CSIR NET - BOOSTER - II (Mathematical Sciences) December 17

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CSIR NET
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Course Structure

          The Curriculum Section of this Course covers the following Content :

  • 20 Units of Theory [PART B & C]

Module: CSIR - NET THEORETICAL COURSE without Part A (Mathematical Sciences)

  • Subject: Mathematical Sciences
    • Section : Part B and C
      • Unit 1: ANALYSIS - I

        Lecture 1: Set Theory and Real Number System

        Lecture 2: Relations and Functions

        Lecture 3: Sequence and Series

      • Unit 2: ANALYSIS - II

        Lecture 1: Function

        Lecture 2: Limit of a Function of One Variable

        Lecture 3: Continuous Functions of One Variable

        Lecture 4: Derivability of a Function of One Variable

        Lecture 5: Rolle’s Theorem

        Lecture 6: Mean Value Theorem

        Lecture 7: Taylor’s Theorem

        Lecture 8: Maxima and Minima of One Variable

        Lecture 9: Functions of Two Variables

        Lecture 10: Limit of a Function of Two Variables

        Lecture 11: Continuity of a Function of Two Variables

        Lecture 12: Partial Derivatives

        Lecture 13: Differentiability of Two Variables

        Lecture 14: Maxima and Minima of Two Variables

        Lecture 15: Method of Lagrange Multipliers

        Lecture 16: Extrema Subject to One Constraint

        Lecture 17: Constrained Extrema of Quadratic Forms

        Lecture 18: Extrema Subject to Two Constraints

        Lecture 19: Euler’s Homogeneous Function Theorem

      • Unit 3: ANALYSIS - III

        Lecture 1: The Riemann Integral and Improper Integral

        Lecture 2: Uniform Convergence of Sequences & Series of Functions

        Lecture 3: Functions of Bounded Variation, Lebesgue Measure and Metric Space

      • Unit 4: MATRIX AND VECTOR SPACES

        Lecture 1: Algebra of Matrices

        Lecture 2: Linear Equation and Vector Space

      • Unit 5: LINEAR TRANSFORMATION, QUADRACTIC FORMS & INNER PRODUCT SPACES

        Lecture 1: Linear Transformation

        Lecture 2: Quadratic Forms and Inner Product Spaces

      • Unit 6: COMPLEX ANALYSIS - I

        Lecture 1: Complex Numbers

        Lecture 2: Complex Plane

        Lecture 3: Stereographic Projection

        Lecture 4: Chardal Distance

        Lecture 5: Multivalued Function

        Lecture 6: Monovalent Function

        Lecture 7: De Moivre’s Theorem

        Lecture 8: Geometry of Complex Numbers

        Lecture 9: Polynomials

        Lecture 10: Power Series

        Lecture 11: Complex Function

        Lecture 12: Analytic Functions

      • Unit 7: COMPLEX ANALYSIS - II

        Lecture 1: Line Integral

        Lecture 2: Important Theorems

        Lecture 3: Expansion of Analytic Functions as Power Series

        Lecture 4: The Zeros of an Analytic Function

        Lecture 5: Residue at a Pole

        Lecture 6: Cauchy’s Residue Theorem

        Lecture 7: Mappings

      • Unit 8: COMBINATORICS

        Lecture 1: Combinatorics

        Lecture 2: Permutations

        Lecture 3: Combinations

        Lecture 4: The Pigeonhole Principle

        Lecture 5: The Inclusion-Exclusion Principle

        Lecture 6: Derangements

        Lecture 7: Fundamental Theorem of Arithmetic

        Lecture 8: Divisibility

        Lecture 9: The Greatest Common Divisor

        Lecture 10: Congruences

        Lecture 11: Chinese Remainder Theorem

        Lecture 12: Euler’s Phi Function

        Lecture 13: Primitive Roots

      • Unit 9: GROUP THEORY

        Lecture 1: Binary Operations

        Lecture 2: Group

        Lecture 3: Subgroup

        Lecture 4: Cyclic Group

        Lecture 5: Cosets

        Lecture 6: Product of Subgroups

        Lecture 7: Permutation Group

        Lecture 8: Homomorphism

        Lecture 9: Conjugate Elements

        Lecture 10: Cayley’s Theorem

        Lecture 11: Dihedral Group Dn

        Lecture 12: Normal Subgroup

        Lecture 13: Simple Group

        Lecture 14: Conjugate Subgroup

        Lecture 15: Quotient Group

        Lecture 16: Maximal Normal Subgroup

        Lecture 17: Sylow Packages

        Lecture 18: Generalized Caylay Theorem (GCT)

      • Unit 10: RING THEORY AND TOPOLOGY

        Lecture 1: Ring Theory

        Lecture 2: Topology

      • Unit 11: ORDINARY DIFFERENTIAL EQUATIONS (ODES)

        Lecture 1: Ordinary Differential Equations

        Lecture 2: Differential Equations of the First Order and First Degree

        Lecture 3: Singular Solution

        Lecture 4: Existence and Uniqueness Theorem

        Lecture 5: Homogeneous and Non-Homogeneous Linear Differential Equations

        Lecture 6: Variation of Parameters

        Lecture 7: Self-Adjoint Equation

        Lecture 8: Green’s Function

      • Unit 12: PARTIAL DIFFERENTIAL EQUATIONS

        Lecture 1: Partial Differential Equations

        Lecture 2: Lagrange’s Solution of the Linear PDE

        Lecture 3: Charpit’s Method

        Lecture 4: Cauchy Problem for First Order PDEs

        Lecture 5: Classification of Second Order Partial Differential Equation

        Lecture 6: Method of Separation of Variables for Laplace Heat and Wave Equation

      • Unit 13: NUMERICAL ANALYSIS

        Lecture 1: Bisectional Method

        Lecture 2: False Position or Regula Falsi Method

        Lecture 3: Newton-Raphson Method

        Lecture 4: Solution of Simultaneous Linear Equations

        Lecture 5: Interpolation

        Lecture 6: Numerical Differentiation

        Lecture 7: Numerical Integration

        Lecture 8: Numerical Solution of Ordinary Differential Equations

      • Unit 14: CALCULUS OF VARIATIONS AND LINEAR INTEGRAL EQUATIONS

        Lecture 1: Calculus of Variations

        Lecture 2: Linear Integral Equations

      • Unit 15: CLASSICAL MECHANICS

        Lecture : Classical Mechanics

      • Unit : DESCRIPTIVE STATISTICS THEORY OF PROBABILITY

        Lecture 1: Cumulative Frequency Distribution

        Lecture 2: Measure of Dispersion

        Lecture 3: Theory of Probability

        Lecture 4: Markov Chain

        Lecture 5: Standard Discrete Distributions

        Lecture 6: Theoritical Continuous Distribution

        Lecture 7: Order Statistics

        Lecture 8: Sampling Distribution

      • Unit 17: STATISTICAL INFERENCES

        Lecture 1: Methods of Estimation

        Lecture 2: Confidence Interval and Confidence Limit

        Lecture 3: Test of Significance

        Lecture 4: Chi-Square Test of Goodness of Fit

        Lecture 5: Rank Correlation

        Lecture 6: Non-Parametric Test

      • Unit 18: GAUSS-MARKOV MODEL

        Lecture 1: Gauss - Markov Model

        Lecture 2: Confidence Intervals

        Lecture 3: Testing of Hypothesis

        Lecture 4: Analysis of Variance

        Lecture 5: Fixed and Random Effects Models

        Lecture 6: Analysis of Covariance (ANOCOVA)

        Lecture 7: Mixed Effect Model

        Lecture 8: Regression Analysis

        Lecture 9: Logistic Regression

        Lecture 10: Multivariate Normal Distribution

        Lecture 11: The Wishart Distribution

        Lecture 12: Partial Correlation and Partial Regression

        Lecture 13: Data Reduction Techniques

      • Unit 19: SAMPLING and DESIGNS

        Lecture 1: Theory of Sampling

        Lecture 2: Ratio and Regression Methods

        Lecture 3: Experimental Design

        Lecture 4: Hazard Function

        Lecture 5: Censoring

      • Unit 20: LINEAR PROGRAMMING AND QUEUING THEORY

        Lecture 1: Linear Programming Problem

        Lecture 2: Simplex Method to Solve LPP

        Lecture 3: Primal Dual Problem

        Lecture 4: Queuing Theory

        Lecture 5: Inventory Problems

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