![]() So the ith component of the curl of u, we can write using the Levi's Civita Tensor as Epsilon i j k. So typically when you're dealing with a vector quantity, you need to look at its components. We're going to be using the Levi's Civita Tensor and the Kronecker Deltas in these proofs. One is that you need to know how to write the curl of a vector field. So let me show you the identities you need to do a proof of these vector identities. We need some tools before we are going to a proof. I'll give you a couple of them to do as problems. In this video, I want to show you at least how to prove one of them. You may be wondering how do you prove identities like that. So in the last video, I introduced eight of these vector derivative identities. Watch the promotional video from the link ![]() Solutions to the problems and practice quizzes can be found in the instructor-provided lecture notes. At the end of each week, there is an assessed quiz. After each major topic, there is a short practice quiz. The course includes 53 concise lecture videos, each followed by a few problems to solve. A prerequisite for this course is two semesters of single variable calculus (differentiation and integration). Note that this course may also be referred to as Multivariable or Multivariate Calculus or Calculus 3 at some universities. These theorems are essential for subjects in engineering such as Electromagnetism and Fluid Mechanics. Line and surface integrals are covered in the fourth week, while the fifth week explores the fundamental theorems of vector calculus, including the gradient theorem, the divergence theorem, and Stokes' theorem. The third week focuses on multidimensional integration and curvilinear coordinate systems. In the second week, they will differentiate fields. During the first week, students will learn about scalar and vector fields. H.This course covers both the theoretical foundations and practical applications of Vector Calculus. A candidate's best TWO answers will be used for assessment. The final mark for Multivariable Calculus is calculated from a 1 ½ -hour written examination in April consisting of THREE questions. Lectures (15 in all), problems classes, homework and solutions (issued later). ![]() understand the main integral theorems of vector calculusĬlear logical thinking, problem solving, assimilation of abstract ideas and application to particular problems.understand and be able to evaluate line, surface and volume integrals. ![]()
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