Linear Algebra & Calculus

This book has been written strictly as per the latest syllabus (R-23) prescribed by Jawaharlal Nehru Technological University and Colleges, Kakinada, with effect from 2023-24 academic year for all branches of B.Tech. First Year students. The book delves into the fundamental concepts of Linear Algebra and Calculus, offering a clear and structured approach to complex topics. In the Linear Algebra section, students explore essential topics such as Matrices, System of Equations, Eigenvalues, Eigenvectors, and Quadratic Forms. Each chapter provides in-depth explanations, step-by-step problem-solving techniques, and real-world applications of these mathematical concepts. Topics like Matrix Diagonalization, the Cayley-Hamilton Theorem, and Orthogonal Transformations are presented in a manner that is both accessible and rigorous.

The Calculus section introduces key concepts like Mean Value Theorems, Partial Differentiation, and Multiple Integrals. Students will develop a solid understanding of Rolle's, Lagrange's, and Cauchy's Theorems, along with methods for solving multi-variable calculus problems. The book also covers important applications of calculus, such as maximizing and minimizing functions of several variables, and the use of Lagrange multipliers.

With its clear explanations, extensive problem sets, and practical applications.