CSIR NET BOOSTER II (Mathematical Sciences) Dec 19

Eduncle
CSIR NET
8

This Course is designed and developed by a team of Highly Experienced and Qualified Faculties. It covers entire Syllabus and promise to make Student full prepared to give NET Exam with confidence

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  • Complete Syllabus Covered
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Course Structure

          The Curriculum Section of this Course covers the following Content :

  • 20 Units of Theory [PART B & C]

Module: NET - THEORETICAL COURSE - Mathematical Sciences (Part B & C)

  • Subject: Mathematical Sciences
    • Section 1: ANALYSIS - I

        Attachments 1: Set Theory and Real Number System

        Attachments 2: Relations and Functions

        Attachments 3: Sequence and Series

    • Section 2: ANALYSIS - II

        Attachments 1: Function

        Attachments 2: Limit of a Function of One Variable

        Attachments 3: Continuous Functions of One Variable

        Attachments 4: Derivability of a Function of One Variable

        Attachments 5: Rolle’s Theorem

        Attachments 6: Mean Value Theorem

        Attachments 7: Taylor’s Theorem

        Attachments 8: Maxima and Minima of One Variable

        Attachments 9: Functions of Two Variables

        Attachments 10: Limit of a Function of Two Variables

        Attachments 11: Continuity of a Function of Two Variables

        Attachments 12: Partial Derivatives

        Attachments 13: Differentiability of Two Variables

        Attachments 14: Maxima and Minima of Two Variables

        Attachments 15: Method of Lagrange Multipliers

        Attachments 16: Extrema Subject to One Constraint

        Attachments 17: Constrained Extrema of Quadratic Forms

        Attachments 18: Extrema Subject to Two Constraints

        Attachments 19: Euler’s Homogeneous Function Theorem

    • Section 3: ANALYSIS - III

        Attachments 1: The Riemann Integral and Improper Integral

        Attachments 2: Uniform Convergence of Sequences & Series of Functions

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

    • Section 4: MATRIX AND VECTOR SPACES

        Attachments 1: Algebra of Matrices

        Attachments 2: Linear Equation and Vector Space

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

        Attachments 1: Linear Transformation

        Attachments 2: Quadratic Forms and Inner Product Spaces

    • Section 6: COMPLEX ANALYSIS - I

        Attachments 1: Complex Numbers

        Attachments 2: Complex Plane

        Attachments 3: Stereographic Projection

        Attachments 4: Chardal Distance

        Attachments 5: Multivalued Function

        Attachments 6: Monovalent Function

        Attachments 7: De Moivre’s Theorem

        Attachments 8: Geometry of Complex Numbers

        Attachments 9: Polynomials

        Attachments 10: Power Series

        Attachments 11: Complex Function

        Attachments 12: Analytic Functions

    • Section 7: COMPLEX ANALYSIS - II

        Attachments 1: Line Integral

        Attachments 2: Important Theorems

        Attachments 3: Expansion of Analytic Functions as Power Series

        Attachments 4: The Zeros of an Analytic Function

        Attachments 5: Residue at a Pole

        Attachments 6: Cauchy’s Residue Theorem

        Attachments 7: Mappings

    • Section 8: COMBINATORICS

        Attachments 1: Combinatorics

        Attachments 2: Permutations

        Attachments 3: Combinations

        Attachments 4: The Pigeonhole Principle

        Attachments 5: The Inclusion-Exclusion Principle

        Attachments 6: Derangements

        Attachments 7: Fundamental Theorem of Arithmetic

        Attachments 8: Divisibility

        Attachments 9: The Greatest Common Divisor

        Attachments 10: Congruences

        Attachments 11: Chinese Remainder Theorem

        Attachments 12: Euler’s Phi Function

        Attachments 13: Primitive Roots

    • Section 9: GROUP THEORY

        Attachments 1: Binary Operations

        Attachments 2: Group

        Attachments 3: Subgroup

        Attachments 4: Cyclic Group

        Attachments 5: Cosets

        Attachments 6: Product of Subgroups

        Attachments 7: Permutation Group

        Attachments 8: Homomorphism

        Attachments 9: Conjugate Elements

        Attachments 10: Cayley’s Theorem

        Attachments 11: Dihedral Group Dn

        Attachments 12: Normal Subgroup

        Attachments 13: Simple Group

        Attachments 14: Conjugate Subgroup

        Attachments 15: Quotient Group

        Attachments 16: Maximal Normal Subgroup

        Attachments 17: Sylow Packages

        Attachments 18: Generalized Caylay Theorem (GCT)

    • Section 10: RING THEORY AND TOPOLOGY

        Attachments 1: Ring Theory

        Attachments 2: Topology

    • Section 11: ORDINARY DIFFERENTIAL EQUATIONS (ODES)

        Attachments 1: Ordinary Differential Equations

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

        Attachments 3: Singular Solution

        Attachments 4: Existence and Uniqueness Theorem

        Attachments 5: Homogeneous and Non-Homogeneous Linear Differential Equations

        Attachments 6: Variation of Parameters

        Attachments 7: Self-Adjoint Equation

        Attachments 8: Green’s Function

    • Section 12: PARTIAL DIFFERENTIAL EQUATIONS

        Attachments 1: Partial Differential Equations

        Attachments 2: Lagrange’s Solution of the Linear PDE

        Attachments 3: Charpit’s Method

        Attachments 4: Cauchy Problem for First Order PDEs

        Attachments 5: Classification of Second Order Partial Differential Equation

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

    • Section 13: NUMERICAL ANALYSIS

        Attachments 1: Bisectional Method

        Attachments 2: False Position or Regula Falsi Method

        Attachments 3: Newton-Raphson Method

        Attachments 4: Solution of Simultaneous Linear Equations

        Attachments 5: Interpolation

        Attachments 6: Numerical Differentiation

        Attachments 7: Numerical Integration

        Attachments 8: Numerical Solution of Ordinary Differential Equations

    • Section 14: CALCULUS OF VARIATIONS AND LINEAR INTEGRAL EQUATIONS

        Attachments 1: Calculus of Variations

        Attachments 2: Linear Integral Equations

    • Section 15: CLASSICAL MECHANICS

        Attachments 1: Classical Mechanics

    • Section 16: DESCRIPTIVE STATISTICS THEORY OF PROBABILITY

        Attachments 1: Cumulative Frequency Distribution

        Attachments 2: Measure of Dispersion

        Attachments 3: Theory of Probability

        Attachments 4: Markov Chain

        Attachments 5: Standard Discrete Distributions

        Attachments 6: Theoritical Continuous Distribution

        Attachments 7: Order Statistics

        Attachments 8: Sampling Distribution

    • Section 17: STATISTICAL INFERENCES

        Attachments 1: Methods of Estimation

        Attachments 2: Confidence Interval and Confidence Limit

        Attachments 3: Test of Significance

        Attachments 4: Chi-Square Test of Goodness of Fit

        Attachments 5: Rank Correlation

        Attachments 6: Non-Parametric Test

    • Section 18: GAUSS-MARKOV MODEL

        Attachments 1: Gauss - Markov Model

        Attachments 2: Confidence Intervals

        Attachments 3: Testing of Hypothesis

        Attachments 4: Analysis of Variance

        Attachments 5: Fixed and Random Effects Models

        Attachments 6: Analysis of Covariance (ANOCOVA)

        Attachments 7: Mixed Effect Model

        Attachments 8: Regression Analysis

        Attachments 9: Logistic Regression

        Attachments 10: Multivariate Normal Distribution

        Attachments 11: The Wishart Distribution

        Attachments 12: Partial Correlation and Partial Regression

        Attachments 13: Data Reduction Techniques

    • Section 19: SAMPLING and DESIGNS

        Attachments 1: Theory of Sampling

        Attachments 2: Ratio and Regression Methods

        Attachments 3: Experimental Design

        Attachments 4: Hazard Function

        Attachments 5: Censoring

    • Section 20: LINEAR PROGRAMMING AND QUEUING THEORY

        Attachments 1: Linear Programming Problem

        Attachments 2: Simplex Method to Solve LPP

        Attachments 3: Primal Dual Problem

        Attachments 4: Queuing Theory

        Attachments 5: Inventory Problems

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Deepika



Material were good and very informative too.