Linear Algebra & Calculus (JNTUK | JNTUA | APSCHE) (R26)

Linear Algebra & Calculus develops the matrix and calculus methods required at the start of an engineering programme. Its seven chapters are arranged within five units, moving from matrices and linear systems to eigenvalues, diagonalization, quadratic forms, mean value theorems, partial differentiation and multiple integrals.

The linear algebra chapters cover matrix types and operations, rank, inverse matrices, homogeneous and non-homogeneous systems, Gaussian elimination, and Jacobi and Gauss-Seidel iteration. Eigenvalues and eigenvectors lead to matrix diagonalization, the Cayley-Hamilton theorem, singular value decomposition and the reduction of quadratic forms by orthogonal transformations.

The calculus treatment includes Rolle's, Lagrange's and Cauchy's mean value theorems, Taylor and Maclaurin expansions, partial and total derivatives, Euler's theorem, Jacobians, functional dependence and constrained optimization. Double and triple integrals are developed with changes of order and variables, polar, cylindrical and spherical coordinates, and applications to areas and volumes. Solved examples, exercises, objective questions and previous GATE questions support independent practice and examination preparation.