Matrices and Calculus (MA3151)

label_important 1.1 Introduction

label_important1.2 Characteristic Equation

label_important 1.3 Eigen values and Eigen vectors

label_important 1.4 Properties of Eigen values and Eigen vectors

label_important 1.5 Cayley Hamilton Theorem

label_important 1.6 Diagonalisation of Matrix (Orthogonal Transformation)

label_important 1.7 Quadratic Forms and Nature of Quadratic Forms

label_important 1.8 Stretching of an Elastic Membrance

label_important 2.1 Representation of Functions

label_important2.2 Limit of a Functions

label_important 2.3 Continuity

label_important 2.4 Derivatives

label_important 2.5 Differentiation Rules

label_important 2.6 Implicit Differentiation

label_important 2.7 Logarithmic Differentiation

label_important 2.8 Maxima and Minima of functions of one variable

label_important 3.1 Partial Differentiation

label_important3.2 Euler's Theorems

label_important 3.3 Total Derivatives

label_important 3.4 Derivative of an Implicit functions

label_important 3.5 Change of variable

label_important 3.6 Jacobian's

label_important 3.7 Taylors Series & Maclaurin Series

label_important 3.8 Maxima & Minima

label_important 3.9 Lagrange's Method

label_important 4.1 Definite Integral

label_important4.2 Definite Integral - Reimann Sum

label_important 4.3 Indefinite Integral

label_important 4.4 Properties of Definite Integral

label_important 4.5 Substitution Rule

label_important 4.6 Integration by Parts

label_important 4.7 Trigonometric Integrals

label_important 4.8 Trigonometric Substitutions

label_important 4.9 Integration of rational functions by partial fraction

label_important4.10 Improper Integrals

label_important 4.11 Applications - Hydrostatic force and Pressure

label_important 4.12 Applications - Moments and center of mass

label_important 5.1 Double Integral

label_important5.2 Change of Order of Integration

label_important 5.3 Change of Variables (Double Integral)

label_important 5.4 Application of Double Integral (Area)

label_important 5.5 Triple Integral

label_important 5.6 Change of Variables (Triple Integral)

label_important 5.7 Application of Triple Integral (Volume)