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



Elementary Canonical Forms

Rational and Jordan Forms

Complex Analysis


Elementary Functions

Analytic Functions

Singularites of Analytic Functions

Limit, Continuity & Differentiability

Sequence and Series in Complex

Complex Integration

Laurent Series & Residue Theorem

Entire and Meromorphic Functions

Important Theorems & Applications

Max. and Min. Modulus Principle and Schwarz Lemma

Argument and Rouche’s Theorem

Calculus of Residues

Conformal Mapping

Bilinear Transformation & Mapping

Applications of Cauchy's Theorem

Harmonic Functions

Riemann Mapping Theorem

Analytic Continuation

Special Functions:The Exponential

Taylor and Laurent Expansion

Stereographic Projection & Point Set Topology

Fundamental Concepts of Complex Analysis


Algebraic Extension of Fields

Basic Algebraic Structure

Ordinary Differential Equation

Introduction and Preliminaries

First Order First Degree Differential Equation

General Theory of Linear Differential Equation of Higher Order

Solution of Linear Differential Equations with Constant and Variable Coefficients

Uniqueness and Existence

System of Differential Equations

Boundary Value Problems

Equtn of the 1st Order but Not of The 1st Degree

Equations of First Order & Degree


Sol. of 1st Order & Higher Degree

LDE with Constant Coefficients

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

Integration in Series

Legendre Polynomials

Legendre Functions of Second Kind

Bessel Functions

Orthogonal Sets of Functions

LDE Solution with Const. & Var. Coefficients

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

Numerical Analysis

Soln. of Algebraic & Trans Eqn

Interpolation and Approximation

Numerical Differentiation

Initial Value Problems for ODE

Boundary Value Problems-ODE & PDE

Linear System of Algebraic Eqn

Numerical Integration

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

Descriptive Statistics

Introduction Meaning and Scope

Frequency Distributions

Measures of Central Tendency

Measures of Dispersion

Skewness and Kurtosis

Theory of Probability

Random Variables

Mathematical Expectation

Discrete Distributions

Continuous Distributions

Curve Fitting

Correlation and Regression

Theory of Attributes

Sampling and Large Sample Tests

Chi-Square Distribution

t,F and z distributions

Theory of Estimation

Statistical Inference-II


Special Univariate Distributions

Joint & Conditional Distributions

Inference - Parameter Estimation

Maximum Likelihood Estimation

Hypothesis Testing

Elements of Bayesian Inference

Markov Chains



Sets & Number System

Series & Convergence

Theorem's in Analysis

Notions of Continuity

Integration Theory

Multivariable Calculus

Metric Spaces & Functions