Course

Syllabus

Differential Equations: First-order, second-order, homogeneous, non-homogeneous, RLC circuits, damping, resonance, solution methods, Review of Laplace Transforms and Fourier series and transforms with applications. System Modeling: State-space, transfer function, controllability, observability, Basic non-linear system models.

Z-transform and Discrete-Time Systems: Inverse Z-transform – Z-transform solution of difference equations – Discrete-time system analysis – Applications in digital control systems.

Linear Algebra: Vector spaces, Linear Transformation, Eigenvalues and Eigenvectors, diagonalization, Matrix decompositions LU, QR, and SVD.

Probability & Statistics: Bayes’ theorem, random variables, distributions, expectation, variance, hypothesis testing.

Optimization: Single and Multivalued optimizations. Introduction to Convex optimization, Linear Programming Basic duality concepts.

Numerical modelling Studies using MATLAB/Simulink and Python

Course Objectives

• Understand the basic concepts of vector space, subspace, basis and dimension. Understand and apply linear transform for various matrix decompositions.
• To analyse and solve ordinary differential equations (ODE) and to analyse stability of systems of first order ordinary differential equations.
• Familiarise the basic concepts in statistics and apply to engineering problems.
• Understand the different methods for single and multivariable optimization problems.

CO-PO Mapping

CO1: To understand the basic concepts of vector space, subspace, basis and dimension. Also to understand the apply different matrix decompositions.

CO2: To understand and apply differential equations into electrical engineering problems.

CO3: To understand and apply statistical hypotheses testing for small and large data.

CO4: To solve the difference equations using Z-Transform and apply to discrete single problems

CO5: To use single and multivariable optimization models for solving multi-object models.

Course Outcomes

Textbooks/References

1. Erwin Kreyszig, “Advanced Engineering Mathematics”, Wiley, 10th Edition, 2011.
2. Chi-Tsong Chen, “Linear System Theory and Design”, Oxford University Press, 4th Edition, 2013.
3. Sheldon M. Ross, “Probability and Statistics for Engineers and Scientists”, Academic Press, 5th Edition, 2014.
4. Gilbert Strang, “Linear Algebra and Its Applications”, Cengage Learning, 4th Edition, 2006.
5. William Flannery, “Mathematical Modeling and Computational Calculus”, Vol-1, Berkeley Science Books, 2013.
6. Stephen Boyd and Lieven Vandenberghe, “Convex Optimization”, Cambridge University Press, 2018.
7. Gilbert Strang, “Linear Algebra and Learning from Data”, Wellesley-Cambridge Press, 2019.