Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Jaikrishnan J
NPTEL Co-ordinating Institute : IIT Palakkad
NPTEL Lecture Count : 74
NPTEL Course Size : 2.8 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Metric Spaces
Lecture 2 - Examples of metric spaces
Lecture 3 - Loads of definitions
Lecture 4 - Normed vector spaces
Lecture 5 - Examples of normed vector spaces
Lecture 6 - Basic properties open closed sets metric
Lecture 7 - Continuity in metric spaces
Lecture 8 - Equivalent metrics and product spaces
Lecture 9 - Completeness
Lecture 10 - Completeness (Continued...)
Lecture 11 - Completeness of B(x,y)
Lecture 12 - Completion
Lecture 13 - Compactness
Lecture 14 - The Bolzano-Weierstrass Property
Lecture 15 - Open covers and Compactness
Lecture 16 - The Heine-Borel Theorem for Metric Spaces
Lecture 17 - Connectedness
Lecture 18 - Path-Connectedness
Lecture 19 - Connected Components
Lecture 20 - The Arzela-Ascolli theorem
Lecture 21 - Upper and lower limits
Lecture 22 - The Stone-Weierstrass theorem
Lecture 23 - All norms are equivalent
Lecture 24 - Vector-valued functions
Lecture 25 - Scalar-valued functions of a vector variable
Lecture 26 - Directional derivatives and the gradient
Lecture 27 - Interpretation and properties of the gradient
Lecture 28 - Higher-order partial derivatives
Lecture 29 - The derivative as a linear map
Lecture 30 - Examples of differentiation
Lecture 31 - Properties of the derivative map
Lecture 32 - The mean-value theorem
Lecture 33 - Differentiating under the integral sign
Lecture 34 - Higher-order derivatives
Lecture 35 - Symmetry of the second derivative
Lecture 36 - Taylor's theorem
Lecture 37 - Taylor's theorem with remainder
Lecture 38 - The Banach fixed point theorem
Lecture 39 - Newton's method
Lecture 40 - The inverse function theorem
Lecture 41 - Diffeomorphismsm and local diffeomorphisms
Lecture 42 - The implicit function theorem
Lecture 43 - Tangent space to a hypersurface
Lecture 44 - The definition of a manifold
Lecture 45 - Examples and non examples of manifolds
Lecture 46 - The tangent space to a manifold
Lecture 47 - Maxima and minima in several variables
Lecture 48 - The Hessian and extrema
Lecture 49 - Completing the squares
Lecture 50 - Constrained extrema and lagrange multipliers
Lecture 51 - Curves
Lecture 52 - Rectifiability and arc-length
Lecture 53 - The Riemann integral revisited
Lecture 54 - Monotone sequences of functions
Lecture 55 - Upper functions and their integrals
Lecture 56 - Riemann integrable functions as upper functions
Lecture 57 - Lebesgue integrable functions
Lecture 58 - Approximation of Lebesgure integrable functions
Lecture 59 - Levi monotone convergence theorem for step functions
Lecture 60 - Monotone convergence theorem for upper functions
Lecture 61 - Monotone convergence theorem for Lebesgue integrable functions
Lecture 62 - The Lebesgue dominated convergence theorem
Lecture 63 - Applications of the convergence theorems
Lecture 64 - The problem of measure
Lecture 65 - The Lebesgue integral on unbounded intervals
Lecture 66 - Measurable functions
Lecture 67 - Solution to the problem of measure
Lecture 68 - The Lebesgue integral on arbitrary subsets
Lecture 69 - Square integrable functions
Lecture 70 - Norms and inner-products on complex vector spaces
Lecture 71 - Convergence in L2
Lecture 72 - The Riesz-Fischer theorem
Lecture 73 - Multiple Riemann integration
Lecture 74 - Multiple Lebesgue integration