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Mathematical Sciences
Common Subject
Linear Algebra
Linear Equations
Matrices and Determinants
Vector Spaces
Linear Transformations
Diagonalizability & Canonical Forms
Inner Product Spaces
Operators on Inner Product Spaces
Bilinear Forms
Polynomials
Determinants
Elementary Canonical Forms
Rational and Jordan Forms
Real Analysis
Sets and Number System
Point Set Topology
Series and Convergence
Function and its Property
Sequence and Series of Function
Complex Analysis
Preliminaries
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
Algebra
Fundamental Theory of Arithmetic
Group Theory
Ring Theory
Fields
Permutations & Combinations
Uniform Convergence (Sequence & Series of Function)
Some Important Structures
Basic Algebraic Structure
Ring of Polynomials
Continuity
Reimann Integration & Bounded Variation and Improper Integral
Differentiability
Set and Relations
Homomorphism and their Counting
Some Important Groups of Infinite Order
Invariant/Normal Subgroup
Groups within Groups
Basic Concepts and Definitions
Algebraic Extension of Fields
ED, PID & UFD
Subring and Ideals
Some Important Groups of Finite Order
Conjugate Classes and Class Equation
Symmetric Group or Permutation Group
Sylow Theorems
Ordinary Differential Equation
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
Boundary Value Problems
Equtn of the 1st Order but Not of The 1st Degree
Equations of First Order & Degree
Exact Differential Equations
Equations of Special Forms
Chebyshev Polynomials
Beta and Gamma Functions
Bessel 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
Classification & Formation of PDE
Classification of Second Order PDE
Heat, Wave & Laplace Equation
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
Calculus of Variations
Variation of a Functional
Euler-Lagrange Equation
Sufficient Conditions for Extrema
Boundary Value Problems in PDE
Miscellaneous
Linear Integral Equations
Fredholm and Volterra Type
Sol. with Separable Kernels
Characteristic Numbers
Eigen Functions
Resolvent Kernel
Hilbert Schmidt Theory
Integral Equation
Volterra’s Integral Equation
Fredholm 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
Maximum Likelihood Estimation
Probability
Markov Chains
Miscellaneous
Joint & Conditional Distributions
Elements of Bayesian Inference
Special Univariate Distributions
Inference - Parameter Estimation
Hypothesis Testing
Analysis
Sets & Number System
Series & Convergence
Theorem's in Analysis
Notions of Continuity
Integration Theory
Multivariable Calculus
Metric Spaces & Functions
General Aptitude
General Aptitude
Operation Research
Linear Programming
Classical Mechanics
Generalized Coordinates
Lagrange’s Equations
Hamilton’s Canonical Equations
Hamilton’s Principle
Principle of Least Action
2-D Motion of Rigid Bodies
Euler’s Eq. (Rigid Body)
