Integral and Vector Calculus
Integral and Vector Calculus. Instructor: Prof. Hari Shankar Mahato, Department of Mathematics, IIT Kharagpur. This course will cover a detailed introduction to integral and vector calculus. We'll start with the concepts of partition, Riemann sum and Riemann Integrable functions and their properties. We then move to antiderivatives and will look into a few classical theorems of integral calculus such as a fundamental theorem of integral calculus. We'll then study improper integral, their convergence and learn about a few tests which conform the convergence. Afterwards we'll look into multiple integrals, Beta and Gamma functions, Differentiation under the integral sign.
(from nptel.ac.in)
Lecture 01  Partition, Riemann Integrability and One Example 
Lecture 02  Partition, Riemann Integrability and One Example (cont.) 
Lecture 03  Condition of Integrability 
Lecture 04  Theorems on Riemann Integrations 
Lecture 05  Examples 
Lecture 06  Examples (cont.) 
Lecture 07  Reduction Formula 
Lecture 08  Reduction Formula (cont.) 
Lecture 09  Improper Integral 
Lecture 10  Improper Integral (cont.) 
Lecture 11  Improper Integral (cont.) 
Lecture 12  Improper Integral (cont.) 
Lecture 13  Introduction to Beta and Gamma Function 
Lecture 14  Beta and Gamma Function 
Lecture 15  Differentiation under Integral Sign 
Lecture 16  Differentiation under Integral Sign (cont.) 
Lecture 17  Double Integral 
Lecture 18  Double Integral over a Region E 
Lecture 19  Examples of Integral over a Region E 
Lecture 20  Change of Variables in a Double Integral 
Lecture 21  Change of Order of Integration 
Lecture 22  Triple Integral 
Lecture 23  Triple Integral (cont.) 
Lecture 24  Area of Plane Region 
Lecture 25  Area of Plane Region (cont.) 
Lecture 26  Rectification 
Lecture 27  Rectification (cont.) 
Lecture 28  Surface Integral 
Lecture 29  Surface Integral (cont.) 
Lecture 30  Surface Integral (cont.) 
Lecture 31  Volume Integral, Gauss Divergence Theorem 
Lecture 32  Vector Calculus 
Lecture 33  Limit, Continuity, Differentiability 
Lecture 34  Successive Differentiation 
Lecture 35  Integration of Vector Function 
Lecture 36  Gradient of a Function 
Lecture 37  Divergence and Curl 
Lecture 38  Divergence and Curl Examples 
Lecture 39  Divergence and Curl Important Identities 
Lecture 40  Level Surface Relevant Theorems 
Lecture 41  Directional Derivative (Concept and Few Results) 
Lecture 42  Directional Derivative (Concept and Few Results) (cont.) 
Lecture 43  Directional Derivatives, Level Surfaces 
Lecture 44  Application to Mechanics 
Lecture 45  Equation of Tangent, Unit Tangent Vector 
Lecture 46  Unit Normal, Unit Binormal, Equation of Normal Plane 
Lecture 47  Introduction and Derivation of SerretFrenet Formula, Few Results 
Lecture 48  Example on Binormal, Normal Tangent, SerretFrenet Formula 
Lecture 49  Osculating Plane, Rectifying Plane, Normal Plane 
Lecture 50  Application to Mechanics, Velocity, Speed, Acceleration 
Lecture 51  Angular Momentum, Newton's Law 
Lecture 52  Example on Derivation of Equation of Motion of Particle 
Lecture 53  Line Integral 
Lecture 54  Surface Integral 
Lecture 55  Surface Integral (cont.) 
Lecture 56  Green's Theorem and Example 
Lecture 57  Volume Integral, Gauss Theorem 
Lecture 58  Gauss Divergence Theorem 
Lecture 59  Stokes' Theorem 
Lecture 60  Overview of Course 
References 
Integral and Vector Calculus
Instructor: Prof. Hari Shankar Mahato, Department of Mathematics, IIT Kharagpur. This course will cover a detailed introduction to integral and vector calculus.
