Media Storage Type : DVD-ROM
NPTEL Course Name : Mathematics - I
NPTEL Subject Matter Expert : Prof. Inder K Rana
NPTEL Co-ordinating Institute : IIT Bombay
NPTEL Lecture Count : 54
Lecture Titles:
Lecture 1 - Real Numbers, Functions
Lecture 2 - Convergent and Bound Sequences
Lecture 3 - Monotone Sequence and Limit theorem
Lecture 4 - Limit at a point
Lecture 5 - Continuity
Lecture 6 - Properties of Continuous Functions
Lecture 7 - Differentiation
Lecture 8 - Chain Rule
Lecture 9 - Roll's theorem and Mean Value Theorem
Lecture 10 - Sufficient conditions for increasing / decreasing
Lecture 11 - Absolute Maximum / Minimum
Lecture 12 - Asymptoes
Lecture 13 - Linear Approximations
Lecture 14 - Taylor's Theorem
Lecture 15 - Newton's method
Lecture 16 - Integral from upper and lower sums
Lecture 17 - Fundamental theorem of calculus
Lecture 18 - Approximating Integral : Trapezoidal Rule
Lecture 19 - Definition of the natural logarithmic function
Lecture 20 - Definition of the power function and logarithmic function with positive base
Lecture 21 - Relative rate of growth of functions
Lecture 22 - Arc Length of a Plane Curve
Lecture 23 - Area of Surface of revolution
Lecture 24 - Volume of solids of revolution by washer method
Lecture 25 - Series of numbers
Lecture 26 - Absolute convergence
Lecture 27 - Series of functions
Lecture 28 - Series of function
Lecture 29 - Limit of scaler fields
Lecture 30 - Continuity of scaler fields
Lecture 31 - Partial derivatives
Lecture 32 - Chain rules
Lecture 33 - Implicit differentiation
Lecture 34 - Gradient of a scaler field
Lecture 35 - Tangent plane and normal
Lecture 36 - Mean value theorem and Linearization
Lecture 37 - Maxima and Minima
Lecture 38 - Second derivative test for local maxima / minima & saddle points
Lecture 39 - Absolute maxima / minima
Lecture 40 - Double integrals over rectangular domains
Lecture 41 - Triple integrals
Lecture 42 - Change of variables
Lecture 43 - Vector fields and their properties
Lecture 44 - Gradient Divergence and Curl
Lecture 45 - Curves in space
Lecture 46 - Line integrals
Lecture 47 - Fundamental Theorems of Calculus for Line integrals
Lecture 48 - Green's Theorem
Lecture 49 - Surfaces and parameterizations
Lecture 50 - Surface Integrals
Lecture 51 - Divergence theorem
Lecture 52 - Orienting the boundary of an orientable surface
Lecture 53 - Stokes' theorem for general domains
Lecture 54 - Application of Stokes' theorem