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Vector Calculus for Engineers Lecture Notes for Jeffrey R. Chasnov The Hong Kong University of Science and Technology Department of Mathematics Clear Water Bay, Kowloon HongKong Copyright ©2019-2022 by Jeffrey Robert Chasnov This work is licensed under the Creative Commons Attribution 3.0 Hong Kong License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/hk/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. Preface View the promotional video on YouTube These are the lecture notes for my online Coursera course, Vector Calculus for Engineers. Students who take this course are expected to already know single-variable differential and integral calculus to the level of an introductory college calculus course. Students should also be familiar with matrices, and be able to compute a three-by-three determi- nant. I have divided these notes into chapters called Lectures, with each Lecture correspond- ing to a video on Coursera. I have also uploaded all my Coursera videos to YouTube, and links are placed at the top of each Lecture. There are some problems at the end of each lecture chapter. These problems are designed to exemplify the main ideas of the lecture. Students taking a formal university course in multivariable calculus will usually be assigned many more problems, some of them quite difficult, but here I follow the philosophy that less is more. I give enough problems for students to solidify their understanding of the material, but not so many that students feel overwhelmed. I do encourage students to attempt the given problems, but, if they get stuck, full solutions can be found in the Appendix. I have also included practice quizzes as an additional source of problems, with solutions also given. Jeffrey R. Chasnov HongKong October 2019 Contents I Vectors 1 1 Vectors 2 2 Cartesian coordinates 4 3 Dot product 6 4 Cross product 8 Practice quiz: Vectors 10 5 Analytic geometry of lines 11 6 Analytic geometry of planes 13 Practice quiz: Analytic geometry 15 7 Kronecker delta and Levi-Civita symbol 16 8 Vector identities 18 9 Scalar triple product 20 10 Vector triple product 22 Practice quiz: Vector algebra 24 11 Scalar and vector fields 25 II Differentiation 27 12 Partial derivatives 28 13 The method of least squares 30 14 Chain rule 32 15 Triple product rule 34 16 Triple product rule (example) 35 Practice quiz: Partial derivatives 37 17 Gradient 38 iv
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