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# Mathematics (CH_30)

### Syllabus

Discriminant Analysis and Classification (Ch-30).
Chebyshev inequality, Borel-Cantelli Lemmas and related issues (Ch-30).
Back To Linear Systems Part 1 (Ch-30).
Local Analysis of Normality and the Zooming Process - Motivation for Zalcman\'s (Ch-30).
Convex Optimization (Ch-30).
Min-cost-flow Sensitivity analysis Shortest path problem sensitivity analysis.(Ch-30).
Tests of Convergence.
Any Variety is a smooth manifold with or without Non-smooth boundary.
Finding Estimators - I.
Solution of Nonlinear algebraic Equations - Part 8.
Power series.
Any variety is a smooth hypersurface on an open dense subset.
Linear transformations - part 3.
Existence using fixed point theorem.
Finding Estimators - II.
Riemann Integral.
Introduction to PDE.
Why Local rings provide calculus without limits for Algaebraic geometric pun intended?.
Basis Part 3.
Picard's existence and uniqueness theorem.
Basic concepts of point Estimations - I.
Special continuous distributions - V.
Solution of non-linear algebraic equations - part 6.
Infinite series II.
How local rings detect smoothness or non-singularity in algaebraic geometry.
Special continuous distributions - III.
solution of non-linear algebraic equations - part 4.
Curve sketching.
Local Ring isomorphism,Equals Function Field Isomorphism.
Introduction and Motivation.
Special continuous distributions - IV.
Linear Independence and subspaces part 2.
Second order linear equations Continued I.
Proofs in Indian Mathematics - Part 2.
Solution of Non-linear algebraic equations - part I.
Mean Value Theorems.
Linear independence and subspaces part 3.
Second order linear equations Continued II.
Solution of Nonlinear Algebraic equations - part 2.
Maxima-Minima.
The Importance of Local rings - A Rational functional in Every local ring is globally regular.
Linear independence and subspaces part 4.
Well-posedness and examples of IVP.
Mathematics in Modern India 1.
Special continuous distributions - II.
Taylor's theorem.
Geometric meaning of Isomorphism of Local Rings - Local rings are almost global.
Basis Part 1.
Gronwall's Lemma.
Linear Transformations - part 1.
Picard's existence and uniqueness continued.
Basic concepts of point Estimations - II.
Normal distribution.
Solution of Nonlinear algaebraic Equations - part 7 (Contd.). Polynomial equations.
Solution of non-linear algebraic equations - part 5.
Properties of continuous function.
Proofs in Indian Mathematics - 3.
Solution of Non-linear algebraic equations - part 3.
First order linear equations.
Trigonometry and Spherical trigonometry 2.
Fields of Rational Functions or Function fields of Affine and Projective varieties.
vector spaces part -2.
Trigonometry and spherical trigonometry 3.
Linear Independence and subspaces part 1.
Second order linear equations.
Proofs in Indian Mathematics 1.
The D-uple embedding and the non-intrinsic nature of the homogeneous coordinate ring.
Introduction to multilinear maps.
Signature of a permutation.
Computational rules for determinants.
Introduction to determinants.
Penalty and barrier method.
multi - attribute decision making.
Multi - objective decision making.
Continuation of solutions.
Series solution.
Linear transformations - part 4.
General System and Diagonalizability.
Linear transformations - part 5.
The Importance of Local rings - A morphism is an isomorphism if it is a homeomorphis.
constrained optimization.
Graphical solution of LPP-II.
Problems on Big-M method.
Graphical solution of LPP-I.
Selecting the best regression model(Contd.).
Solution of LPP : Simplex method.
Constrained geometric programming problem.
simplex method.
Multicollinearity(Contd.).
Transformation and weighting to correct model inadequacies (Contd.).
Ito formula and its variants.
Introduction to Big-M method.
Direct sums of vector spaces.
Selecting the best regression model.
Convergence of sequence of operators and functionals.
Cluster Analysis.
Hotelling T2 distribution and its applications..
Random sampling from multivariate normal distribution and Wishart distribution III.
Meromorphic Functions on the Extended Complex Plane are Precisely Quotients of Polynomials.
S30 0347.
Multivariate normal distribution II.
sets and strings.
Convex Optimization.
algorithm of Big -M method.
Selecting the best regression model(Contd.).
Optimization.
Tutorial - III.
Introduction to geometric programming.
Numerical optimization : Region elimination techniques.
Lp - space.
Introduction to optimization.
Renewal function and renewal equation.
Assumptions & Mathematical modeling of LPP.
Geometry of LPP.
Multi objective decision making.
problems on sensitivity analysis.
five results about pl.
Non markovian queues.
unique parsing.
Degeneracy in LPP.
Generalized renewal processes and renewal limit theorems.
SAT and 3SAT.
Polynomial Interpolation 3.
Functions of Complex Variables Part - I.
Cluster Analysis.
Analytic Functions, C-R Equations.
First Order Logic (1).
Lagrange Interpolation Polynomial, Error in Interpolation -1.
Functions of Complex Variables Part - 2.
Types of Sets with Examples,Metric Space.
Integration - 3 : Newton and Leibnitz style.
Cluster Analysis (Contd.).
Harmonic Functions.
First Order Logic (2).
Self adjoint, Unitary and Normal operators.
Lagrange Interpolation Polynomial, Error in Interpolation -1 Part 2.
Total Orthonormal Sets and Sequences.
Divide Difference Interpolation Polynomial.
Complex Numbers and Their Geometrical Representation.
Weiersstrass Theorem, Heine Borel Theorem,Connected set.
Fundamental Theorem of Calculus (in Riemann Style).
Correspondence Analysis.
Cauchy Integral Formula.
Sample Space ,Events.
Partially Ordered Set and Zorns Lemma.
Properties of Divided difference, Introduction to Inverse Interpolation.
Solution of ODE of First Order and First Degree.
Tutorial II.
The Kurzweil - henstock Integral (K-H Integral).
Correspondence Analysis (Contd.).
Power and Taylor Series of Complex Numbers.
Probability, Conditional probability.
Hahn Banach Theorem for Real Vector Spaces.
Properties of Divided difference, Introduction to Inverse Interpolation Part 2.
Concept of limit of a sequence.
Calculating Indefinite Integrals.
Convex sets and Functions.
Power and Taylor Series of Complex Numbers (Contd.).
Independent Events, Bayes Theorem.
Hahn Banach Theorem for Complex V.S. & Normed Spaces.
Inverse Interpolation, Remarks on Polynomial Interpolation.
Approximate Solution of An Initial Value.
Some Important limits, Ratio tests for sequences of Real Numbers.
Improper Integral - I.
Properties of Convex functions - I.
Taylor's , Laurent Series of f(z) and Singularities.
Information and mutual information.
Baires Category & Uniform Boundedness Theorems.
Numerical Differentiation - 1 Taylor Series Method.
Series Solution of Homogeneous Linear II.
Cauchy theorems on limit of sequences with examples.
Improper Integral -II.
Properties of Convex functions - II.
Classification of Singularities, Residue and Residue Theorem.
Basic definition.
Open Mapping Theorem.
Numerical Differentiation - 2 Method of Undetermined Coefficients.
Series Solution of Homogeneous Linear II (contd.).
Fundamental Theorems on Limits,Bolzano - Weiersstrass Theorem.
Application of Definite Integral - I.
Properties of Convex functions - III.
Laplace Transform and its Existence.
Isomorphism and sub graphs.
Closed Graph Theorem.
Numerical Differentiation -2 Polynomial Interpolation Method.
Bessel Functions and Their Properties.
Theorems on Convergent and Divergent sequences.
Application of Definite Integral - II.
Convex Programming Problems.
Properties of Laplace Transform.
Walks,paths and circuits, operations on graphs.
Numerical Differentiation -3 Operator Method Numerical Integration - 1.
Bessel Functions and Their Properties (Continued…).
Cauchy sequence and its properties.
Application of Definite Integral - III.
KKT Optimality conditions.
Evaluation of Laplace and Inverse Laplace Transform.
Euler graphs, Hamiltonian circuits.
Strong and Weak Convergence.
Numerical Integration 2 Error in Trapezoidal Rule Simpsons Rule.
Laplace Transformation.
Infinite series of real numbers.
Application of Definite Integral - III (Continued)...
Examples of Programming (CH_30).
Bivariate and Three dimensional plots (CH_30).
Statistical Functions - Boxplots, Skewness and Kurtosis (CH_30).
Parametric methods - VII (CH_30).
Data Handling - Importing Data Files from Other software (CH_30).
Statistical Functions : Frequency and Partition values (CH_30).
Statistical Functions : Graphics and Plots (CH_30).
Statistical Functions - Central Tendency and Variation (CH_30).
Quadratic Programming Problems - I.
S30 2072.
Shortest path problem.
S30 2074.
Numerical Integration 3 Error in Simpsons Rule Composite in Trapezoidal Rule, Error.
Laplace Transformation Continued….
Comparision tests for series, Absolutely convergent and Conditional Convergent series.
Numerical Integration - I (Trapezoidal Rule).
Quadratic Programming Problems - II.
Applications of Laplace Transform to PDEs.
Planar graphs.
LP - Space.
Numerical Integration 4 Composite Simpsons Rule, Error Method of Undetermined Coefficients.
Applications of Laplace Transformation.
Tests for absolutely convergent series.
Separable Programming - I.
Basic definitions.
LP - space (contd.).
Numerical Integration 5 Gaussian Quadrature (Two point Method).
Applications of Laplace Transformation (Continued).
Raabe's test, limit of functions, Cluster point.
Sequences.
Separable Programming - II.
Fourier Series (Contd.).
Properties of relations.
Introduction to Linear differential equations.
Numerical Integrature - 5 Gaussian Quadrature (Three Point Method) Adaptive Quadrature.
One Dimensional Wave Equation.
Some results on limit of functions.
Sequence (Continued).
Geometric programming I.
Fourier Integral Representation of a Function.
Graph of Relations.
Linear dependance, independence and Wronskian of functions.
Numerical Solution of Ordinary Differential Equation (ODE) - 1.
One Dimensional Heat Equation.
Limit Theorems for Functions.
Infinite Series.
Geometric programming II.
Introduction to Fourier Transform.
Matrix of a Relation.
Solution of second order homogenous linear differential equations with constant coefficients - I.
Numerical Solution of ODE - 2 , Stability, Single Step Methods - 1 Taylor Series Method.
Introduction to Differential Equation.
Extension of limit concept (One sided limits).
Infinite series (Continued).
Geometric programming III.
Applications of Fourier Transform to PDEs.
Closure of a Relation (1).
Solution of second order homogenous linear differential equations with constant coefficients - II.
Numerical Solution of ODE - 3 Examples of Taylor Series Method Euler's method.
First Order Differential Equations and Their Geometric Interpretation.
Continuity of Functions.
Taylors Theorem , other issues and end of the course - I.
Dynamic programming I.
Laws of probability I.
Closure of a Relation (2).
Method of Undetermined Coefficients.
Numerical solution of ODE-4 Runge-Kutta Methods.
Differential Equations of First Order Higher Degree.
Properties of Continuous functions.
Taylors Theorem , other issues and end of the course - II.
Dynamic programming II.
Laws of probability II.
Methods for finding particular integral for second-order.
Numerical solution of ODE-5 Example for RK-Method of Order 2 Modified Euler's Method.
Linear Differential Equation of Second Order - Part 1.
Boundedness theorem, Max-Min Theorem and Bolzano's theorem.
Introduction to Error analysis and linear systems.
Dynamic programming approach to find shortest path in any network (Dynamic Programming III).
Problems in probability.
Partial Ordered Relation.
Methods for finding particular integral for second-order.
Numerical solution of Ordinary Differential Equations - 6.
Linear Differential Equation of Second Order - Part 2.
Uniform continuity and Absolute continuity.
Gaussian elimination with partial pivoting.
Dynamic programming IV.
Random variables.
Partially ordered sets.
Methods for finding Particular integral for second-order linear.
Numerical solution of Ordinary Differential Equations -7 (Predictor - Corrector Methods(Milne)).
Euler - Cauchy Theorem.
Types of Discontinuities, Continuity and Compactness.
LU Decomposition.
Search Techniques - I.
Special Discrete Distributions.
Lattices.
Euler-Cauchy Equations.
Numerical solution of Differential Equations - 8.
Higher Order Linear Differential Equations.
Continuity and Compactness (Contd.) Connectedness.
Jacobi and Gauss Seidel Methods.
Search Techniques - II.
Special Continuous distributions.
Boolean algebra.
Method of Reduction for second-order linear differential equations.
Fourier Series.
Numerical Integration - II (Simpson's Rule).
Matrix Algebra Part - 2.
Permutations and Combinations (Continued).
Completion of Metric Spaces + Tutorial.
Non parametric Methods - III.
Queuing Models M/M/I Birth and Death Process Little's Formulae.
Tutorial.
Introduction to Numbers.
Standardized Regression Coefficients and Testing of Hypothesis.
Strong law of large numbers, Joint mgf.
Matrix Algebra Part - 1.
Multivariate Analysis - XI.
Hypothesis Testing.
Permutations and Combinations.
Applications of N-P-Lemma - II.
Reducible markov chains.
Simple Linear Regression Analysis.
Examples of Complete and Incomplete Metric Spaces.
Analysis of Variance.
Cauchy's Integral Formula.
Chi-Square Test for Goodness Fit - I.
Software Implementation in Simple Linear Regression Model using MINITAB.
Trees and Graphs.
Non parametric methods - II.
Evaluation of Real Improper Integrals - 2.
Inter-arrival times, Properties of Poisson processes.
Functions.
Multivariate Analysis-III.
Multivariate Analysis of Variance (Contd.).
Holder inequality and Minkowski Inequality.
Testing for Independence in rxc Contingency Table - II.
Applications of central limit theorem.
Estimation of Model Parameters in Multiple Linear Regression Model (Continued).
Estimation Part -II.
Evaluation of Real Integrals-Revision.
Applications of N-P-Lemma - I.
Multivariate Analysis - X.
Regression Model - A Statistical Tool.
Pigeonhole principle.
Cauchy's Integral Theorem.
Random walk, periodic and null states.
Multivariate Inferential statistics(Contd.).
Trees.
Convergence, Cauchy Sequence, Completeness.
Testing Equality of Proportions.
Testing of Hypothesis and Confidence Interval Estimation in Simple Linear Regression Model.
Non parametric methods - I.
Evaluation of Real Improper Integrals -1.
Multivariate Analysis-II.
Poisson processes.
Equivalence Relations and partitions.
Central limit theorem.
Multivariate Analysis of Variance.
Testing for Independence in rxc Contingency Table - I.
Estimation Part-I.
Metric Spaces with Examples.
Estimation of Model Parameters in Multiple Linear Regression Model.
Evaluation of Real Improper Integrals - 4.
Neyman- Pearson Fundamental Lemma.
Basic Fundamental concepts of modelling.
Multivariate Analysis - IX.
Contour Integration.
First passage and first return prob. Classification of states.
Multivariate Inferential statistics.
Graphs (Continued.).
Examples.
Testing of Hypothesis and Confidence Interval Estimation in Simple Linear Regression Model.
Evaluation of Real Integrals.
Functions (Continued).
Multivariate Analysis-I.
Order and Relations and Equivalence Relations.
Examples of More Programming.
Separable Metrics Spaces with Examples.
Convergence and limit theorems.
Sampling Distribution.
Multivariate Analysis - VIII.
Multivariate Analysis - XII.
Two Types of Errors.
State prob.First passage and First return prob.
Confidence Intervals (Continued).
Banach Spaces and Schauder Basic.
Multivariate Normal Distribution (Contd.).
Complex Integration.
Paired t-Test.
Maximum Likelihood of Parameters in Simple Linear Regression Model.
Graphs.
Non parametric Methods - VI.
Residue Theorem.
M/M/I/K & M/M/S/K Models.
Order Relations.
Multiple Regression.
Functions.
Diagnostics in Multiple Linear Regression Model (continued).
Inequalities and bounds.
Determinants Part - 2.
Multivariate Analysis - VII.
Univariate descriptive statistics.
Basic Definitions.
Generating Functions (Continued).
Transition and state probabilities.
Confidence Intervals.
Multivariate Normal Distribution.
Normed Spaces with Examples.
Testing for Normal Variance.
Large Sample Test for Variance and Two Sample Problem.
Estimation of Parameters in Simple Linear Regression Model(continued):Some nice properties.
Estimation of Parameters in Simple Linear Regression Model(continued).
Non parametric Methods - V.
Zeros,Singularities and Poles.
Residue Integration Method.
M/M/S M/M/I/K Model.
Closure of Relations.
Closure Properties of Relations (Contd..).
MANOVA Case study.
Examples of Irrational Numbers.
Multivariate Analysis -VI.
Diagnostics in Multiple Linear Regression Model.
Multivariate Analysis-V.
Stochastic processes:Markov process.
Determinants Part - 1.
Convolutions.
Multivariate Descriptive Statistics (contd.).
Generating Functions.
Introduction to Multivariate statistical modeling Part - I.
Time Reversible Markov Chains.
Testing for Normal Mean.
Estimation of Parameters in Simple Linear Regression Model.
Vector Spaces with Examples.
Analysis of Variance (Contd.).
Chi-Square Test for Goodness Fit - II.
Application of Cauchy Integral Formula.
Multiple Linear Regression Model.
Non parametric Methods - IV.
Evaluation of Real Improper Integrals - 3.
Special properties of Relations.
Analysis of L,Lq,W and Wq, M/M/S Model.
Functions (Continued).
Tutorial(Contd.).
Countability and Uncountability.
Multivariate Analysis - IV.
Various Concepts in a Metric Space.
Testing of Hypothesis (continued) and Goodness of Fit of the model.
Non parametric Methods - XI.
Vector Spaces, Subspaces, Linearly Dependent / Independent of Vectors.
MLR Case Study.
Maximum Value Theorem.
Within sample forecasting.
Linear Algebra Part - 4.
Algebras (Continued).
Bounded Linear Operators in a Normed Space.
Non parametric Methods - X.
Review Groups, Fields and Matrices.
MLR Model Diagnostics.
Intermediate Value Theorem.
Forecasting in Multiple linear Regression Model.
Linear Algebra Part -3.
Algebras.
Linear Operators - Definitions and Examples.
Non parametric Methods - IX.
Reliability of systems.
MLR Test of Assumptions.
Continous Functions.
Software Implementation in Multiple Linear Regression Model using MINITAB (continued).
Linear Algebra Part - 2.
Recurrence Relations (Continued).
Compactness of Metric/Normed Spaces.
Non parametric Methods - VIII.
Exponential Failure law, Weibull Law.
MLR Model Adequacy Tests.
Limits of Functions - II.
Software Implementation in Multiple Linear Regression Model using MINITAB.
Linear Algebra Part - 1.
Recurrence Relations (Continued).
Finite Dimensional Normed Spaces and Subspaces.
Non parametric Methods - VII.
Application to Reliability theory failure law.
MLR Sampling Distribution of Regression Coefficients.
Limits of Functions - I.
Diagnostics in Multiple Linear Regression Model (continued).
Solution of System Equation.
Recurrence Relations.
Linear Transformation Part - 1.
Finite State Automaton.
Concept of Algebraic Dual and Reflexive Space.
Non Parametric Methods - XII.
Basis, Dimension, Rank and Matrix Inverse.
Multivariate Linear Regression.
Supremum and Infimum.
Outside Sample Forecasting.
Inner product.
Algebras (Continued).
Bounded Linear Functionals in a Normed Space.
Tutorial - II.
The principle of Inclusion and Exclusion.
Jordan Canonical Form,Cayley Hamilton Theorem.
Principal component analysis - Model Adeaquacy & Interpretation.
Rolles Theorem and Lagrange Mean Value Theorem (MVT).
Representation of Functionals on a Hilbert Spaces.
Methods of Proof of an Implication.
Continuum and Exercises.
Concept of Domain, Limit, Continuity and Differentiability.
Eigenvalues & Eigenvectors Part - 2.
Introduction, Motivation.
Factor Analysis - Model Adequacy, Rotation , Factor Scores & Case study.
Tutorial - I.
Integration - 1 : In the style of Newton and Leibnitz.
Mathematical Induction.
Equivalence of Dedekind and Cantor's Theory.
Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices.
Solution of System of Linear Equation.
Part 2 Polynomial Interpolation II.
Principal Component Analysis.
Projection theorem, Orthonormal Sets and Sequences.
Maxima And Minima.
Logical Inferences.
Irrational numbers, Dedekind's Theorem.
Spectrum of special matrices,positive/negative definite matrices.
Eigenvalues & Eigenvectors Part - 1.
Factor Analysis Estimation & Model Adequacy testing.
Lattices.
Dual Spaces with Examples.
Introduction to the theory of sets.
System of Linear Equations, Eigen values and Eigen vectors.
Multivariate Linear Regression Model Adequacy tests.
Rules of Differentiation.
Rational Numbers and Rational Cuts.
Linear Transformation Part - 2.
Finite State Automaton (Continued).
Dual Basis & Algebraic Reflexive Space.
Non Parametric Methods - XIII.
Linear Transformation, Isomorphism and Matrix Representation.
Multivariate Linear Regression Estimation.
Derivatives - Derivative of a Function.
Software Implementation of Forecasting using MINITAB.
Optimization Problems.
Cantor's Theory of Irrational Numbers (Contd.).
Diagonalization Part - 2.
Part 1 Polynomial Interpolation II.
Fundamentals of Logic.
Factor Analysis.
Newton's Method for Solving Equations.
Cantor's Theory of Irrational Numbers.
Diagonalization Part -1.
Mathematical preliminaries, Polynomial Interpolation I Part 2.
Inner product & Hilbert space.
Application of the principle of Inclusion and Exclusion.
Inner Product Spaces, Cauchy - Schwarz Inequality.
Regression Modeling Using SPSS.
Monotonic Functions and Inverse Functions.
Continuum and Exercises (Contind..).
Mathematical preliminaries, Polynomial Interpolation I Part 1.
Strings -Display and Formating, Paste function.
Function of Random variables,moment generating function.
Numerical Differentiation and Integration - Part 3.
Examples on MLE - I.
Likelihood Ratio Tests - I.
Integration - 2.
Integration - 1.
Strings - Display and Formatting , Print and Format with Concatenate.
Continuous random variables and their distributions.
Numerical Differentiation and Integration - Part 2.
Examples on MME, MLE.
Unbiased Tests for Normal Populations (Continued…).
Mean - Value Theorem and Taylor's Expansion - 2.
Mean - Value Theorem and Taylor's Expansion - 1.
Strings - Display and Formatting , Print and Format Functions.
Continuous random variables and their distributions.
Numerical Differentiation and Integration - Part 1.
LSE, MME.
Unbiased Tests for Normal Populations.
Derivative -2.
Data Management - Factors (continued).
Continuous random variables and their distributions.
Interpolation and Approximation - Part 9.
UMP Unbiased Tests : Applications.
Derivative - 1.
Limits and Continuity - 3.
Data Management - (Factors).
Discreet random variables and their distributions.
Interpolation and Approximation - Part 8.
Introduction to Estimation.
UMP Unbiased Tests.
Limits and continuity - 2.
Limits and continuity - 1.
Vector Indexing (continued).
Discreet random variables and their distributions.
Interpolation and Approximation - Part 7.
Descriptive Statistics - IV.
UMP Unbiased Tests.
Sequence-II.
Sequence - I.
Epilogue.
Data Management - Vector Indexing.
Discrete random variables and their distributions.
Interpolation and Approximation - Part 6.
Descriptive Statistics - III.
UMP Tests (Contd.).
Functions - I.
Numbers.
Back to Linear Systems Part 2.
Data Management - Lists (continued).
Examples of Application Oriented Problems (Contd.).
Interpolation and Approximation - Part 5.
Descriptive Statistics - II.
UMP Tests.
General Second Order Equations - Continued.
Back to Linear Systems Part 1.
Data Management - Lists.
Examples of Application Oriented Problems.
Interpolation and Approximation - Part 4.
Descriptive Statistics - I.
Applications of NP Lemma.
General Second Order Equations.
Singular value decomposition - Part 2.
Data Management - Sorting and Ordering.
Example of Generalized 3 Dimensional Problem.
Interpolation and Approximation - Part 3.
F-Distribution.
Neyman Pearson fundamental Lemma.
Linear Second Order Equations.
Singular value decomposition - Part 1.
Data Management Repeats.
Spherical Polar Coordinate System (Contd.).
Interpolation and Approximation - Part 2.
Chi - Square Distribution (Contd.)., t-Distribution.
Testing of Hypothesis : Basic concepts.
Periodic orbits and Poincare Bendixon Theory Continued.
Hermitian and Symmetric Matrices Part 4.
Data Management Sequences.
Spherical Polar Coordinate System.
Gauss Divergence Theorem.
Interpolation and Approximation - Part I.
Chi - Square Distribution.
Bayes and Minimax Estimation - III.
Periodic orbits and Poincare Bendixon Theory.
Hermitian and Symmetric Matrices Part 3.
Data Management Sequences.
Cylindrical Coordinate System -3 Dimensional Problem.
Stokes Theorem.
Hermitian and Symmetric matrices Part 1.
Basic Calculations : Conditional executions and loops.
Solution of Hyperbolic PDE.
Surface Integrals.
Solution of a system of Linear Algebraic Equations - Part - 12.
Transformation of Random Variables.
Invariance - II.
Second Order Linear Equations Continued - III.
Diagonalization Part 4.
Basic Calculations : Truth table and conditional executions.
Solution of Elliptical PDE.
Multiple Integrals.
Solution of a system of Linear Algebraic Equations - Part - 11.
Additive Properties of Distributions - II.
Invariance-I.
Stability Equilibrium points continued II.
Diagonalization Part 3.
Basic Calculations : Logical Operators.
Solution of 4 Dimensional Parabolic Problem (Contd.).
Method of Lagrange Multipliers.
Solution of a system of Linear Algebraic Equations - Part - 10.
Additive Properties of Distributions - I.
UMVU Estimation,Ancillarity.
Stability Equilibrium points continued I.
Diaggonalization Part 2.
Basic calculations : Missing data and logical operators.
Solution of 4 Dimensional Parabolic Problem.
Maxima - Minima.
Solution of a system of Linear Algebraic Equations - Part - 9.
Bivariate Normal Distribution - II.
Minimal Sufficiency,Completeness.
Stability Equilibrium points.
Diagonalization Part 1.
Basic calculations : Matrix Operations.
Solution of 3 Dimensional Parabolic Problem.
Mean Value Theorems.
Solution of a system of Linear Algebraic Equations - Part - 8.
Bivariate Normal Distribution - I.
Sufficiency & Information.
Basic Definitions and Examples.
Inner Product and Orthogonality Part 6.
Separation of variables : Rectangular Coordinate systems.
Derivatives.
Solution of a system of Linear Algebraic Equations - Part - 7.
Linearity property of Correlation and Examples.
Sufficiency.
General Systems Continued and Non-homogeneous systems.
Inner product and orthogonality Part 5.
Functions and Matrices.
Properties of Adjoint Operator.
Differentiation.
Solution of a system of Linear Algebraic Equations - Part - 6.
Independence , product moments.
Lower bounds of variance - IV.
General systems.
Inner Product and Orthogonality Part 4.
R as calculator, Built in functions and Assignment.
Generalized sturm - Louiville problem.
Functions of several variables.
Solution of a system of Linear Algebraic Equations - Part - 5.
Joint Distributions - II.
Lower bounds for variance - III.
2 by 2 Systems and Phase Plane Analysis Continued.
Inner Product and Orthogonality Part 3.
Basics of calculations , Basics and R as a calculator.
Line Integrals.
Solution of a system of Linear Algebraic Equations - Part - 4.
Joint Distributions - I.
Lower bounds for variance - II.
2 by 2 Systems Phase Plane Analysis.
Inner Product and Orthogonality Part 2.
Introduction command line, Data Editor and R studio.
Standard Eigen value problem and special ODEs.
Length of a curve.
Solution of a system of Linear Algebraic Equations - Part - 3.
Function of a random variable - II.
Lower bounds for Variance - I.
General System and Diagonalizability.
Inner product and Orthogonality part 1.
Introduction Help demo examples packages libraries.
Principle of Linear Superposition.
Applications of Rieman integral.
Solution of a system of Linear Algebraic Equations - Part - 2.
Function of a random variable - I.
Properties of MLEs.
Series solution.
Linear transformations - part 5.
Why R and installation procedure.
Classification of PDE.
Riemann Integrable Functions.
Solution of a system of Linear Algebraic Equations - Part - 1.
Problems on special distributions - II.
Finding Estimators - III.
Continuation of solutions.
Linear transformations - part 4.
Solution of Nonlinear algebraic equations - part 09.
Problems on special distributions - I.
Problems on normal distribution.
Linear transformations - part 2.
Basic Lemma and Uniqueness Theorem.
Infinite series I.
Mathematics in Modern India 2.
Differentiable Function.

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Ch 30 NIOS: Gyanamrit

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