Integral and Vector Calculus
Indian Institute of Technology, Kharagpur and NPTEL via Swayam
- Provider Swayam
- Cost Free Online Course
- Session In progress
- Language English
- Certificate Certificate Available
- Duration 12 weeks long
- Learn more about MOOCs
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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, anti-derivatives, 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, Arc-length, partial derivative of vector function, directional derivative gradient, divergence and curl.
Week 9: Irrotational, conservative and Solenoidal fields, tangent, normal, binormal, Serret-Frenet 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
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