Mathematical Sciences

Linear Algebra

Matrices

Diagonalizability & Canonical Forms

Linear Equations

Vector Spaces

Linear Transformations

Polynomials

Determinants

Elementary Canonical Forms

Rational and Jordan Forms

Inner Product Spaces

Operators on Inner Product Spaces

Bilinear Forms

Partial Differential Equation

Origin of PDE

Linear PDE of Order One

Non-linear PDE of Order One

Linear PDE with Constant Coeff.

PDE Reducible to Equations

2nd Order Variable Coeff. PDE

PDE into Cononial/Normal Form

Monge’s Method

Classification & Formation of PDE

Heat, Wave & Laplace Equation

Classification of Second Order PDE

Linear Integral Equations

Fredholm and Volterra Type

Sol. with Separable Kernels

Characteristic Numbers

Eigen Functions

Resolvent Kernel

Volterra’s Integral Equation

Fredholm Integral Equation

Hilbert Schmidt Theory

Integral Equation

Calculus of Variations

Variation of a Functional

Euler-Lagrange Equation

Sufficient Conditions for Extrema

Boundary Value Problems in PDE

Miscellaneous

Real Analysis

Countability

Point Set Topology

Sequence

Series

Function and its Property

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