation

Optimization: Unconstrained optimization problems – Linear programming, Simplex methods. Constrained optimization problems – Penalty methods. Modern Methods of optimization – Genetic Algorithm, Simulated Annealing, Particle Swarm Optimization, Ant Colony Optimization, Neural Network based optimization.

Course Outcomes:

CO1: Apply the concepts of linear algebra and vector calculus to solve engineering problems.

CO2: Solve computational problems using numerical analysis techniques.

CO3: Implement Laplace and Fourier transform techniques for signal processing problems.

CO4: Apply classical and modern meta-heuristic methods to solve optimization problems.

Textbooks / References:

1. Ervin Kreyszig, “Advanced Engineering Mathematics”, 10th edition, Wiley, 2015.
2. Gilbert Strang, “Linear algebra and its applications”, 5th edition, Cengage Learning, 2018.
3. George F Simmons, “Differential equations with applications and Historical notes”, Tata McGraw Hill, 3rd edition, Taylor & Francis, 2016.
4. Rao, Singiresu S. Engineering optimization: theory and practice. John Wiley & Sons, 2019.