ALGEBRA
Group:
Subgroup, Product Group:
Cyclic group:
Normal Subgroup:
Automorphism:
Permutations:
Problems on Permutations:
Sylow’s Theorem:
Rings:
Field:
Types of Ideals:
Euclidean Ring:
Commutator Subgroup:
Types of Polynomial:
Extension Field:
Splitting Field:
Fixed Field:
Vector Space:
Dual Space:
Quotient Space:
Eigen Values & Eigen Vectors:
Matrices:
Transformations:
Projection:
Canonical Form:
Full Chapter Revision:
REAL ANALYSIS
Basic Definitions:
Countable and Uncountable Set:
Bounded and Unbounded Set:
Metric Space:
Open Sets:
Closed Sets:
Closure:
Complete Metric Space:
Connectedness:
Compactness:
Totally Bounded:
Continuous Functions:
Derivative Functions:
Taylor & Maclurin Series:
Sequence:
Cauchy Sequence:
Theorems on Limits:
Series:
Test in Series:
Alternating Series:
Problems on Limits: Part – 1
Problems on Limits: Part – 2
Problems on Continuity: Part – 1
Problems on Continuity: Part – 2
Problems on Comparison Test:
Problems on Ratio Test: Part – 1
Problems on Ratio Test: Part – 2
Measure Zero:
Riemann Integral:
Riemann Stieltjes Integral:
Measurable Set:
Measurable Function:
Problems on Fourier Series:
Full Chapter Revision:
COMPLEX ANALYSIS
Basic Concepts:
Limits:
Continuous:
Differentiability:
Analytic Function:
Problems on Analytic Functions:
Harmonic Function:
Problems on Harmonic Function:
Sequence:
Series:
Uniform Converges:
Problems:
Conformal Mapping:
Bilinear Transformation:
Types of Bilinear Transformation:
Mappings:
Taylor Series:
Maclaurin’s Series:
Laurent’s Series:
Cauchy’s Theorem:
Cauchy’s Integral Formula:
Cauchy’s Integral Formula for Higher Derivatives:
Zeros of Analytic Function:
Singularities:
Problems on Singularities:
Important Definitions:
Residues:
Cauchy’s Residue Theorem:
DIFFERENTIAL EQUATIONS
Ordinary Differential Equation:
Order & Degree:
Formation of DE:
Equation of I-Order & I-Degree:
(i) Variable Separable Method:
(ii) Homogeneous Method:
(iii) Linear Differential Equation:
(iv) Bernoulli’s Equation:
Linear DE with Constant Co-efficient:
(i) Type – I:
(ii) Type – II:
(iii) Type – III:
(iv) Type – IV:
(v) Type – V:
Homogeneous Equations:
(i) Euler’s Type:
(ii) Legendre’s Type:
Simultaneous LDE:
Method of Variation of Parameter:
Exact Differential Equation:
Equation of I-Order & Higher Degree:
(i) Solvable for P:
(ii) Solvable for y:
(iii) Solvable for x:
(iv) Clairaut’s Form:
(v) Extended Clairaut’s Form:
Total Differential Equation:
(i) Grouping Method:
(ii) Dividing Common term:
(iii) General Method:
Wronskian:
(i) L.I & L.D:
(ii) Form DE:
Types of Points:
Frobenius Method:
Legendre Polynomial:
Bessel’s Polynomial:
Hermite Polynomial:
Partial Differential Equation:
Formation of PDE:
(i) Elimination of Arbitrary Constants:
(ii) Elimination of Arbitrary Functions:
PDE in Ordinary Cases:
I – Order Non-linear PDE:
(i) Type – I:
(ii) Type – II:
(iii) Type – III:
(iv) Type – IV:
Lagrange’s Linear Equation:
(i) Grouping Method:
(ii) Multiplier Method:
Second & Higher Order PDE:
(i) Homogeneous Type:
(ii) Non-Homogeneous Type:
Classification of Second order PDE:
Charpit’s Method:
OPERATION RESEARCH
Linear Programming Problem:
Graphical Method:
Simplex Method:
Artificial Variable Technique:
Duality:
Primal – Dual Problems:
Integer Programming:
Non-Linear Programming Problem:
Queueing Theory:
Queueing Models:
Problems on Queueing Models:
Inventory Control:
Network Analysis:
Full Chapter Revision:
STATISTICS
Arithmetic Mean:
Median:
Mode:
Geometric & Harmonic Mean:
Measures of Dispersion:
Range, Q.D, M.D, S.D:
Moments & Cumulants:
Skewness & Kurtosis:
Correlation & Rank Correlation:
Partial & Multiple Correlation:
Regression:
PROBABILITY THEORY
Probability:
Problems on Probability:
Probability Function:
Problems on Probability Function:
Joint Probability Function & Problems:
Chebychev’s Inequality:
Problems on Chebychev’s Inequality:
Discrete Distributions:
Binomial Distribution:
Problems on Binomial Distribution:
Poisson Distribution:
Problems on Poisson Distribution:
Continuous Distribution:
Uniform Distribution:
Problems on Uniform Distribution:
Exponential Distribution:
Normal Distribution:
Problems on Normal Distribution:
Gamma Distribution:
Beta Distribution:
Cauchy Distribution:
Cauchy Distribution:
Student – t – Distribution:
F – Distribution:
Samplings:
Small Samples:
Large Samples:
ANOVA:
DISTRIBUTIONS PROBLEMS:
Problems on Binomial Distribution:
Problems on Binomial Distribution:
Problems on Poisson Distribution:
Problems on Poisson Distribution:
Problems on Uniform Distribution:
Problems on Exponential Distribution:
Problems on Normal Distribution:
Problems on Samplings:
Problems on Chi-square Test:
Problems on t – test: