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Index

Unit 1: Analysis

Unit 2: Complex Analysis

Unit 3: Algebra

Unit 4: Ordinary Differential Equations (ODEs)

Unit 5: Partial Differential Equations (PDEs)

Unit 6: Numerical Analysis

Unit 7: Calculus of Variations

Unit 8: Linear Integral Equations

Unit 9: Classical Mechanics

Unit 10: Descriptive Statistics, Exploratory Data Analysis

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All videos of CSIR NET Crash Course for Mathematics for CSIR NET Mathematics Exam

Unit 1: Analysis

Elementary Set Theory

59:35 min

Finite, Countable, and Uncountable Sets

06:19 min

Real Number System

31:39 min

Archimedean Property

13:11 min

Supremum

42:49 min

Infimum

42:49 min

Sequence and Series

00:59 min

Convergence

61:30 min

Limsup

11:29 min

Liminf

11:00 min

Bolzano Weierstrass Theorem

30:03 min

Heine Borel Theorem

09:25 min

Continuity

61:30 min

Uniform Continuity

00:57 min

Differentiability

58:00 min

Mean Value Theorem

30:31 min

Uniform Convergence

61:30 min

Riemann Sums and Riemann Integral

32:13 min

Improper Integrals

33:57 min

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Unit 2: Complex Analysis

Algebra of Complex Numbers

11:41 min

The Complex Plane

54:19 min

Polynomials

41:34 min

Power Series

05:00 min

Transcendental Functions Such as Exponential, Trigonometric, and Hyperbolic Functions

09:50 min

Analytic Functions

24:21 min

Cauchy-riemann Equations

32:31 min

Contour Integral

62:24 min

Cauchy's Theorem

27:14 min

Cauchy's Integral Formula

04:39 min

Maximum Modulus Principle

24:00 min

Schwarz Lemma

04:06 min

Open Mapping Theorem

09:19 min

Taylor Series

14:26 min

Laurent Series

133:00 min

Calculus of Residues

64:04 min

Mobius Transformations

89:55 min

Unit 3: Algebra

Permutations

56:48 min

Combinations

83:07 min

Pigeon-hole Principle

34:48 min

Inclusion-exclusion Principle

22:37 min

Derangements

09:06 min

Fundamental Theorem of Arithmetic

17:28 min

Divisibility in Z

21:35 min

Congruences

05:17 min

Chinese Remainder Theorem

73:17 min

Euler's -function

01:00 min

Primitive Roots

09:17 min

Groups

09:54 min

Subgroups

59:02 min

Normal Subgroups

23:43 min

Quotient Groups

24:58 min

Homomorphisms

29:30 min

Cyclic Groups

37:00 min

Permutation Groups

56:48 min

Cayley's Theorem

32:10 min

Class Equations

67:08 min

Sylow Theorems

71:46 min

Ideals

38:04 min

Quotient Rings

58:34 min

Unique Factorization Domain

34:55 min

Principal Ideal Domain

28:05 min

Euclidean Domain

17:11 min

Basis

09:54 min

Dense Sets

12:30 min

Subspace and Product Topology

39:15 min

Separation Axioms

64:25 min

Connectedness

10:43 min

Compactness

59:41 min

Prime and Maximal Ideals

07:20 min

Unit 4: Ordinary Differential Equations (ODEs)

Existence and Uniqueness of Solutions of Initial Value Problems for First-order Ordinary Differential Equations

12:22 min

Singular Solutions of First-order Odes

83:46 min

System of First-order Odes

64:06 min

A General Theory of Homogenous and Non-homogeneous Linear Odes

04:11 min

Variation of Parameters

16:29 min

Sturm-liouville Boundary Value Problem

72:25 min

Green's Function

75:45 min

Unit 5: Partial Differential Equations (PDEs)

Lagrange and Charpit Methods for Solving First-order Pdes

16:29 min

Cauchy Problem for First-order Pdes

48:20 min

Classification of Second-order Pdes

02:54 min

General Solution of Higher-order Pdes With Constant Coefficients

16:40 min

Method of Separation of Variables for Laplace

24:38 min

Heat

62:20 min

Wave Equations

08:04 min

Unit 6: Numerical Analysis

Numerical Solutions of Algebraic Equations

66:05 min

Method of Iteration and Newton-raphson Method

03:11 min

Rate of Convergence

09:52 min

Solution of Systems of Linear Algebraic Equations Using Gauss Elimination and Gauss-seidel Methods

17:18 min

Finite Differences

43:57 min

Lagrange

11:35 min

Hermite

04:38 min

Spline Interpolation

56:36 min

Numerical Differentiation and Integration

10:15 min

Numerical Solutions of Odes Using Picard

11:03 min

Modified Euler and Runge-kutta Methods

13:24 min

Unit 7: Calculus of Variations

Variation of a Functional

05:35 min

Euler-lagrange Equation

21:10 min

Necessary and Sufficient Conditions for Extrema

93:41 min

Variational Methods for Boundary Value Problems in Ordinary and Partial Differential Equations

11:47 min

Unit 8: Linear Integral Equations

Linear Integral Equation of the First and Second Kind of Fredholm and Volterra Type

07:26 min

Solutions With Separable Kernels

06:42 min

Characteristic Numbers and Eigenfunctions

03:19 min

Resolvent Kernel

06:42 min

Unit 9: Classical Mechanics

Generalized Coordinates

04:54 min

Lagrange's Equations

28:59 min

Hamilton's Canonical Equations

14:49 min

Hamilton's Principle and the Principle of Least Action

17:55 min

Two-dimensional Motion of Rigid Bodies

58:12 min

Euler's Dynamical Equations for the Motion of a Rigid Body About an Axis

41:28 min

Theory of Small Oscillations

48:37 min

Unit 10: Descriptive Statistics, Exploratory Data Analysis

Markov Chains With Finite and Countable State Space

23:41 min

Classification of States

55:46 min

Limiting Behavior of N-step Transition Probabilities

20:41 min

Stationary Distribution

18:18 min

Poisson, and Birth-and Death Processes

03:06 min

Distribution of Order Statistics

13:51 min

Range

22:20 min

Methods of Estimation

01:01 min

Properties of Estimators

15:26 min

Confidence Intervals

14:47 min

Tests of Hypotheses: Most Powerful and Uniformly Most Powerful Tests

06:57 min

Likelihood Ratio Tests

08:19 min

Analysis of Discrete Data and Chi-square Test of Goodness of Fit

05:23 min

Large Sample Tests

01:01 min

Simple Nonparametric Tests for One and Two Sample Problems

05:19 min

Rank Correlation

17:55 min

Test for Independence

27:45 min

Simple Random Sampling

13:19 min

Stratified Sampling

04:51 min

Systematic Sampling

03:47 min

Probability is Proportional to Size Sampling

25:32 min

Ratio and Regression Methods

54:50 min

Hazard Function and Failure Rates

65:41 min

Censoring and Life Testing

01:01 min

Series and Parallel System

20:03 min

Standard Discrete and Continuous Univariate Distributions

43:06 min

Distribution of Order Statistics

13:51 min

Estimation of Population Mean and Population Variance

13:12 min

Degrees of Freedom

07:34 min

The Sampling Distribution

06:25 min

Central Limit Theorem

09:37 min

Shape of the Sampling Distribution

09:36 min

Calculating the Standard Error of the Mean

05:58 min

The Estimated Standard Error of the Mean

08:56 min

Introduction to JASP

07:19 min

What Is a Standard Error?

02:17 min

CSIR NET Crash Course for Mathematics

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