We cover both basic theory and applications. In the first week we learn about scalar and vector fields, in the second week about differentiating fields, in the third week about integrating fields. The fourth week covers the fundamental theorems of vector calculus, including the gradient theorem, the divergence theorem and Stokes’ theorem. These theorems are needed in core engineering subjects such as Electromagnetism and Fluid Mechanics.
Vector Calculus for Engineers
Université des sciences et technologies de Hong KongÀ propos de ce cours
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Niveau débutant
A course in single variable calculus
Approx. 23 heures pour terminer
Anglais
Sous-titres : Anglais
Ce que vous allez apprendre
The dot product and cross product
The gradient, divergence, curl, and Laplacian
Multivariable integration, line integrals, flux integrals, cylindrical and spherical coordinates
The gradient theorem, divergence theorem and Stokes' theorem
Compétences que vous acquerrez
Multivariable CalculusEngineering MathematicsCalculus Three
Certificat partageable
Obtenez un Certificat lorsque vous terminez
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
Niveau débutant
A course in single variable calculus
Approx. 23 heures pour terminer
Anglais
Sous-titres : Anglais
Offert par
Université des sciences et technologies de Hong Kong
HKUST - A dynamic, international research university, in relentless pursuit of excellence, leading the advance of science and technology, and educating the new generation of front-runners for Asia and the world.
Programme du cours : ce que vous apprendrez dans ce cours
6 heures pour terminer
Vectors
A vector is a mathematical construct that has both length and direction. We will define vectors and learn how to add and subtract them, and how to multiply them using the scalar and vector products (dot and cross products). We will use vectors to learn some analytical geometry of lines and planes, and learn about the Kronecker delta and the Levi-Civita symbol to prove vector identities. The important concepts of scalar and vector fields will be introduced.
6 heures pour terminer
15 vidéos (Total 133 min), 21 lectures, 5 quiz
15 vidéos
Promotional Video3 min
Course Overview2 min
Introduction1 min
Vectors | Lecture 18 min
Cartesian Coordinates | Lecture 210 min
Dot Product | Lecture 39 min
Cross Product | Lecture 410 min
Analytic Geometry of Lines | Lecture 510 min
Analytic Geometry of Planes | Lecture 612 min
Kronecker Delta and Levi-Civita Symbol | Lecture 716 min
Vector Identities | Lecture 812 min
Vector Triple Product | Tutorial7 min
Scalar and Vector Fields | Lecture 98 min
Matrix Addition and Multiplication9 min
Matrix Determinants and Inverses8 min
21 lectures
Welcome and Course Information1 min
How to Write Math in the Discussions using MathJax1 min
Associative Law5 min
Triangle Midpoint Theorem10 min
Newton's equation for the force between two masses10 min
Commutative and Distributive Properties10 min
Dot Product between Standard Unit Vectors5 min
Law of Cosines10 min
Do you know matrices?1 min
Commutative and Distributive Properties10 min
Cross Product Between Standard Unit Vectors5 min
Associative Property10 min
Parametric Equation for a Line5 min
Equation for a Plane10 min
Levi-Civita Identities10 min
The Levi-Civita Symbol and the Cross Product5 min
Kronecker-Delta Identities5 min
Levi-Civita and Kronecker-Delta Identities10 min
Jacobi Identity5 min
Lagrange's Identity in Three Dimensions5 min
Examples of Scalar and Vector Fields5 min
5 exercices pour s'entraîner
Diagnostic Quiz5 min
Vectors15 min
Analytic Geometry15 min
Vector Algebra10 min
Week One Assessment30 min
5 heures pour terminer
Differentiation
Scalar and vector fields can be differentiated. We define the partial derivative and derive the method of least squares as a minimization problem. We learn how to use the chain rule for a function of several variables, and derive the triple product rule used in chemical engineering. From the del differential operator, we define the gradient, divergence, curl and Laplacian. We learn some useful vector calculus identities and how to derive them using the Kronecker delta and Levi-Civita symbol. Vector identities are then used to derive the electromagnetic wave equation from Maxwell's equation in free space. Electromagnetic waves form the basis for all modern communication technologies.
5 heures pour terminer
13 vidéos (Total 122 min), 13 lectures, 4 quiz
13 vidéos
Introduction57s
Partial Derivatives | Lecture 1010 min
The Method of Least Squares | Lecture 1113 min
Chain Rule | Lecture 129 min
Triple Product Rule | Lecture 1310 min
Triple Product Rule: Example | Lecture 147 min
Gradient | Lecture 157 min
Divergence | Lecture 1612 min
Curl | Lecture 1712 min
Laplacian | Lecture 186 min
Vector Derivative Identities | Lecture 197 min
Vector Derivative Identities (Proof) | Lecture 2013 min
Electromagnetic Waves | Lecture 219 min
13 lectures
Computing Partial Derivatives10 min
Taylor Series Expansions10 min
Least-squares Method10 min
Chain Rule10 min
Triple Product Rule for a Linear Function10 min
Quadruple Product Rule10 min
Computing the Gradient10 min
Computing the Divergence5 min
Computing the Curl10 min
Computing the Laplacian10 min
Vector Derivative Identities10 min
The Material Acceleration10 min
Wave Equation for the Magnetic Field10 min
4 exercices pour s'entraîner
Partial Derivatives15 min
The Del Operator15 min
Vector Calculus Algebra15 min
Week Two Assessment30 min
5 heures pour terminer
Integration and Curvilinear Coordinates
Scalar and vector fields can be integrated. We learn about double and triple integrals, and line integrals and surface integrals. Curvilinear coordinates, namely polar coordinates in two dimensions, and cylindrical and spherical coordinates in three dimensions, are used to simplify problems with cylindrical or spherical symmetry. We learn how to change variables in multidimensional integrals using the Jacobian of the transformation.
5 heures pour terminer
12 vidéos (Total 117 min), 20 lectures, 5 quiz
12 vidéos
Introduction1 min
Double and Triple Integrals | Lecture 229 min
Example: Double Integral with Triangle Base | Lecture 239 min
Polar Coordinates | Lecture 2415 min
Central Force | Lecture 2514 min
Change of Variables (single integral) | Lecture 269 min
Change of Variables (double integral) | Lecture 2710 min
Cylindrical Coordinates | Lecture 288 min
Spherical Coordinates (Part A) | Lecture 296 min
Spherical Coordinates (Part B) | Lecture 306 min
Line Integral of a Vector Field | Lecture 3114 min
Surface Integral of a Vector Field | Lecture 3210 min
20 lectures
Computing the Mass of a Cube10 min
Volume of a surface above a parallelogram10 min
Inverse Formula5 min
Some Common Two-Dimensional Vectors5 min
Angular Momentum5 min
Mass of a Disk10 min
Gaussian Integral10 min
Del in Cylindrical Coordinates5 min
Divergence of a Unit Vector5 min
Divergence and Curl of the Unit Vectors5 min
Spherical and Cartesian Unit Vectors5 min
Change-of-variables formula5 min
Integrating a function that only depends on distance from the origin5 min
Mass of a Sphere5 min
Derivatives of the Unit Vectors5 min
Divergence and Curl of the Unit Vectors5 min
Laplacian of 1/r5 min
Line Integral around a Square5 min
Line Integral around a Circle5 min
Surface Integral over a Sphere5 min
5 exercices pour s'entraîner
Multidimensional Integration15 min
Polar Coordinates15 min
Cylindrical and Spherical Coordinates15 min
Vector Integration15 min
Week Three Assessment30 min
6 heures pour terminer
Fundamental Theorems
The fundamental theorem of calculus links integration with differentiation. Here, we learn the related fundamental theorems of vector calculus. These include the gradient theorem, the divergence theorem, and Stokes' theorem. We show how these theorems are used to derive continuity equations, define the divergence and curl in coordinate-free form, and convert the integral version of Maxwell's equations into their more famous differential form.
6 heures pour terminer
12 vidéos (Total 111 min), 19 lectures, 4 quiz
12 vidéos
Introduction1 min
Gradient Theorem | Lecture 339 min
Conservative Vector Fields | Lecture 3413 min
Divergence Theorem | Lecture 3515 min
Divergence Theorem: Example I | Lecture 3612 min
Divergence Theorem: Example II | Lecture 3710 min
Continuity Equation | Lecture 389 min
Green's Theorem | Lecture 399 min
Stokes' Theorem | Lecture 405 min
Meaning of the Divergence and the Curl | Lecture 4110 min
Maxwell's Equations | Lecture 4211 min
Concluding Remarks1 min
19 lectures
Gradient Theorem10 min
Conservative Vector Fields10 min
Divergence Theorem for a Sphere10 min
Test the Divergence Theorem for a Cube10 min
Divergence Theorem for a Cube10 min
Test the Divergence Theorem for a Sphere10 min
Flux Integral of the Position Vector10 min
Volume Integral of the Laplacian of 1/r10 min
Continuity Equation5 min
Electrodynamics Continuity Equation10 min
Test Green's Theorem for a Square10 min
Test Green's Theorem for a Circle10 min
Stokes' Theorem in Two Dimensions5 min
Test Stokes' Theorem10 min
The Navier-Stokes Equation20 min
Electric Field of a Point Charge10 min
Magnetic Field of a Wire10 min
Please Rate this Course1 min
Acknowledgments1 min
4 exercices pour s'entraîner
Gradient Theorem15 min
Divergence Theorem15 min
Stokes' Theorem15 min
Week Four Assessment30 min
Avis
Meilleurs avis pour VECTOR CALCULUS FOR ENGINEERS
par DK22 mai 2020
i have completed Three courses of Professor Jeffrey. I'm so happy that i learnt a lot from him. Thanks to our professor Jeffrey and thanks to The Hong Kong University of Science and Technology.
par KO17 juil. 2020
It was great, the professor did a great job in explanation, but at the same time, he didn't explain further with examples for some topics which made it really challenging for me to understand.
par RB3 mai 2020
This course is very well organized and well explained. I am very much thankful to Prof Jeffrey R. Chasnov for his fruitful videos which help us to update our knowledge in this area.
par AO1 août 2020
This course is very well organized and well explained. I am very much thankful to Prof Jeffrey R. Chasnov for his fruitful videos which help us to update our knowledge in this area.
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