SI & BHS (Mathematics) 2024

Introduction Class Video

TNPSC  Combined Technical Services Exam 2024  Reseach Assistant, SI & BHS  Intoduction Class


UNIT III DIFFERENTIAL EQUATIONS AND LAPLACE TRANSFORMS

Order and Degree of a Differential Equations

Solvable for y,x & Clairaut's Equations

Second order differential equations with constant coefficients

Second and Higher Order Ordinary Differential Equations Type II, III & IV

UNIT III Differential Equations Class 5  Method of variation of Parameters & Total DE

Formation of PDE by eliminating arbitrary constants

Formation of PDE by eliminating arbitrary functions & Lagrange Equation

Solving Lagrange Equestion and Standard types

Standard Types f(z,p,q) =0, f(x,p) = f(y,q), Clairaut's Equations & Charpits Methods

Laplace Transforms and its Properties  Simple Problems

Inverse Laplace Transforms


UNIT 4 VECTOR CALCULUS

FOURIER SERIES CLASS 1

FOURIER TRANSFORM CLASS 1

FOURIER TRANSFORM

UNIT 4 Differential Calculus

Unit 4 Vector Integration

UNIT 4 VECTOR Differentiation class 1

Unit 4 vector Differentiation class 2

Unit 4 Vector Differentiation class 3

UNIT 4 Vector Integration Class 1

UNIT 4 Vector integration  surface integral CLASS 2

UNIT 4 Vector Integration Question Discussion

UNIT 4 Vector Integration Gauss ,Stock ,Green Therom

UNIT 4 Revision class

UG TRB UNIT 4 VECTOR CALCULUS Line Integral 2


UNIT VII COMPLEX ANALYSIS

Functions of a complex variable and Limits of a function

Continuity, Differentiability and Cauchy RiemannCR Equations

Analytic Functions and Harmonic Functions

Complex Integration and Cauchy's Integral Formula

Cauchy's Integral formula for Higher order Derivatives

Taylor’s & Laurent’s series Expansion

Laurents Series Problems and Zeros of ananlytic function

Singularities, Poles and Calculation of Residues

Cauchy's Residue Theorem and Removable, Essential Sigularity

Evaluation of improper real integrals, Trigonometric Function & PYQ Discussion Class


UNIT 10 Mathematical Statistics

SI & BHS UNIT 10 Skewness & kurtosis

UNIT 10 SI & BHS CORRELATION

SI & BHS UNIT 10 Binomial Distribution

SI & BHS UNIT 10 Regression

SI & BHS UNIT 10 Partial & multiple CORRELATION

SI & BHS UNIT 10 Uniform Distribution

SI & BHS UNIT 10 Normal Distribution

SI & BHS UNIT 10 Probability function ,Addition theorem

SI & BHS UNIT 10 Probability Generating Function

SI & BHS UNIT 10 Measure of Dispression

SI & BHS UNIT 10 Probability Function

SI & BHS UNIT 10 Measure of Central tendency


UNIT 2 CALCULUS

UNIT 2 nth derivative

UNIT 2 ENVELOPE,EVOLUTE

UNIT 2 nth derivative ,Lebiniz Theorem

UNIT 2 Maxima minima,Lagrange Multipliers

UNIT 2 Partial Diff Equqtion,Total Diff coefficient

UNIT 2 Beta Gamma function

UNIT 2 Radius of curvature

UNIT 2 Property of Definite integral

UNIT 2 Double integral

UNIT 2 Triple integral


UNIT IX OPERATIONS RESEARCH

Basics and Models of OR, Introduction of LPP and Formulation of LPP

Solving LPP for Graphical Method

General LPP Degenerate and NonDegenerate BFS

Simplex Method Introduction

Simplex Method, Big M Method & Two Phase Method

Primal Dual Pairs Duality Concepts

Transportation Problems for NWCR and LCM Methods

VAM Method and Assignment Problem

Network Techniques Introdcution and CPM Method

Network Techniques PERT Methods

Game Theory  Twoperson Zerosum game with saddle point and Without saddle Point

Game Theory Algebraic Method, Dominance Property and Graphical Method

Inventory Models

Sequencing problem – n jobs through 2 machines & n jobs through 3 machines

Sequencing Problems  Two jobs through m machines & n jobs through m machines


UNIT I ALGEBRA AND TRIGONOMETRY

Relations between roots and Coefficients, Complex ans Irrational roots

Symmetric functions of roots and Reciprocal equarions

Summation of Series Binomial Series

Exponential and Logarithmic series

Expansion of Con^nx and Sin^nx

Expansion of sinnx,cosnx,tannx and Expansion of sin(x), cos(x), tan(x) in terms of x

Hyperbolic and Inverse Hyperbolic Functions

Hyperbolic and Inverse Hyperbolic Functions problems

Matrix Theory Introduction and Types of Matrices

Rank of a Matrix

Consistency of a system of simultaneous linear equations, Eigen Values of a matrix

Cayley Hamilton Theorem, Eigen values and Eigen Vectors


UNIT 5 ALGEBRA

UNIT 5 Algebra Group theory class 1

UNIT 5 Algebra Group theory class 2

UNIT 5 Algebra Subgroup ,Cyclic group

UNIT 5 Algebra Normal Subgroup

UNIT 5 Algebra Homomarphism

UNIT 5 Algebra Perumutation

UNIT 5 Algebra Permutation

UNIT 5 Algebra Homeomorphism

UNIT 5 Algebra AUTOMORPHISM

UNIT 5 Algebra Linear Transformation

UNIT 5 Algebra Linear Transformation class 2

UNIT 5 Algebra Permutation

UNIT 5 Algebra Vector space


UNIT IV REAL ANALYSIS

Introduction of Real Number System and Sets

Operations on a sets

Functions, type of functions and Countability of sets

Limit point of a set and Dense of a set

Sequence of real Numbers

Monotonicaly Increasing and decreasing Problems

Cauchy first and Second theorems on limits

Infinite series

Alternatiing Series

Limits and Continuity

Differentiable of a functions and Rolle's Theorem

Lagrange MVT & Cauchy MVT

Metric Space, Open Set, Closed Set , Sequences and Series of functions


UNIT 8 DYNAMICS

UNIT 8 Projectile

UNIT 8 Centre of force

UNIT 8 Simple Harmonic fuction

UNIT 8 Centre of force Class 2

UNIT 8 Centre of force Class 3

UNIT 2 Pedal equation

UNIT 2 Pedal equation

UNIT 8 Velocity ,Relative Velosity,Angular velocity

UNIT 8 Moment of Inertia
