About this Course

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Beginner Level

A course in single variable calculus

Approx. 22 hours to complete

English

Subtitles: English

What you will learn

  • 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

Skills you will gain

Multivariable CalculusEngineering MathematicsCalculus Three

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Beginner Level

A course in single variable calculus

Approx. 22 hours to complete

English

Subtitles: English

Offered by

The Hong Kong University of Science and Technology logo

The Hong Kong University of Science and Technology

Syllabus - What you will learn from this course

Content RatingThumbs Up97%(1,018 ratings)Info
Week
1

Week 1

6 hours to complete

Vectors

6 hours to complete
15 videos (Total 133 min), 20 readings, 5 quizzes
15 videos
Course Overview2m
Introduction1m
Vectors | Lecture 18m
Cartesian Coordinates | Lecture 210m
Dot Product | Lecture 39m
Cross Product | Lecture 410m
Analytic Geometry of Lines | Lecture 510m
Analytic Geometry of Planes | Lecture 612m
Kronecker Delta and Levi-Civita Symbol | Lecture 716m
Vector Identities | Lecture 812m
Vector Triple Product | Tutorial7m
Scalar and Vector Fields | Lecture 98m
Matrix Addition and Multiplication9m
Matrix Determinants and Inverses8m
20 readings
Welcome and Course Information1m
How to Write Math in the Discussions using MathJax1m
Associative Law5m
Triangle Midpoint Theorem10m
Newton's equation for the force between two masses10m
Commutative and Distributive Properties10m
Dot Product between Standard Unit Vectors5m
Law of Cosines10m
Do you know matrices?1m
Commutative and Distributive Properties10m
Cross Product Between Standard Unit Vectors5m
Associative Property10m
Parametric Equation for a Line5m
Equation for a Plane10m
Cross Product5m
Kronecker Delta Identities5m
Levi-Civita Identities5m
Jacobi Identity5m
Lagrange's Identity in Three Dimensions5m
Examples of Scalar and Vector Fields5m
5 practice exercises
Diagnostic Quiz5m
Vectors15m
Analytic Geometry15m
Vector Algebra10m
Week One Assessment30m
Week
2

Week 2

5 hours to complete

Differentiation

5 hours to complete
13 videos (Total 122 min), 13 readings, 4 quizzes
13 videos
Partial Derivatives | Lecture 1010m
The Method of Least Squares | Lecture 1113m
Chain Rule | Lecture 129m
Triple Product Rule | Lecture 1310m
Triple Product Rule: Example | Lecture 147m
Gradient | Lecture 157m
Divergence | Lecture 1612m
Curl | Lecture 1712m
Laplacian | Lecture 186m
Vector Derivative Identities | Lecture 197m
Vector Derivative Identities (Proof) | Lecture 2013m
Electromagnetic Waves | Lecture 219m
13 readings
Computing Partial Derivatives10m
Taylor Series Expansions10m
Least-squares Method10m
Chain Rule10m
Triple Product Rule for a Linear Function10m
Quadruple Product Rule10m
Computing the Gradient10m
Computing the Divergence5m
Computing the Curl10m
Computing the Laplacian10m
Vector Derivative Identities10m
The Material Acceleration10m
Wave Equation for the Magnetic Field10m
4 practice exercises
Partial Derivatives15m
The Del Operator15m
Vector Calculus Algebra15m
Week Two Assessment30m
Week
3

Week 3

5 hours to complete

Integration and Curvilinear Coordinates

5 hours to complete
12 videos (Total 117 min), 20 readings, 5 quizzes
12 videos
Double and Triple Integrals | Lecture 229m
Example: Double Integral with Triangle Base | Lecture 239m
Polar Coordinates | Lecture 2415m
Central Force | Lecture 2514m
Change of Variables (single integral) | Lecture 269m
Change of Variables (double integral) | Lecture 2710m
Cylindrical Coordinates | Lecture 288m
Spherical Coordinates (Part A) | Lecture 296m
Spherical Coordinates (Part B) | Lecture 306m
Line Integral of a Vector Field | Lecture 3114m
Surface Integral of a Vector Field | Lecture 3210m
20 readings
Computing the Mass of a Cube10m
Volume of a surface above a parallelogram10m
Inverse Formula5m
Some Common Two-Dimensional Vectors5m
Angular Momentum5m
Mass of a Disk10m
Gaussian Integral10m
Del in Cylindrical Coordinates5m
Divergence of a Unit Vector5m
Divergence and Curl of the Unit Vectors5m
Spherical and Cartesian Unit Vectors5m
Change-of-variables formula5m
Integrating a function that only depends on distance from the origin5m
Mass of a Sphere5m
Derivatives of the Unit Vectors5m
Divergence and Curl of the Unit Vectors5m
Laplacian of 1/r5m
Line Integral around a Square5m
Line Integral around a Circle5m
Surface Integral over a Sphere5m
5 practice exercises
Multidimensional Integration15m
Polar Coordinates15m
Cylindrical and Spherical Coordinates15m
Vector Integration15m
Week Three Assessment30m
Week
4

Week 4

5 hours to complete

Fundamental Theorems

5 hours to complete
12 videos (Total 111 min), 18 readings, 4 quizzes
12 videos
Gradient Theorem | Lecture 339m
Conservative Vector Fields | Lecture 3413m
Divergence Theorem | Lecture 3515m
Divergence Theorem: Example I | Lecture 3612m
Divergence Theorem: Example II | Lecture 3710m
Continuity Equation | Lecture 389m
Green's Theorem | Lecture 399m
Stokes' Theorem | Lecture 405m
Meaning of the Divergence and the Curl | Lecture 4110m
Maxwell's Equations | Lecture 4211m
Concluding Remarks1m
18 readings
Gradient Theorem10m
Conservative Vector Fields10m
Divergence Theorem for a Sphere10m
Test the Divergence Theorem for a Cube10m
Divergence Theorem for a Cube10m
Test the Divergence Theorem for a Sphere10m
Divergence Theorem for a Sphere10m
Continuity Equation5m
Electrodynamics Continuity Equation10m
Test Green's Theorem for a Square10m
Test Green's Theorem for a Circle10m
Stokes' Theorem in Two Dimensions5m
Test Stokes' Theorem10m
The Navier-Stokes Equation2m
Electric Field of a Point Charge5m
Magnetic Field of a Wire5m
Please Rate this Course1m
Acknowledgments1m
4 practice exercises
Gradient Theorem15m
Divergence Theorem15m
Stokes' Theorem15m
Week Four Assessment30m

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