21MAB101T - Calculus and Linear Algebra

Course Description

This foundational mathematics course is designed to equip first year B.Tech. students with essential analytical and computational skills through a rigorous study of Calculus and Linear Algebra. The course is divided into five comprehensive units covering Matrices, Functions of Several Variables, Ordinary Differential Equations, Differential Calculus and Beta Gamma Functions and Sequences and Series.

Students will learn the theory and applications of eigenvalues and eigenvectors, Cayley-Hamilton theorem and diagonalization of matrices. In Functions of Several Variables, the course introduces partial derivatives, Jacobian and optimization techniques, including Lagrange method of multipliers.

The curriculum includes second-order linear differential equations with constant and variable coefficients, as well as systems of differential equations, laying the groundwork for Advanced Engineering Analysis. Topics in Differential Calculus such as Radius of Curvature, Envelopes and Evolutes are explored, along with special functions like Beta and Gamma functions.

The final unit delves into Convergence Tests for infinite series, ensuring that students gain a robust understanding of sequences, series and convergence criteria essential for Engineering problem-solving.

Throughout the course, tutorial sessions reinforce theoretical concepts through practical problem-solving, promoting both analytical thinking and mathematical maturity.

Prerequisites

Nil

Assessment Plan

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