Multivariable Differential Calculus and Ordinary Differential Equations BYTKQQTJ0Q

URI	`m2://res/BYTKQQTJ0Q`
Kind	course
Creators	Vamsi Pritham Pingali (instructor)
Date	2026-06-17
MSC	34-XX
Scope	in
Ids	course 04dese585:111108002

Expressions

e1: edition

Language	en
Date	2026-06-17

m1: page, IISc Bangalore (record). nptel 111108002
m2: page, 2026-06-17 (record). nptel 111108002

Contents

part 1: Week 1 Review of Some Prerequisites (Linear Algebra and Topology of Euclidean Spaces)
session 1: Vector Spaces and Subspaces, Linear Span and Linear Independence, Linear Transformations
session 2: The Matrix Representation of a Linear Transformation
session 3: Systems of Linear Equations and Gauss-Jordan Elimination Method
session 4: The Row and Column Spaces of a Matrix, Rank and Determinant
session 5: Inner Product Spaces and Normed Vector Spaces
part 2: Week 2 Review of Some Prerequisites (Topology of Euclidean Spaces and Limits and Continuity of Scalar and Vector Fields)
session 6: Eigenvalues, Eigenvectors and Diagonalizability
session 7: Interior Points and Open Sets, Convergent Sequences and Continuous Functions
session 8: Closed Sets and Limit Points, Connectedness and Compactness, Limits and Continuity
session 9: Further Discussion on Limits and Continuity
session 10: Detailed Review of Algebra of Limits and Algebra of Continuous Functions
part 3: Week 3 Introduction to Multivariable Differentiability
session 11: Directional Derivatives and Partial Derivatives
session 12: Differentiability of a Multivariable Function
session 13: Differentiability of Vector Fields, Gradient and Jacobian Matrix
session 14: Continuous Differentiability
session 15: Algebra of Differentiable Functions and Some Other Properties of Differentiability
part 4: Week 4 Chain Rule, LMVT, and Mixed Partial Derivatives
session 16: More Discussion On Differentiation Of Several Variable Functions, and Derivative Computation For Some Functions
session 17: Chain Rule
session 18: Further Discussion On Chain Rule
session 19: LMVT in Multivariable Calculus, and Directional Derivative Along Regular Paths
session 20: Further Discussion On Directional Derivative, and Mixed Partial Derivatives
part 5: Week 5 Clairaut's Theorem, Taylor's Theorem, and Second Derivative Test For Multivariable Functions
session 21: Clairaut's Theorem
session 22: Taylor's Theorem and Second Derivative Test in Single Variable Functions
session 23: Taylor's Theorem For Multivariable Functions
session 24: Second Derivative Test For Multivariable Functions
session 25: Further Discussion on Second Derivative Test
part 6: Week 6 Inverse Function Theorem (IFT) For Several Variables
session 26: Discussion about convergence of Taylor series and bump functions
session 27: Inverse Function Theorem for one variable functions
session 28: Proof of the Inverse Function Theorem for several variables
session 29: Proof of the Inverse Function Theorem for several variables (Contd.)
session 30: Proof of the Inverse Function Theorem for several variables (Contd.)
part 7: Week 7 Implicit Function Theorem
session 31: The Implicit Function Theorem for Functions of Two Variables
session 32: The Implicit Function Theorem for Functions of Several Variables
session 33: Some Further Applications of the Implicit Function Theorem
session 34: Constrained Optimization Problem and the Lagrange Multiplier Method
session 35: The Lagrange Multiplier Method (Contd.)
part 8: Week 8 Embedded Manifolds, Gradient Descent Algorithm
session 36: About the Constraining Sets in the Lagrange Multiplier Method
session 37: Introduction to Manifolds Embedded in R^n
session 38: Gradient Descent
session 39: Gradient Descent (Contd.)
session 40: Gradient Descent (Contd.)
part 9: Week 9 Applications of Gradient Descent (Backpropagation), Introduction to ODEs
session 41: Some Applications of Gradient Descent
session 42: Backpropagation (contd.), Introduction to ODEs
session 43: Some Applications of ODEs to Real-World Problems
session 44: Systems of ODEs (contd.)
session 45: Methods of Solving a First-Order System of ODEs
part 10: Week 10 Exponential of Square Matrices and Solving Linear Systems
session 46: Triangularization Theorem
session 47: Exponential of Square Matrices
session 48: Properties of Matrix Exponential
session 49: Properties of Matrix Exponential (Contd.)
session 50: Solving Homogeneous and Inhomogeneous Linear Systems
part 11: Week 11 Existence and Uniqueness Theory for ODEs
session 51: Uniqueness of Solutions to Inhomogeneous Linear System
session 52: Existence of Solutions to Inhomogeneous Linear System
session 53: Uniqueness of Solutions to ODEs in General Form
session 54: General Existence Theory for ODEs
session 55: Picard's Existence Theorem for ODEs
part 12: Week 12 Continuous or Smooth Dependence on Parameters
session 56: Improvement of Picard's Existence Theorem
session 57: Characterization of Maximal Interval of Existence
session 58: Continuous Dependence on Parameters
session 59: Smooth Dependence on Parameters
session 60: Smooth Dependence on Parameters (Contd.), and Numerical Methods to Solve ODEs

Catalogue records

nptel: 111108002 (manifestation)
nptel_video: 111108002 (manifestation)