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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