Chapter 1

Matrix Algebra

Rank of a matrix

medium • 1 min read

Elementary transformations

medium • 2 min read

Consistency of linear system of equations

medium • 3 min read

Eigen values and Eigen vectors

medium • 4 min read

Cayley-Hamilton Theorem

medium • 5 min read

Chapter 2

Differential Calculus I

Successive differentiation

medium • 1 min read

Leibnitz theorem

medium • 2 min read

Partial differentiation

medium • 3 min read

Euler’s theorem on homogeneous functions

medium • 4 min read

Total differentiation

medium • 5 min read

Chapter 3

Differential Calculus II

Expansion of function

medium • 1 min read

Taylor's and Maclaurin's series

medium • 2 min read

Jacobians

medium • 3 min read

Approximation of errors

medium • 4 min read

Extrema of functions of several variables

medium • 5 min read

Chapter 4

Multivariable Calculus I

Multiple integrals

medium • 1 min read

Change of order of integration

medium • 2 min read

Change of variables

medium • 3 min read

Beta and Gamma functions

medium • 4 min read

Applications to area and volume

medium • 5 min read

Chapter 5

Vector Calculus

Vector differentiation

medium • 1 min read

Gradient, curl and divergence

medium • 2 min read

Vector integration

medium • 3 min read

Gauss Divergence theorem

medium • 4 min read

Stokes theorem

medium • 5 min read