Linear Algebra
Linear Equations
Matrices and Determinants
Vector Spaces
Linear Transformations
Inner Product Spaces
Operators on Inner Product Spaces
Bilinear Forms
Elementary Canonical Forms
Rational and Jordan Forms
Complex Analysis
Sequence and Series in Complex
Laurent Series & Residue Theorem
Entire and Meromorphic Functions
Bilinear Transformation & Mapping
Applications of Cauchy's Theorem
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
Sol. of 1st Order & Higher Degree
LDE with Constant Coefficients
Homogeneous Linear Equations
Method of Variation of Parameters
Exact Differential Equations
Equations of Special Forms
Linear Equations of Second Order
Picard’s Method & Existence
Partial Differential Equations
Legendre Functions of Second Kind
Orthogonal Sets of Functions
Partial Differential Equation
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
Calculus of Variations
Variation of a Functional
Sufficient Conditions for Extrema
Boundary Value Problems in PDE
Linear Integral Equations
Fredholm and Volterra Type
Sol. with Separable Kernels
Descriptive Statistics
Introduction Meaning and Scope
Measures of Central Tendency
Correlation and Regression
Sampling and Large Sample Tests
Analysis
Sets & Number System
Series & Convergence
Theorem's in Analysis
Metric Spaces & Functions