#### Linear Algebra

### Matrices and Determinants

### Diagonalizability & Canonical Forms

### Operators on Inner Product Spaces

### Elementary Canonical Forms

### Rational and Jordan Forms

#### Complex Analysis

### Singularites of Analytic Functions

### Limit, Continuity & Differentiability

### Sequence and Series in Complex

### Laurent Series & Residue Theorem

### Entire and Meromorphic Functions

### Important Theorems & Applications

### Max. and Min. Modulus Principle and Schwarz Lemma

### Argument and Rouche’s Theorem

### Bilinear Transformation & Mapping

### Applications of Cauchy's Theorem

### Special Functions:The Exponential

### Taylor and Laurent Expansion

### Stereographic Projection & Point Set Topology

### Fundamental Concepts of Complex Analysis

#### Algebra

### 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

### System of Differential Equations

### 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

### 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

### LDE Solution with Const. & Var. Coefficients

#### 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

### 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

#### Linear Integral Equations

### Fredholm and Volterra Type

### Sol. with Separable Kernels

### Volterra’s Integral Equation

### Fredholm Integral Equation

#### Descriptive Statistics

### Introduction Meaning and Scope

### Frequency Distributions

### Measures of Central Tendency

### Measures of Dispersion

### Theory of Probability

### Random Variables

### Mathematical Expectation

### Continuous Distributions

### Correlation and Regression

### Sampling and Large Sample Tests

### Chi-Square Distribution

### Theory of Estimation

### Statistical Inference-II

### Special Univariate Distributions

### Joint & Conditional Distributions

### Inference - Parameter Estimation

### Maximum Likelihood Estimation

### Elements of Bayesian Inference

### Markov Chains

#### Analysis

### Metric Spaces & Functions