Integral and Vector Calculus
Indian Institute of Technology, Kharagpur and NPTEL via Swayam

60

 Write review
Overview
INTENDED AUDIENCE : MathematicsPREREQUISITES : Differential calculus of one and several variables.INDUSTRY SUPPORT : None
Syllabus
COURSE LAYOUT
Week 1: Partition, concept of Riemann integral, properties of Riemann integrable functions, antiderivatives, Fundamental theorem of Integral calculus, mean value theorems.Week 2: Reduction formula and derivation of different types of formula, improper integrals and their convergence, tests of convergence.
Week 3: Beta and Gamma function, their properties, differentiation under the integral sign, Leibnitz rule.
Week 4: Double integrals. change of order of integration, Jacobian transformations, triple integrals.
Week 5: Area of plane regions, rectification, surface integrals.
Week 6: Volume integrals, center of gravity and moment of Inertia.
Week 7: Collection of vector algebra results, scalar and vector fields, level surfaces, limit, continuity, differentiability of vector functions
Week 8: Curves, Arclength, partial derivative of vector function, directional derivative gradient, divergence and curl.
Week 9: Irrotational, conservative and Solenoidal fields, tangent, normal, binormal, SerretFrenet formula.
Week 10: Application of vector calculus in mechanics, lines, surface and volume integrals. line integrals independent of path.
Week 11: The divergence theorem of Gauss, Stokes theorem, and Green’s theorem.
Week 12: Integral definition of gradient, divergence and curl. revision of problems from Integral and Vector calculus.
Taught by
Prof. Hari Shankar Mahato
Related Courses

Vector Calculus for Engineers
The Hong Kong University of Science and Technology
4.8 
Engineering Mathematics II
Indian Institute of Technology, Kharagpur, NPTEL

Calculus through Data & Modelling: Vector Calculus
Johns Hopkins University

Electromagnetism
NPTEL, Indian Institute of Science Education and Research Bhopal

Basic Real Analysis
Indian Institute of Technology Bombay, NPTEL

Mathematical Analysis
CEC, MES College of Engineering
Reviews
0.0 rating, based on 0 reviews