UNIT – 1 – ALGEBRA
01 – STUDY PLAN | 10 DAYS | FULL OUTLINE
02 – Group:
03 – Subgroup, Product Group:
04 – Cyclic group:
05 – Normal Subgroup:
06 – Automorphism:
07 – Permutations:
08 – Problems on Permutations:
09 – Rings:
10 – Field:
11- Types of Ideals:
12 – Vector Space:
13 – Dual Space:
14 – Syllow’s Theorem:
15 – Euclidean Ring:
16 – Commutator Subgroup:
17 – Types of Polynomial:
18 – Quotient Space:
19 – Eigen Values & Eigen Vectors:
20 – Extension Field:
21 – Splitting Field:
22 – Fixed Field:
23 – Matrices:
24 – Transformations:
25 – Projection:
26 – Canonical Form:
27 – Full Chapter Revision:
UNIT – 2 – REAL ANALYSIS
01 – STUDY PLAN | 10 DAYS | FULL OUTLINE
02 – Basic Definitions:
03 – Countable and Uncountable Set:
04 – Bounded and Unbounded Set:
05 – Metric Space:
06 – Open Sets:
07 – Closed Sets:
08 – Closure:
09 – Complete Metric Space:
10 – Connectedness:
11 – Compactness:
12 – Totally Bounded:
13 – Continuous Functions:
14 – Derivative Functions:
14 – Taylor & Maclurin Series:
16 – Sequence:
17 – Cauchy Sequence:
18 – Theorems on Limits:
19 – Series:
20 – Test in Series:
21 – Alternating Series:
22 – Measure Zero:
23 – Riemann Integral:
24 – Riemann Stieltjes Integral:
25 – Measurable Set:
26 – Measurable Function:
27 – Problems on Limits: Part – 1
28 – Problems on Limits: Part – 2
29 – Problems on Continuity: Part – 1
30 – Problems on Continuity: Part – 2
31 – Problems on Comparison Test:
32 – Problems on Ratio Test: Part – 1
33 – Problems on Ratio Test: Part – 2
34 – Full Chapter Revision:
UNIT – 3 – FOURIER SERIES & FOURIER INTEGRALS
01 – STUDY PLAN | 5 DAYS | FULL OUTLINE
02 – Basic Definitions:
03 – Inner Product:
04 – Naming Theorem 1:
05 – Naming Theorem 2:
06 – Naming Theorem 3:
07 – Fourier Transforms:
08 – Problems on Fourier Series:
09 – Problems on Fourier Transforms:
10 – Problems on Fourier Sine Transform:
11 – Problems on Fourier Cosine Transform:
12 – Full Chapter Revision:
UNIT – 4 – DIFFERENTIAL GEOMETRY
01 – STUDY PLAN | 10 DAYS | FULL OUTLINE
02 – Curves in Spaces:
03 – Fundamental Planes:
04 – Curvature and Torsion:
05 – Problems on Curvature and Torsion:
06 – Osculating Circle, Sphere:
07 – Involute & Evolute:
08 – Helices:
09 – Surfaces:
10 – First Fundamental Form:
11 – Second Fundamental Form:
12 – Curvature:
13 – Line of Curvature:
14 – Family of Curves:
15 – Family of Surfaces:
16 – Developable Surface:
17 – Asymptotic Lines:
18 – Isometric Lines:
19 – Geodesics:
20 – Geodesic Curvature:
21 – Torsion of a Geodesic:
22 – Full Chapter Revision:
UNIT – 5 – OPERATION RESEARCH
01 – STUDY PLAN | 10 DAYS | FULL OUTLINE
02 – Linear Programming Problem:
03 – Graphical Method:
04 – Simplex Method:
05 – Artificial Variable Technique:
06 – Duality:
07 – Primal – Dual Problems:
08 – Integer Programming:
09 – Method to find IBFS:
10 – Optimality | Assignment | Travelling Salesman Problem:
11 – Non-Linear Programming Problem:
12 – Game Theory:
13 – Queueing Theory:
14 – Queueing Models:
15 – Problems on Queueing Models:
16 – Inventory Control:
17 – Replacement Theory:
18 – Network Analysis:
19 – Full Chapter Revision:
UNIT – 6 – FUNCTIONAL ANALYSIS
01 – STUDY PLAN | 10 DAYS | FULL OUTLINE
02 – Basic Concepts:
03 – Normed Linear Space:
04 – Quotient Space:
05 – Linear Subspace:
06 – Dual Space:
07 – Natural Imbedding:
08 – Hilbert Space:
09 – Orthogonal:
10 – Orthonormal Set:
11 – Complete Orthonormal Set:
12 – Operators on Hilbert Space:
13 – Operators on Hilbert Space:
14 – Projections:
15 – Projections:
16 – Matrices:
17 – Spectral Resolution:
UNIT – 7 – COMPLEX ANALYSIS
01 – STUDY PLAN | 10 DAYS | FULL OUTLINE
02 – Basic Concepts:
03 – Limits:
04 – Continuous:
05 – Differentiability:
06 – Analytic Function:
07 – Problems on Analytic Functions:
08 – Harmonic Function:
09 – Problems on Harmonic Function:
10 – Sequence:
11 – Series:
12 – Uniform Converges:
13 – Problems:
14 – Conformal Mapping:
15 – Bilinear Transformation:
16 – Types of Bilinear Transformation:
17 – Mappings:
18 – Taylor Series:
19 – Maclaurin’s Series:
20 – Laurent’s Series:
21 – Cauchy’s Theorem:
22 – Cauchy’s Integral Formula:
23 – Cauchy’s Integral Formula for Higher Derivatives:
24 – Zeros of Analytic Function:
25 – Singularities:
26 – Problems on Singularities:
27 – Important Definitions:
28 – Residues:
29 – Cauchy’s Residue Theorem:
UNIT – 8 – DIFFERENTIAL EQUATIONS
01 – STUDY PLAN | 10 DAYS | FULL OUTLINE
Ordinary Differential Equation:
02 – Order & Degree:
03 – Formation of DE:
Equation of I-Order & I-Degree:
04 – (i) Variable Separable Method:
05 – (ii) Homogeneous Method:
06 – (iii) Linear Differential Equation:
07 – (iv) Bernoulli’s Equation:
Linear DE with Constant Co-efficient:
08 – (i) Type – I:
09 – (ii) Type – II:
10 – (iii) Type – III:
11 – (iv) Type – IV:
12 – (v) Type – V:
Homogeneous Equations:
13 – (i) Euler’s Type:
14 – (ii) Legendre’s Type:
15 – Simultaneous LDE:
16 – Method of Variation of Parameter:
17 – Exact Differential Equation:
Equation of I-Order & Higher Degree:
18 – (i) Solvable for P:
19 – (ii) Solvable for y:
20 – (iii) Solvable for x:
21 – (iv) Clairaut’s Form:
22 – (v) Extended Clairaut’s Form:
Total Differential Equation:
23 – (i) Grouping Method:
24 – (ii) Dividing Common term:
25 – (iii) General Method:
Wronskian:
26 – (i) L.I & L.D:
27 – (ii) Form DE:
28 – Types of Points:
29 – Frobenius Method:
30 – Legendre Polynomial:
31 – Bessel’s Polynomial:
32 – Hermite Polynomial:
Partial Differential Equation:
Formation of PDE:
33 – (i) Elimination of Arbitrary Constants:
34 – (ii) Elimination of Arbitrary Functions:
35 – PDE in Ordinary Cases:
I – Order Non-linear PDE:
36 – (i) Type – I:
37 – (ii) Type – II:
38 – (iii) Type – III:
39 – (iv) Type – IV:
Lagrange’s Linear Equation:
40 – (i) Grouping Method:
41 – (ii) Multiplier Method:
Second & Higher Order PDE:
42 – (i) Homogeneous Type:
43 – (ii) Non-Homogeneous Type:
44 – Classification of Second order PDE:
45 – Charpit’s Method:
UNIT – 9 – STATISTICS – I
01 – STUDY PLAN | 10 DAYS | FULL OUTLINE
Measures of Location:
02 – Arithmetic Mean:
03 – Median:
04 – Mode:
05 – Geometric & Harmonic Mean:
Measures of Dispersion:
06 – Range, Q.D, M.D, S.D:
07 – Moments & Cumulants:
08 – Skewness & Kurtosis:
09 – Correlation & Rank Correlation:
10 – Partial & Multiple Correlation:
11 – Regression:
12 – Probability:
13 – Problems on Probability:
14 – Probability Function:
15 – Problems on Probability Function:
16 – Joint Probability Function & Problems:
UNIT – 10 – STATISTICS – II
01 – STUDY PLAN | 10 DAYS | FULL OUTLINE
Discrete Distributions:
02 – Binomial Distribution:
03 – Problems on Binomial Distribution:
04 – Poisson Distribution:
05 – Problems on Poisson Distribution:
06 – Negative Binomial Distribution:
07 – Geometric, Hypergeometric & Multinomial Distribution:
Continuous Distribution:
08 – Uniform Distribution:
09 – Problems on Uniform Distribution:
10 – Exponential Distribution:
11 – Normal Distribution:
12 – Problems on Normal Distribution:
13 – Gamma Distribution:
14 – Beta Distribution:
15 – Cauchy Distribution:
16 – Cauchy Distribution:
17 – Student – t – Distribution:
18 – F – Distribution:
19 – Chebychev’s Inequality:
20 – Samplings:
21 – Small Samples:
22 – Large Samples:
23 – ANOVA:
PROBLEMS – STATISTICS – II
01 – Problems on Binomial Distribution:
02 – Problems on Binomial Distribution:
03 – Problems on Poisson Distribution:
04 – Problems on Poisson Distribution:
05 – Problems on Geometric Distribution:
06 – Problems on Negative Binomial Distribution:
07 – Problems on Uniform Distribution:
08 – Problems on Exponential Distribution:
09 – Problems on Normal Distribution:
10 – Problems on Chebychev’s Inequality:
11 – Problems on Samplings:
12 – Problems on Chi-square Test:
13 – Problems on t – test: