Unit 1

Basics of Linear Algebra – Linear Dependence and independence of vectors – Gaussian Elimination – Rank of set of vectors forming a matrix – Vector space and Basis set for a Vector space – Dot product and Orthogonality -CR decomposition – Rotation matrices – Eigenvalues and Eigenvectors and its interpretation-Introduction to SVD, Computational experiments using Matlab/Excel/Simulink.

Unit 2

Ordinary Linear differential equations, formulation – concept of slope, velocity and acceleration – analytical and numerical solutions- Impulse Response computations- converting higher order into first order equations – examples of ODE modelling of falling objects, satellite and planetary motion, Electrical and mechanical systems– Introduction to solving simple differential equations with Simulink- Introduction to one variable optimization – Taylor series- Computational experiments using Matlab /Excel/Simulink.

Unit 3

Introduction to random variables (continuous and discrete), mean, standard deviation, variance, sum of independent random variable, convolution, probability distributions.

Unit 4

Introduction to quantum computing, Quantum Computing Roadmap, Quantum Mission in India, A Brief Introduction to Applications of Quantum computers, Quantum Computing Basics, Bracket Notation, Inner product, outer product, concept of state.

Course Objectives

1. To introduce students to the fundamental concepts and techniques of linear algebra, ordinary differential equations, probability theory, complex numbers, and quantum computing that are necessary for further study in science and related fields.
2. To enable students to apply the concepts they learn in practical situations by using analytical and numerical methods to model real-world problems.
3. To expose students to the wide range of applications of linear algebra, ordinary differential equations, probability theory, complex numbers, and quantum computing within the scientific field and to inspire them to pursue further study or research in these areas.
4. To introduce students to the fundamental concepts of quantum computing
5. To develop students’ ability to communicate mathematical concepts and solutions clearly and effectively.

Course Outcomes

After completing this course, students should be able to

• CO1: Apply the fundamental concepts of linear algebra and calculus to solve canonical problems analytically and computationally
• CO2: Model and simulate simple physical systems using ordinary differential equations
• CO3: Apply the concept of probability and random variables to solve elementary real-life problems
• CO4: Explain the basic concepts of quantum computing and differentiate it from conventional computing.

CO-PO Mapping

1. Gilbert Strang, Introduction to Linear Algebra, Fifth Edition, Wellesley-Cambridge Press, 2016.
2. Gilbert Strang, Linear Algebra and Learning from Data, Wellesley, Cambridge press, 2019.
3. William Flannery, Mathematical Modelling and Computational Calculus, Vol-1, Berkeley Science Books, 2013.
4. Stephen Boyd and Lieven Vandenberghe, Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares, 2018.