But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres. The course is free to enroll and learn from. ![]() revision of problems from Integral and Vector calculus. Week 12 : Integral definition of gradient, divergence and curl. Week 11 : The divergence theorem of Gauss, Stokes theorem, and Green’s theorem. Week 10 : Application of vector calculus in mechanics, lines, surface and volume integrals. Week 9 : Irrotational, conservative and Solenoidal fields, tangent, normal, binormal, Serret-Frenet formula. Week 8 : Curves, Arc-length, partial derivative of vector function, directional derivative gradient, divergence and curl. Week 7 : Collection of vector algebra results, scalar and vector fields, level surfaces, limit, continuity, differentiability of vector functions Week 6 : Volume integrals, center of gravity and moment of Inertia. Week 5 : Area of plane regions, rectification, surface integrals. change of order of integration, Jacobian transformations, triple integrals. Week 3 : Beta and Gamma function, their properties, differentiation under the integral sign, Leibnitz rule. Week 2 : Reduction formula and derivation of different types of formula, improper integrals and their convergence, tests of convergence. ![]() Week 1 : Partition, concept of Riemann integral, properties of Riemann integrable functions, anti-derivatives, Fundamental theorem of Integral calculus, mean value theorems. Then we’ll look into the line, volume and surface integrals and finally we’ll learn the three major theorems of vector calculus: Green’s, Gauss’s and Stoke’s theorem. We’ll look into the concepts of tangent, normal and binormal and then derive the Serret-Frenet formula. ![]() We’ll also study the concepts of conservative, irrotational and solenoidal vector fields. In the following weeks, we’ll learn about scalar and vector fields, level surfaces, limit, continuity, and differentiability, directional derivative, gradient, divergence and curl of vector functions and their geometrical interpretation. We’ll start the first lecture by the collection of vector algebra results. In the next part, we’ll study the vector calculus. Finally, we’ll finish the integral calculus part with the calculation of area, rectification, volume and surface integrals. Afterwards we’ll look into multiple integrals, Beta and Gamma functions, Differentiation under the integral sign. We’ll then study improper integral, their convergence and learn about few tests which confirm the convergence. We then move to anti-derivatives and will look in to few classical theorems of integral calculus such as fundamental theorem of integral calculus. We’ll start with the concepts of partition, Riemann sum and Riemann Integrable functions and their properties.
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