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Mathematical Sciences
Linear Algebra
Linear Equations
Matrices and Determinants
Vector Spaces
Linear Transformations
Diagonalizability & Canonical Forms
Inner Product Spaces
Operators on Inner Product Spaces
Bilinear Forms
Polynomials
Determinants
Elementary Canonical Forms
Rational and Jordan Forms
Real Analysis
Sets and Number System
Point Set Topology
Series and Convergence
Function and its Property
Sequence and Series of Function
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
Calculus of Variations
Variation of a Functional
Euler-Lagrange Equation
Sufficient Conditions for Extrema
Boundary Value Problems in PDE
Miscellaneous
Linear Integral Equations
Fredholm and Volterra Type
Sol. with Separable Kernels
Characteristic Numbers
Eigen Functions
Resolvent Kernel
Hilbert Schmidt Theory
Integral Equation
Volterra’s Integral Equation
Fredholm Integral Equation
