subjectId
Discipline Name
Subject Name
Coordinators
Type
Institute
Content
111101001
Mathematics
Algebra II
Prof. Jugal K. Verma
Web
IIT Bombay
Select
Lecture 1 : Introduction and Overview
Lecture 2 : Algebraic extensions I
Lecture 3 : Algebraic Extensions II
Problem Set 1 : Algebraic Extensions
Lecture 4 : Ruler and Compass Constructions I
Lecture 5 : Ruler and Compass Constructions II
Problem Set 2 : Ruler and Compass Constructions
Tutorial 1 : Algebraic Extensions and Ruler and Compass Constructions
Lecture 6 : Symmetric Polynomials I
Lecture 7 : Symmetric Polynomials II
Problem set 3 : Symmetric Polynomials
Lecture 8 : Algebraic Closure of a Field
Problem set 4 : Splitting Fields
Tutorial 2 : Symmetric Polynomials and Splitting Fields
Lecture 9 : Separable Extensions I
Lecture 10 : Separable Extensions II
Problem set 5 : Separable Extensions
Lecture 11 : Finite Fields I
Tutorial 3 : Separable Extensions and Finite Fields
Problem set 6 : Finite Fields
Lecture 12 : The Primitive Element Theorem
Problem set 7 : Primitive elements
Tutorial 4 : Finite Fields and Primitive Elements
Lecture 13 : Normal Extensions
Lecture 14 : Galois group of a Galois Extension I
Lecture 15 : Galois group of a Galois Extension II
Problem set 8 : Fundamental Theorem of Galois Theory
Tutorial 5 : Fundamental Theorem of Galois Theory
Lecture 16 : Applications and Illustrations of the FTGT
Lecture 17 : Cyclotomic Extensions I
Lecture 18 : Cyclotomic Extensions II
Problem Set 9 : Cyclotomic Extensions
Lecture 19 : Abelian and Cyclic Extensions
Lecture 20 : Cyclic Extensions and Solvable Groups
Tutorial 6 : Cyclotomic Extensions
Lecture 21 : Galois Groups of Composite Extensions
Lecture 22 : Solvability by Radicals
Problem Set 10 : Solvability by Radicals
Lecture 23 : Solutions of Cubic and Quartic Equations
Lecture 24 : Galois Groups of Quartic Polynomials
Problem Set 11 : Galois groups of Quartic Polynomials.
Tutorial 7 : Galois Groups of Quartics and Solvability by Radicals
Lecture 25 : Norm, Trace and Hilbert's Theorem 90
Problem Set 12 : Cyclic Extensions
Lecture 26 : Polynomials with Galois Group Sn:
111101002
Mathematics
Algebraic Topology
Prof. G.K. Srinivasan
Web
IIT Bombay
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Lecture 1: Introduction
Lecture 2 : Preliminaries from general topology
Lecture 3 : More Preliminaries from general topology
Lecture 4 : Further preliminaries from general topology
Lecture 5 : Topological groups
Lecture 6 : Test - 1
Lecture 7 : Paths, homotopies and the fundamental group
Lecture 8 : Categories and Functors
Lecture 9 : Functorial properties of the fundamental group
Lecture 10 : Brouwers theorem and its applications
Lecture 11 : Homotopies of maps. Deformation retracts
Lecture 12 & 13 : The fundamental group of the circle.
Lecture 14 : Test - II
Lecture 15 : Covering Projections
Lecture 16 : Lifting of paths and homotopies
Lecture 17 : Action of the fundamental group on the fibers
Lecture 18 : The lifting criterion
Lecture 19 : Deck transformations
Lecture 20 : Orbit Spaces
Lecture 21 : Test - III
Lecture 22 : Fundamental groups of certain orthogonal groups
Lecture 23 & 24 : Coproducts and push-outs
Lecture 25 : Adjunction Spaces
Lecture 26 : Seifert Van Kampen theorem
Lecture 27 : Test - IV
Lecture 28 : Introductory remarks on homology theory
Lecture 29 & 30 : The Singular chain complex and homology groups
Lecture 31 : The homology groups and their functoriality
Lecture 32 : The abelianization of the fundamental group
Lecture 33 : Homotopy invariance of homology
Lecture 34 : Small Simplicies
Lecture 35 : The Mayer Vietoris sequence and its applications
Lecture 36 : Maps of Spheres
Lecture 37 : Test - V
Lecture 38 : Relative homology
Lecture 39 : Excisim Theorem
Lecture 40 : Inductive limits
Lecture 41 : The Jordan-Brouwer separation theorem
111101003
Mathematics
Elementary Numerical Analysis
Prof. Rekha P. Kulkarni
Video
IIT Bombay
Select
L1- Introduction
L2-Polynomial Approximation
L3-Interpolating Polynomials
L4-Properties of Divided Difference
L5-Error in the Interpolating polynomial
L6-Cubic Hermite Interpolation
L7-Piecewise Polynomial Approximation
L8-Cubic Spline Interpolation
L9-Tutorial 1
L10-Numerical Integration: Basic Rules
L11-Composite Numerical Integration
L12-Gauss 2-point Rule: Construction
L13-Gauss 2-point Rule: Error
L14-Convergence of Gaussian Integration
L15-Tutorial 2
L16-Numerical Differentiation
L17-Gauss Elimination
L18-L U decomposition
L19-Cholesky decomposition
L20-Gauss Elimination with partial pivoting
L21-Vector and Matrix Norms
L22-Perturbed Linear Systems
L23-Ill-conditioned Linear System
L24-Tutorial 3
L25-Effect of Small Pivots
L26-Solution of Non-linear Equations
L27-Quadratic Convergence of Newton's Method
L28-Jacobi Method
L29-Gauss-Seidel Method
L30-Tutorial 4
L31-Initial Value Problem
L32-Multi-step Methods
L33-Predictor-Corrector Formulae
L34-Boundary Value Problems
L35-Eigenvalues and Eigenvectors
L36-Spectral Theorem
L37-Power Method
L38-Inverse Power Method
L39-Q R Decomposition
L40-Q R Method
111101004
Mathematics
Introduction to Probability Theory
Dr. K. Suresh Kumar
Web
IIT Bombay
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Chapter 1 : Introduction
Chapter 2 : Random Variables
Chapter 3 : Conditional Probability and Independence
Chapter 4 : Distributions
Chapter 5 : Random Vectors , Joined Distributions
Chapter 6 : Expectation and Conditional Expectation
Chapter 7 : Characteristic Functions
Chapter 8 : Limit Theorems
111101005
Mathematics
Measure and Integration
Prof. Inder K Rana
Video
IIT Bombay
Select
L1- Introduction ,Extended Real numbers
L2-Algebra and Sigma Algebra of a subset of a set
L3-Sigma Algebra generated by a class
L4-Monotone Class
L5-Set function
L6-The Length function and its properties
L7-Countably additive set functions on intervals
L8-Uniqueness Problem for Measure
L9-Extension of measure
L10-Outer measure and its properties
L11-Measurable sets
L12-Lebesgue measure and its properties
L13-Characterization of Lebesque measurable sets
L14-Measurable functions
L15-Properties of measurable functions
L16-Measurable functions on measure spaces
L17-Integral of non negative simple measurable functions
L18-Properties of non negative simple measurable functions
L19-Monotone convergence theorem & Fatou's Lemma
L20-Properties of Integral functions & Dominated Convergence Theorem
L21-Dominated Convergence Theorem and applications
L22-Lebesgue Integral and its properties
L23-Denseness of continuous function
L24-Product measures, an Introduction
L25-Construction of Product Measure
L26-Computation of Product Measure-I
L27-Computation of Product Measure-II
L28-Integration on Product spaces
L29-Fubini's Theorems
L30-Lebesgue Measure and integral on R2
L31-Properties of Lebesgue Measure and integral on Rn
L32-Lebesgue integral on R2
L33-Integrating complex-valued functions
L34-Lp - spaces
L35-L2(X,S,mue)
L36-Fundamental Theorem of calculas for Lebesgue Integral-I
L37-Fundamental Theorem of calculus for Lebesgue Integral-II
L38-Absolutely continuous measures
L39-Modes of convergence
L40-Convergence in Measure
111102011
Mathematics
Linear Algebra
Dr. R. K. Sharma,Dr. Wagish Shukla
Web
IIT Delhi
Select
Vectors Spaces
Polynomials in one Variable
Matrices and linear transformations
Classical and Quantum Computation of dual basis1
More onVector Spaces and Linear transformations
Eigenvalues and Eigenvectors
Diagonalization
Sesqui or Bi-Linear Forms
More on sesqui or bi-linear forms
Inner Product Space
Orthogonal and Orthonormal Basis
Generalized Inverse
111102012
Mathematics
Linear Programming Problems
Dr. Aparna Mehra
Web
IIT Delhi
Select
Linear programming modeling, Optimal solutions and grap
Notion of convex set, convex function, their prope
Preliminary definitions (like convex combination,
Optimal hyper-plane and existence of optimal solut
Basic feasible solutions: algebraic interpretation
Relationship between extreme points and correspond
Adjacent extreme points and corresponding BFS alo
Fundamental theorem of LPP and its illustration th
LPP in canonical form to get the initial BFS & meth
Case of unbounded LPP, Simplex algorithm and illustrati
Artificial variables and its interpretation in co
Two phase method and illustration
Degeneracy and its consequences including cases of cycl
Introduction to duality & formulation of dual LPP for d
Duality theorems and their interpretations
Complementary slackness theorem, Farkas Lemma, Ex
Economic interpretation & applications of duality
Dual simplex method and its illustration
Post optimality analysis: the cases of change in re
Sensitivity analysis for addition and deletion of
Lecture 3
Karmarkar's interior point method
How to model the given LPP in Karmarkar's framewo
Complexity issue of Karmarkar's method
Integer programming: modeling & a look at its feasi
Gomory cut algorithm and derivation of cut equatio
Examples
Branch and Bound algorithm
Special LPPs: Transportation programming problem, m
Initial BFS and optimal solution of balanced TP pr
Other forms of TP and requisite modifications
Assignment problems and permutation matrix
Hungarian Method
Duality in Assignment Problems
Network Problems and LPP Formulation
Network Simplex Method:
111102014
Mathematics
Stochastic Processes
Dr. S. Dharmaraja
Video
IIT Delhi
Select
Introduction to Stochastic Processes
Introduction to Stochastic Processes (Contd.)
Problems in Random Variables and Distributions
Problems in Sequences of Random Variables
Definition, Classification and Examples
Simple Stochastic Processes
Stationary Processes
Autoregressive Processes
Introduction, Definition and Transition Probability Matrix
Chapman-Kolmogrov Equations
Classification of States and Limiting Distributions
Limiting and Stationary Distributions
Limiting Distributions, Ergodicity and Stationary Distributions
Time Reversible Markov Chain, Application of Irreducible Markov Chain in Queueing Models
Reducible Markov Chains
Definition, Kolmogrov Differential Equations and Infinitesimal Generator Matrix
Limiting and Stationary Distributions, Birth Death Processes
Poisson Processes
M/M/1 Queueing Model
Simple Markovian Queueing Models
Queueing Networks
Communication Systems
Stochastic Petri Nets
Conditional Expectation and Filtration
Definition and Simple Examples
Definition and Properties
Processes Derived from Brownian Motion
Stochastic Differential Equations
Ito Integrals
Ito Formula and its Variants
Some Important SDE`s and Their Solutions
Renewal Function and Renewal Equation
Generalized Renewal Processes and Renewal Limit Theorems
Markov Renewal and Markov Regenerative Processes
Non Markovian Queues
Non Markovian Queues Cont,,
Application of Markov Regenerative Processes
Galton-Watson Process
Markovian Branching Process
111103020
Mathematics
Number Theory
Dr. Anupam Saikia
Web
IIT Guwahati
Select
Introduction
Decimal Expansion of a Positive Integer
Euclid's Algorithm
Coprime Integers
Prime Numbers
Prime Number Theorem
Congruence
Linear Congruence
Simultaneous Linear Congruences
System of Congruences with Non-coprime Moduli
Linear Congruences Modulo Prime Powers
Fermat's Little Theorem
Pseudo-primes
Greatest Integer Function
Euler's function
RSA Cryptosystem
Arithmetic Functions
Mobius Function
Dirichlet Product
Units Modulo an Integer
Existence of Primitive Roots for Primes
Primitive Roots for Powers of 2
Definition and Examples
Gauss Lemma
Quadratic Reciprocity
Quadratic Residues of Powers of an Odd Prime
The Jacobi Symbol
Definition and Examples .
Discriminant of a Quadratic Form
Proper Representation and Equivalent Forms
Uniqueness of Equivalent Reduced Form
Class Number
Fermat Primes
Primes Expressible as a Sum of Two Squares
Sum of Three Squares
Finite Continued Fractions
Euler's Rule
Infinite Continued Fractions
Periodic Continued Fractions
Conjugate of a Quadratic Irrational
Continued Fractions of Reduced Quadratic Irrationals
Best Rational Approximation to an Irrational
Pell's Equation
Riemann Zeta Function
Dirichlet Series
Lucas Test for Primality
Pollard's Method for Factorization
Fermat's Factorization
Fermat's Conjecture
Exercise-1
Exercise-2
Exercise-3
Exercise-4
Exercise-5
Exercise-6
Exercise-7
Exercise-8
Exercise -9
Bibliography
Index
111103021
Mathematics
Partial Differential Equations
Dr. Rajen Kumar Sinha
Web
IIT Guwahati
Select
A Review of Multivariable Calulus
Essential Ordinary Differential Equations
Surfaces and Integral Curves
Solving Equations dx/P = dy/Q = dz/R
First-Order Partial Differential Equations
Linear First-Order PDEs
Quasilinear First-Order PDEs
Nonlinear First-Order PDEs
Compatible Systems and Charpit�s Method
Some Special Types of First-Order PDEs
Jacobi Method for Nonlinear First-Order PDEs
Classification of Second-Order PDEs
Canonical Forms or Normal Forms
Superposition Principle and Wellposedness
Introduction to Fourier Series
Convergence of Fourier Series
Fourier Cosine and Sine Series
Modeling the Heat Equation
The Maximum and Minimum Principle
Method of Separation of Variables
Time-Independent Homogeneous BC
Time-Dependent BC
Mathematical Formulation and Uniqueness Result
The Infinite String Problem
The Semi-Infinite String Problem
The Finite Vibrating String Problem
The Inhomogeneous Wave Equation
Basic Concepts and The Maximum/Minimum Principle
Green�s Identity and Fundamental Solutions
The Dirichlet BVP for a Rectangle
The Mixed BVP for a Rectangle
The Dirichlet Problems for Annuli
The Dirichlet Problem for the Disk
Fourier Transform
Fourier Sine and Cosine Transformations
Heat Flow Problems
Vibration of an Infinite String
Laplace�s Equation in a Half-Plane
The Laplace Equation
The Wave Equation
The Heat Equation
Bibliography
111103070
Mathematics
Complex Analysis
Prof. P. A. S. Sree Krishna
Video
IIT Guwahati
Select
Introduction
Introduction to Complex Numbers
de Moivre's Formula and Stereographic Projection
Topology of the Complex Plane Part-I
Topology of the Complex Plane Part-II
Topology of the Complex Plane Part-III
Introduction to Complex Functions
Limits and Continuity
Differentiation
Cauchy-Riemann Equations and Differentiability
Analytic functions; the exponential function
Sine, Cosine and Harmonic functions
Branches of Multifunctions; Hyperbolic Functions
Problem Solving Session I
Integration and Contours
Contour Integration
Introduction to Cauchy's Theorem
Cauchy's Theorem for a Rectangle
Cauchy's theorem Part - II
Cauchy's Theorem Part - III
Cauchy's Integral Formula and its Consequences
The First and Second Derivatives of Analytic Functions
Morera's Theorem and Higher Order Derivatives of Analytic Functions
Problem Solving Session II
Introduction to Complex Power Series
Analyticity of Power Series
Taylor's Theorem
Zeroes of Analytic Functions
Counting the Zeroes of Analytic Functions
Open mapping theorem – Part I
Open mapping theorem – Part II
Properties of Mobius Transformations Part I
Properties of Mobius Transformations Part II
Problem Solving Session III
Removable Singularities
Poles Classification of Isolated Singularities
Essential Singularity & Introduction to Laurent Series
Laurent's Theorem
Residue Theorem and Applications
Problem Solving Session IV
111104024
Mathematics
Applied Multivariate Analysis
Dr. Amit Mitra,Dr. Sharmishtha Mitra
Video
IIT Kanpur
Select
Prologue
Lecture-01 Basic concepts on multivariate distribution.
Lecture - 02 Basic concepts on multivariate distribution.
Lecture - 03 Multivariate normal distribution. � I
Lecture - 04 Multivariate normal distribution. � II
Lecture - 05 Multivariate normal distribution. � III
Lecture - 06 Some problems on multivariate distributions. � I
Lecture - 07 Some problems on multivariate distributions. � II
Lecture - 08 Random sampling from multivariate normal distribution and Wishart distribution. � I
Lecture - 09 Random sampling from multivariate normal distribution and Wishart distribution. � II
Lecture - 10 Random sampling from multivariate normal distribution and Wishart distribution. � III
Lecture - 11 Wishart distribution and it�s properties. �I
Lecture - 12 Wishart distribution and it�s properties.- II
Lecture -13 Hotelling�s T2 distribution and it�s applications.
Lecture - 14 Hotelling�s T2 distribution and various confidence intervals and regions.
Lecture- 15 Hotelling�s T2 distribution and Profile analysis.
Lecture - 16 Profile analysis.-I
Lecture - 17 Profile analysis. �II
Lecture - 18 MANOVA.-I
Lecture - 19 MANOVA.- II
Lecture - 20 MANOVA .- III
Lecture -21 MANOVA & Multiple Correlation Coefficient
Lecture -22 Multiple Correlation Coefficient
Lecture 23 Principal Component Analysis
Lecture -24 Principal Component Analysis
Lecture -25 Principal Component Analysis
Lecture -26 Cluster Analysis
Lecture -27 Cluster Analysis
Lecture -28 Cluster Analysis
Lecture -29 Cluster Analysis
Lecture -30 Discriminant Analysis and Classification
Lecture -31 Discriminant Analysis and Classification
Lecture -32 Discriminant Analysis and Classification
Lecture -33 Discriminant Analysis and Classification
Lecture -34 Discriminant Analysis and Classification
Lecture -35 Discriminant Analysis and Classification
Lecture -36 Discriminant Analysis and Classification
Lecture -37 Factor_Analysis
Lecture 38 Factor_Analysis
Lecture -39 Factor_Analysis
Lecture -40 Cannonical Correlation Analysis
Lecture -41 Cannonical Correlation Analysis
Lecture -42 Cannonical Correlation Analysis
Lecture -43 Cannonical Correlation Analysis
111104025
Mathematics
Calculus of Variations and Integral Equations
Prof. D. Bahuguna,Dr. Malay Banerjee
Video
IIT Kanpur
Select
Lecture-01-Calculus of Variations and Integral Equations
Lecture-02-Calculus of Variations and Integral Equations
Lecture-03-Calculus of Variations and Integral Equations
Lecture-04-Calculus of Variations and Integral Equations
Lecture-05-Calculus of Variations and Integral Equations
Lecture-06-Calculus of Variations and Integral Equations
Lecture-07-Calculus of Variations and Integral Equations
Lecture-08-Calculus of Variations and Integral Equations
Lecture-09-Calculus of Variations and Integral Equations
Lecture-10-Calculus of Variations and Integral Equations
Lecture-11-Calculus of Variations and Integral Equations
Lecture-12-Calculus of Variations and Integral Equations
Lecture-13-Calculus of Variations and Integral Equations
Lecture-14-Calculus of Variations and Integral Equations
Lecture-15-Calculus of Variations and Integral Equations
Lecture-16-Calculus of Variations and Integral Equations
Lecture-17-Calculus of Variations and Integral Equations
Lecture-18-Calculus of Variations and Integral Equations
Lecture-19-Calculus of Variations and Integral Equations
Lecture-20-Calculus of Variations and Integral Equations
Lecture-21-Calculus of Variations and Integral Equations
Lecture-22-Calculus of Variations and Integral Equations
Lecture-23-Calculus of Variations and Integral Equations
Lecture-24-Calculus of Variations and Integral Equations
Lecture-25-Calculus of Variations and Integral Equations
Lecture-26-Calculus of Variations and Integral Equations
Lecture-27-Calculus of Variations and Integral Equations
Lecture-28-Calculus of Variations and Integral Equations
Lecture-29-Calculus of Variations and Integral Equations
Lecture-30-Calculus of Variations and Integral Equations
Lecture-31-Calculus of Variations and Integral Equations
Lecture-32-Calculus of Variations and Integral Equations
Lecture-33-Calculus of Variations and Integral Equations
Lecture-34-Calculus of Variations and Integral Equations
Lecture-35-Calculus of Variations and Integral Equations
Lecture-36-Calculus of Variations and Integral Equations
Lecture-37-Calculus of Variations and Integral Equations
Lecture-38-Calculus of Variations and Integral Equations
Lecture-39-Calculus of Variations and Integral Equations
Lecture-40-Calculus of Variations and Integral Equations
111104026
Mathematics
Discrete Mathematics
Prof. A.K. Lal
Web
IIT Kanpur
Select
Contents
Basic Set Theory
Well Ordering Principle and the Principle of Mathematical Induction
Strong Form of the Principle of Mathematical Induction
Division Algorithm and the Fundamental Theorem of Arithmetic
Relations, Partitions and Equivalence Relation
Functions
Distinguishable Balls
Binomial Theorem
Onto Functions and the Stirling Numbers of Second Kind
Indistinguishable Balls and Distinguishable Boxes
Indistinguishable Balls in Indistinguishable Boxes
Lattice Paths and Catalan Numbers
Catalan Numbers Continued
Generalizations
Pigeonhole Principle
Pigeonhole Principle Continued
Principle of Inclusion and Exclusion
Formal Power Series
Formal Power Series Continued
Application to Recurrence Relation
Application to Recurrence Relation Continued
Application to Recurrence Relation Continued
Applications to Generating Functions Continued
Groups
Example of Groups
SubGroups
Lagrange�s Theorem
Applications of Lagrange�s Theorem
Group Action
Group Action Continued
The Cycle Index Polynomial
Polya Inventory Theorem
Basic Graph Theory
Graph Operations
Matrices related with Graphs
Matrix Tree Theorem
Eulerian graphs
Planar Graphs
Euler�s Theorem for Planar Graphs
Stereographic Projection
111104027
Mathematics
Linear programming and Extensions
Prof. Prabha Sharma
Video
IIT Kanpur
Select
Lecture_01_Introduction to Linear Programming Problems.
Lecture_02_ Vector space, Linear independence and dependence, basis.
Lec_03_Moving from one basic feasible solution to another, optimality criteria.
Lecture_04_Basic feasible solutions, existence & derivation.
Lecture_5_Convex sets, dimension of a polyhedron, Faces, Example of a polytope.
Lecture_6_Direction of a polyhedron, correspondence between bfs and extreme points.
Lecture_7_Representation theorem, LPP solution is a bfs, Assignment 1.
Lecture_08_Development of the Simplex Algorithm, Unboundedness, Simplex Tableau.
Lecture_9_ Simplex Tableau & algorithm ,Cycling, Bland�s anti-cycling rules, Phase I & Phase II.
Lecture_10_ Big-M method,Graphical solutions, adjacent extreme pts and adjacent bfs.
Lecture_11_Assignment 2, progress of Simplex algorithm on a polytope, bounded variable LPP.
Lecture_12_LPP Bounded variable, Revised Simplex algorithm, Duality theory, weak duality theorem.
Lecture_13_Weak duality theorem, economic interpretation of dual variables, Fundamental theorem of duality.
Lecture_14_Examples of writing the dual, complementary slackness theorem.
Lecture_15_Complementary slackness conditions, Dual Simplex algorithm, Assignment 3.
Lecture_16_Primal-dual algorithm.
Lecture_17_Problem in lecture 16, starting dual feasible solution, Shortest Path Problem.
Lecture_18_Shortest Path Problem, Primal-dual method, example.
Lecture_19_Shortest Path Problem-complexity, interpretation of dual variables, post-optimality analysis-changes in the cost vector.
Lecture_20_ Assignment 4, postoptimality analysis, changes in b, adding a new constraint, changes in {aij} , Parametric analysis.
Lecture_21_Parametric LPP-Right hand side vector.
Lecture_22_Parametric cost vector LPP.
Lecture_23_Parametric cost vector LPP, Introduction to Min-cost flow problem.
Lecture_24_Mini-cost flow problem-Transportation problem.
Lecture_25_Transportation problem degeneracy, cycling
Lecture_26_ Sensitivity analysis.
Lecture_27_ Sensitivity analysis.
Lecture_28_Bounded variable transportation problem, min-cost flow problem.
Lecture_29_Min-cost flow problem
Lecture_30_Starting feasible solution, Lexicographic method for preventing cycling ,strongly feasible solution
Lecture_31_Assignment 6, Shortest path problem, Shortest Path between any two nodes,Detection of negative cycles.
Lecture_32_ Min-cost-flow Sensitivity analysis Shortest path problem sensitivity analysis.
Lecture_33_Min-cost flow changes in arc capacities , Max-flow problem, assignment 7
Lecture_34_Problem 3 (assignment 7), Min-cut Max-flow theorem, Labelling algorithm.
Lecture_35_Max-flow - Critical capacity of an arc, starting solution for min-cost flow problem.
Lecture_36_Improved Max-flow algorithm.
Lecture_37_Critical Path Method (CPM).
Lecture_38_Programme Evaluation and Review Technique (PERT).
Lecture_39_ Simplex Algorithm is not polynomial time- An example.
Lecture_40_Interior Point Methods .
111104030
Mathematics
Numerical Solution of ODEs
Prof. M.K. Kadalbajoo
Web
IIT Kanpur
Select
Preliminaries
Existence, Uniqueness, and Wellposedness
Stability and Asymptotic Stability
The Euler Method
Convergence of Euler�s Method
Improvement of the error bound
Stability
Higher Order Methods
Runge-Kutta Methods
Error bounds for Runge-Kutta methods
Absolute Stability for Runge-Kutta Methods
Systems of Equations
Direct Methods For Higher Order Equations
General Single Step Methods
Convergence of General One-Step Methods
Derivation of Implicit Runge-Kutta methods
Derivation of Implicit Runge-Kutta Methods(Contd.)
Multistep Methods
Multistep Methods(Contd.)
Multistep Methods(Contd..)
The local error of the formulas based on integration
Local Error of Nystrom & Milne-Simpson Methods
Multistep Methods for Special Equations of the Second Order
Special 2nd order equations(Contd.)
Linear Multistep Methods
Linear Multistep Methods(Contd)
Consistency and Zero-Stability of Linear Multistep Methods
Convergence of Linear Multistep Methods
Necessary & Sufficient Conditions for Convergence
Absolute Stability and Relative Stability
General methods for finding intervals of absolute and relative stability
Some more methods for Absolute & Relative Stability
First order linear systems with constant coefficient
Stiffness and Problem of Stiffness
The problem of implicitness for Stiff systems
Linear multistep methods for Stiff systems
Finite Difference Methods
Analysis of Difference System
Analytic Expression of the Error
Nonlinear second order equations
Special Boundary Value Problems
Special Boundary Value Problems(Contd.)
111104031
Mathematics
Ordinary Differential Equations
Prof. V. Raghavendra
Web
IIT Kanpur
Select
Preliminaries
Picard's Successive Approximations
Picard's Theorem
Continuation and Dependence on Initial conditions
Existence of Solutions in the Large
Existence and Uniqueness of Solutions of Systems
Cauchy-Peano theorem
Introduction
Linear Dependence and Wronskian
Basic Theory for Linear Equations
Method of Variation of Parameters
Homogeneous Linear Equations with Constant Coefficients
Introduction- module 3
Systems of First Order Equations
Fundamental Matrix
Non-homogeneous linear Systems
Linear Systems with Constant Coefficients
Phase Portraits-Introduction
Phase Portraits (continued)
Introduction - module 4
Sturm's Comparison Theorem
Elementary Linear Oscillations
Boundary Value Problems
Sturm-Liouville Problem
Green's Functions
Introduction -Module 5
Linear Systems with Constant Coefficient (module5)
Linear Systems with Variable Coefficients
Second Order Linear Differential Equations
Stability of Quasi-linear Systems
Stability of Autonomous Systems
Stability of Non-Autonomous Systems
A Particular Lyapunov Function
111104068
Mathematics
Convex Optimization
Dr. Joydeep Dutta
Video
IIT Kanpur
Select
Lecture-01 Convex Optimization
Lecture-02 Convex Optimization
Lecture-03 Convex Optimization
Lecture-04 Convex Optimization
Lecture-05 Convex Optimization
Lecture-06 Convex Optimization
Lecture-07 Convex Optimization
Lecture-08 Convex Optimization
Lecture-09 Convex Optimization
Lecture-10 Convex Optimization
Lecture-11 Convex Optimization
Lecture-12 Convex Optimization
Lecture-13 Convex Optimization
Lecture-14 Convex Optimization
Lecture-15 Convex Optimization
Lecture-16 Convex Optimization
Lecture-17 Convex Optimization
Lecture-18 Convex Optimization
Lecture-19 Convex Optimization
Lecture-20 Convex Optimization
Lecture-21 Convex Optimization
Lecture-22 Convex Optimization
Lecture-23 Convex Optimization
Lecture-24 Convex Optimization
Lecture-25 Convex Optimization
Lecture-26 Convex Optimization
Lecture-27 Convex Optimization
Lecture-28 Convex Optimization
Lecture-29 Convex Optimization
Lecture-30 Convex Optimization
Lecture-31 Convex Optimization
Lecture-32 Convex Optimization
Lecture-33 Convex Optimization
Lecture-34 Convex Optimization
Lecture-35 Convex Optimization
Lecture-36 Convex Optimization
Lecture-37 Convex Optimization
Lecture-38 Convex Optimization
Lecture-39 Convex Optimization
Lecture-40 Convex Optimization
Lecture-41 Convex Optimization
Lecture-42 Convex Optimization
111104072
Mathematics
Econometric Theory
Prof. Shalabh
Web
IIT Kanpur
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Bibliography
111104073
Mathematics
Sampling Theory
Prof. Shalabh
Web
IIT Kanpur
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Exercises
111104074
Mathematics
Linear Regression Analysis
Prof. Shalabh
Web
IIT Kanpur
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Lecture38
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Lecture40
Lecture41
Lecture42
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Bibliography-RegressionAnalysis
111104075
Mathematics
Analysis of variance and design of experiment-I
Prof. Shalabh
Web
IIT Kanpur
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Exercises
References
111104078
Mathematics
Analysis of variance and design of experiment-II
Prof. Shalabh
Web
IIT Kanpur
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Exercise
111105035
Mathematics
Advanced Engineering Mathematics
Prof. Somesh Kumar,Prof. P.D. Srivastava,Prof. J. Kumar,Dr. P. Panigrahi
Video
IIT Kharagpur
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Review Groups, Fields and Matrices
Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors
Basis, Dimension, Rank and Matrix Inverse
Linear Transformation, Isomorphism and Matrix Representation
System of Linear Equations, Eigenvalues and Eigenvectors
Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices
Jordan Canonical Form, Cayley Hamilton Theorem
Inner Product Spaces, Cauchy-Schwarz Inequality
Orthogonality, Gram-Schmidt Orthogonalization Process
Spectrum of special matrices,positive/negative definite matrices
Concept of Domain, Limit, Continuity and Differentiability
Analytic Functions, C-R Equations
Harmonic Functions
Line Integral in the Complex
Cauchy Integral Theorem
Cauchy Integral Theorem (Contd.)
Cauchy Integral Formula
Power and Taylor's Series of Complex Numbers
Power and Taylor's Series of Complex Numbers (Contd.)
Taylor's, Laurent Series of f(z) and Singularities
Classification of Singularities, Residue and Residue Theorem
Laplace Transform and its Existence
Properties of Laplace Transform
Evaluation of Laplace and Inverse Laplace Transform
Applications of Laplace Transform to Integral Equations and ODEs
Applications of Laplace Transform to PDEs
Fourier Series
Fourier Series (Contd.)
Fourier Integral Representation of a Function
Introduction to Fourier Transform
Applications of Fourier Transform to PDEs
Laws of Probability - I
Laws of Probability - II
Problems in Probability
Random Variables
Special Discrete Distributions
Special Continuous Distributions
Joint Distributions and Sampling Distributions
Point Estimation
Interval Estimation
Basic Concepts of Testing of Hypothesis
Tests for Normal Populations
111105037
Mathematics
Functional Analysis
Prof. P.D. Srivastava
Video
IIT Kharagpur
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Metric Spaces with Examples
Holder Inequality and Minkowski Inequality
Various Concepts in a Metric Space
Separable Metrics Spaces with Examples
Convergence, Cauchy Sequence, Completeness
Examples of Complete and Incomplete Metric Spaces
Completion of Metric Spaces + Tutorial
Vector Spaces with Examples
Normed Spaces with Examples
Banach Spaces and Schauder Basic
Finite Dimensional Normed Spaces and Subspaces
Compactness of Metric/Normed Spaces
Linear Operators-definition and Examples
Bounded Linear Operators in a Normed Space
Bounded Linear Functionals in a Normed Space
Concept of Algebraic Dual and Reflexive Space
Dual Basis & Algebraic Reflexive Space
Dual Spaces with Examples
Tutorial - I
Tutorial - II
Inner Product & Hilbert Space
Further Properties of Inner Product Spaces
Projection Theorem, Orthonormal Sets and Sequences
Representation of Functionals on a Hilbert Spaces
Hilbert Adjoint Operator
Self Adjoint, Unitary & Normal Operators
Tutorial - III
Annihilator in an IPS
Total Orthonormal Sets And Sequences
Partially Ordered Set and Zorns Lemma
Hahn Banach Theorem for Real Vector Spaces
Hahn Banach Theorem for Complex V.S. & Normed Spaces
Baires Category & Uniform Boundedness Theorems
Open Mapping Theorem
Closed Graph Theorem
Adjoint Operator
Strong and Weak Convergence
Convergence of Sequence of Operators and Functionals
LP - Space
LP - Space (Contd.)
111105041
Mathematics
Probability and Statistics
Prof. Somesh Kumar
Video
IIT Kharagpur
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Algebra of Sets - I
Algebra of Sets - II
Introduction to Probability
Laws of Probability - I
Law of Probability - II
Problems in Probability
Random Variables
Probability Distributions
Characteristics of Distribution
Special Distributions - I
Special Distributions - II
Special Distributions - III
Special Distributions - IV
Special Distributions - V
Special Distributions - VI
Special Distributions - VII
Functions of a Random Variable
Joint Distributions - I
Joint Distributions - II
Joint Distributions - III
Joint Distributions - IV
Transformations of Random Vectors
Sampling Distributions - I
Sampling Distributions - II
Descriptive Statistics - I
Descriptive Statistics - II
Estimation - I
Estimation - II
Estimation - III
Estimation - IV
Estimation - V
Estimation - VI
Testing of Hypothesis - I
Testing of Hypothesis - II
Testing of Hypothesis - III
Testing of Hypothesis - IV
Testing of Hypothesis - V
Testing of Hypothesis - VI
Testing of Hypothesis - VII
Testing of Hypothesis - VIII
111105043
Mathematics
Statistical Inference
Prof. Somesh Kumar
Video
IIT Kharagpur
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Introduction and Motivation
Basic Concepts of Point Estimations - I
Basic Concepts of Point Estimations - II
Finding Estimators - I
Finding Estimators - II
Finding Estimators - III
Properties of MLEs
Lower Bounds for Variance - I
Lower Bounds for Variance - II
Lower Bounds for Variance - III
Lower Bounds for Variance - IV
Sufficiency
Sufficiency and Information
Minimal Sufficiency, Completeness
UMVU Estimation, Ancillarity
Invariance - I
Invariance - II
Bayes and Minimax Estimation - I
Bayes and Minimax Estimation - II
Bayes and Minimax Estimation - III
Testing of Hypotheses : Basic Concepts
Neyman Pearson Fundamental Lemma
Applications of NP lemma
UMP Tests
UMP Tests (Contd.)
UMP Unbiased Tests
UMP Unbiased Tests (Contd.)
UMP Unbiased Tests : Applications
Unbiased Tests for Normal Populations
Unbiased Tests for Normal Populations (Contd.)
Likelihood Ratio Tests - I
Likelihood Ratio Tests - II
Likelihood Ratio Tests - III
Likelihood Ratio Tests - IV
Invariant Tests
Test for Goodness of Fit
Sequential Procedure
Sequential Procedure (Contd.)
Confidence Intervals
Confidence Intervals (Contd.)
111105069
Mathematics
A Basic Course in Real Analysis
Prof. P.D. Srivastava
Video
IIT Kharagpur
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Rational Numbers and Rational Cuts
Irrational numbers, Dedekind's Theorem
Continuum and Exercises
Continuum and Exercises (Contd.)
Cantor's Theory of Irrational Numbers
Cantor's Theory of Irrational Numbers (Contd.)
Equivalence of Dedekind and Cantor's Theory
Finite, Infinite, Countable and Uncountable Sets of Real Numbers
Types of Sets with Examples, Metric Space
Various properties of open set, closure of a set
Ordered set, Least upper bound, greatest lower bound of a set
Compact Sets and its properties
Weiersstrass Theorem, Heine Borel Theorem, Connected set
Tutorial - II
Concept of limit of a sequence
Some Important limits, Ratio tests for sequences of Real Numbers
Cauchy theorems on limit of sequences with examples
Fundamental theorems on limits, Bolzano-Weiersstrass Theorem
Theorems on Convergent and divergent sequences
Cauchy sequence and its properties
Infinite series of real numbers
Comparison tests for series, Absolutely convergent and Conditional convergent series
Tests for absolutely convergent series
Raabe's test, limit of functions, Cluster point
Some results on limit of functions
Limit Theorems for functions
Extension of limit concept (one sided limits)
Continuity of Functions
Properties of Continuous Functions
Boundedness Theorem, Max-Min Theorem and Bolzano's theorem
Uniform Continuity and Absolute Continuity
Types of Discontinuities, Continuity and Compactness
Continuity and Compactness (Contd.), Connectedness
Differentiability of real valued function, Mean Value Theorem
Mean Value Theorem (Contd.)
Application of MVT , Darboux Theorem, L Hospital Rule
L'Hospital Rule and Taylor's Theorem
Tutorial - III
Riemann/Riemann Stieltjes Integral
Existence of Reimann Stieltjes Integral
Properties of Reimann Stieltjes Integral
Properties of Reimann Stieltjes Integral (Contd.)
Definite and Indefinite Integral
Fundamental Theorems of Integral Calculus
Improper Integrals
Convergence Test for Improper Integrals
111106046
Mathematics
Fourier Analysis
Dr. R. Radha,Dr. S. Thangavelu
Web
IIT Madras
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Course Title
Contents
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Appendix
Biblography
Mathematicians at a glance
111106047
Mathematics
Functional Analysis
Prof. M.T. Nair
Web
IIT Madras
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Course title
Contents
Preface
Chapter 1
Chapter 2
Chapter 3
Chapter 4
References
111106050
Mathematics
Graph Theory
Prof. S.A. Choudum
Web
IIT Madras
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Course Contents
Preliminaries
Connected graphs and shortest paths
Trees
Special classes of graphs
Eulerian Graphs
Hamilton Graphs
Independent sets, coverings and matchings
Vertex-colorings
Edge colorings
Planar Graphs
Directed Graphs
List of Books
111107063
Mathematics
Numerical Solution of Ordinary and Partial Differential Equations
Dr. Rama Bhargava,Dr. Sunita Gakkhar
Web
IIT Roorkee
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Numerical solution of first order ordinary differential equations
Numerical Methods: Euler method
Modified Euler Method
Runge Kutta Method
Fourth Order Runge Kutta Methods
Higher order Runge Kutta Methods
Multi Step Methods Predictor corrector Methods
Multi Step Methods Predictor corrector Methods Contd�
Multi Step Methods Adams Bashforth method
Multi Step Methods Adams Moulton method
Systems of Differential Equations
Higher Order Equations
Stiff Differential equations
Finite Difference Methods: Dirichlet type boundary condition
Finite Difference Methods: Mixed boundary condition
Shooting Method
Shooting Method contd�
Solution by Finite Difference Methods
Shooting Methods
Shooting Methods Contd�
Introduction of PDE, Classification and Various type of conditions
Finite Difference representation of various Derivatives
Parabolic Partial Differential Equations : One dimensional equation : Explicit method.
Crank Nicolson method and Fully Implicit method
Three Time Level Schemes
Extension to 2d Parabolic Partial Differential Equations
Compatibility and Stability of 1d Parabolic PDE
Stability of one-dimensional Parabolic PDE
Convergence of one?dimensional Parabolic PDE
Elliptic Partial Differential Equations : Solution in Cartesian coordinate system
Successive Over Relaxation Method
Elliptic Partial Differential Equation in Polar System
Alternating Direction Implicit Method
Treatment of Irregular Boundaries
Methods for Solving tridiagonal System
Explicit Method for Solving Hyperbolic PDE
Implicit Method to Hyperbolic PDE
Convergence & Stability
Method of Characteristics
Examples and conclusions
111108066
Mathematics
Advanced Matrix Theory and Linear Algebra for Engineers
Prof. Vittal Rao
Video
IISc Bangalore
Select
Prologue Part 1
Prologue Part 2
Prologue Part 3
Linear Systems Part 1
Linear Systems Part 2
Linear Systems Part 3
Linear Systems Part 4
Vector Spaces Part 1
Vector Spaces Part 2
Linear Independence and Subspaces Part 1
Linear Independence and Subspaces Part 2
Linear Independence and Subspaces Part 3
Linear Independence and Subspaces Part 4
Basis Part 1
Basis Part 2
Basis Part 3
Linear Transformations Part 1
Linear Transformations Part 2
Linear Transformations Part 3
Linear Transformations Part 4
Linear Transformations Part 5
Inner Product and Orthogonality Part 1
Inner Product and Orthogonality Part 2
Inner Product and Orthogonality Part 3
Inner Product and Orthogonality Part 4
Inner Product and Orthogonality Part 5
Inner Product and Orthogonality Part 6
Diagonalization Part 1
Diagonalization Part 2
Diagonalization Part 3
Diagonalization Part 4
Hermitian and Symmetric matrices Part 1
Hermitian and Symmetric matrices Part 2
Hermitian and Symmetric matrices Part 3
Hermitian and Symmetric matrices Part 4
Singular Value Decomposition (SVD) Part 1
Singular Value Decomposition (SVD) Part 2
Back To Linear Systems Part 1
Back To Linear Systems Part 2
Epilogue
111104032
Mathematics
Probability and Distributions
Prof. Neeraj Misra
Web
IIT Kanpur
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Lec1
Lec2
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Problem1
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Problem5
Lec25
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Problem6
Lec37
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Lec41
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Problem7
111104071
Mathematics
Foundations of Optimization
Dr. Joydeep Dutta
Video
IIT Kanpur
Select
Lecture-01
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Lecture-27
Lecture-28
Lecture-29
Lecture-30
Lecture-31
Lecture-32
Lecture-33
Lecture-34
Lecture-35
Lecture-36
Lecture-37
Lecture-38
111105039
Mathematics
Optimization
Prof. A. Goswami Dr. Debjani Chakraborty
Video
IIT Kharagpur
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Lecture-01
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Lecture-29
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Lecture-36
Lecture-37
Lecture-38
Lecture-39
Lecture-40