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Mathematical Sciences
Linear Algebra
Linear Equations
Matrices and Determinants
Vector Spaces
Linear Transformations
Inner Product Spaces
Operators on Inner Product Spaces
Bilinear Forms
Polynomials
Determinants
Elementary Canonical Forms
Rational and Jordan Forms
Complex Analysis
Preliminaries
Elementary Functions
Analytic Functions
Sequence and Series in Complex
Complex Integration
Laurent Series & Residue Theorem
Entire and Meromorphic Functions
Bilinear Transformation & Mapping
Applications of Cauchy's Theorem
Harmonic Functions
Riemann Mapping Theorem
Analytic Continuation
Algebra
Fundamental Theory of Arithmetic
Group Theory
Ring Theory
Fields
Permutations & Combinations
Ordinary Differential Equation
Solution of Linear Differential Equations with Constant and Variable Coefficients
Equations of First Order & Degree
Trajectories
Sol. of 1st Order & Higher Degree
Homogeneous Linear Equations
Method of Variation of Parameters
Ordinary Simultaneous DE
Exact Differential Equations
Equations of Special Forms
Linear Equations of Second Order
Picard’s Method & Existence
Simultaneous Equations
Partial Differential Equations
Riccati’s Equation
Chebyshev Polynomials
Beta and Gamma Functions
Power Series
Legendre Polynomials
Bessel Functions
Orthogonal Sets of Functions
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
Calculus of Variations
Variation of a Functional
Euler-Lagrange Equation
Sufficient Conditions for Extrema
Boundary Value Problems in PDE
Linear Integral Equations
Fredholm and Volterra Type
Sol. with Separable Kernels
Characteristic Numbers
Eigen Functions
Resolvent Kernel
Analysis
Sets & Number System
Series & Convergence
Theorem's in Analysis
Notions of Continuity
Integration Theory
Multivariable Calculus
Metric Spaces & Functions
