## 课程信息

101,061 次近期查看

100% 在线

A course in single variable calculus

### 您将获得的技能

Multivariable CalculusEngineering MathematicsCalculus Three

100% 在线

A course in single variable calculus

### 提供方 1

## Vectors

15 个视频 （总计 133 分钟）, 21 个阅读材料, 5 个测验
15 个视频
Course Overview2分钟
Introduction1分钟
Vectors | Lecture 18分钟
Cartesian Coordinates | Lecture 210分钟
Dot Product | Lecture 39分钟
Cross Product | Lecture 410分钟
Analytic Geometry of Lines | Lecture 510分钟
Analytic Geometry of Planes | Lecture 612分钟
Kronecker Delta and Levi-Civita Symbol | Lecture 716分钟
Vector Identities | Lecture 812分钟
Vector Triple Product | Tutorial7分钟
Scalar and Vector Fields | Lecture 98分钟
Matrix Determinants and Inverses8分钟
21 个阅读材料
Welcome and Course Information1分钟
How to Write Math in the Discussions using MathJax1分钟
Associative Law5分钟
Triangle Midpoint Theorem10分钟
Newton's equation for the force between two masses10分钟
Commutative and Distributive Properties10分钟
Dot Product between Standard Unit Vectors5分钟
Law of Cosines10分钟
Do you know matrices?1分钟
Commutative and Distributive Properties10分钟
Cross Product Between Standard Unit Vectors5分钟
Associative Property10分钟
Parametric Equation for a Line5分钟
Equation for a Plane10分钟
Levi-Civita Identities10分钟
The Levi-Civita Symbol and the Cross Product5分钟
Kronecker-Delta Identities5分钟
Levi-Civita and Kronecker-Delta Identities10分钟
Jacobi Identity5分钟
Lagrange's Identity in Three Dimensions5分钟
Examples of Scalar and Vector Fields5分钟
5 个练习
Diagnostic Quiz5分钟
Vectors15分钟
Analytic Geometry15分钟
Vector Algebra10分钟
Week One Assessment30分钟
2

## Differentiation

13 个视频 （总计 122 分钟）, 13 个阅读材料, 4 个测验
13 个视频
Partial Derivatives | Lecture 1010分钟
The Method of Least Squares | Lecture 1113分钟
Chain Rule | Lecture 129分钟
Triple Product Rule | Lecture 1310分钟
Triple Product Rule: Example | Lecture 147分钟
Divergence | Lecture 1612分钟
Curl | Lecture 1712分钟
Laplacian | Lecture 186分钟
Vector Derivative Identities | Lecture 197分钟
Vector Derivative Identities (Proof) | Lecture 2013分钟
Electromagnetic Waves | Lecture 219分钟
13 个阅读材料
Computing Partial Derivatives10分钟
Taylor Series Expansions10分钟
Least-squares Method10分钟
Chain Rule10分钟
Triple Product Rule for a Linear Function10分钟
Computing the Divergence5分钟
Computing the Curl10分钟
Computing the Laplacian10分钟
Vector Derivative Identities10分钟
The Material Acceleration10分钟
Wave Equation for the Magnetic Field10分钟
4 个练习
Partial Derivatives15分钟
The Del Operator15分钟
Vector Calculus Algebra15分钟
Week Two Assessment30分钟
3

## Integration and Curvilinear Coordinates

12 个视频 （总计 117 分钟）, 20 个阅读材料, 5 个测验
12 个视频
Double and Triple Integrals | Lecture 229分钟
Example: Double Integral with Triangle Base | Lecture 239分钟
Polar Coordinates | Lecture 2415分钟
Central Force | Lecture 2514分钟
Change of Variables (single integral) | Lecture 269分钟
Change of Variables (double integral) | Lecture 2710分钟
Cylindrical Coordinates | Lecture 288分钟
Spherical Coordinates (Part A) | Lecture 296分钟
Spherical Coordinates (Part B) | Lecture 306分钟
Line Integral of a Vector Field | Lecture 3114分钟
Surface Integral of a Vector Field | Lecture 3210分钟
20 个阅读材料
Computing the Mass of a Cube10分钟
Volume of a surface above a parallelogram10分钟
Inverse Formula5分钟
Some Common Two-Dimensional Vectors5分钟
Angular Momentum5分钟
Mass of a Disk10分钟
Gaussian Integral10分钟
Del in Cylindrical Coordinates5分钟
Divergence of a Unit Vector5分钟
Divergence and Curl of the Unit Vectors5分钟
Spherical and Cartesian Unit Vectors5分钟
Change-of-variables formula5分钟
Integrating a function that only depends on distance from the origin5分钟
Mass of a Sphere5分钟
Derivatives of the Unit Vectors5分钟
Divergence and Curl of the Unit Vectors5分钟
Laplacian of 1/r5分钟
Line Integral around a Square5分钟
Line Integral around a Circle5分钟
Surface Integral over a Sphere5分钟
5 个练习
Multidimensional Integration15分钟
Polar Coordinates15分钟
Cylindrical and Spherical Coordinates15分钟
Vector Integration15分钟
Week Three Assessment30分钟
4

## Fundamental Theorems

12 个视频 （总计 111 分钟）, 18 个阅读材料, 4 个测验
12 个视频
Conservative Vector Fields | Lecture 3413分钟
Divergence Theorem | Lecture 3515分钟
Divergence Theorem: Example I | Lecture 3612分钟
Divergence Theorem: Example II | Lecture 3710分钟
Continuity Equation | Lecture 389分钟
Green's Theorem | Lecture 399分钟
Stokes' Theorem | Lecture 405分钟
Meaning of the Divergence and the Curl | Lecture 4110分钟
Maxwell's Equations | Lecture 4211分钟
Concluding Remarks1分钟
18 个阅读材料
Conservative Vector Fields10分钟
Divergence Theorem for a Sphere10分钟
Test the Divergence Theorem for a Cube10分钟
Divergence Theorem for a Cube10分钟
Test the Divergence Theorem for a Sphere10分钟
Divergence Theorem for a Sphere10分钟
Continuity Equation5分钟
Electrodynamics Continuity Equation10分钟
Test Green's Theorem for a Square10分钟
Test Green's Theorem for a Circle10分钟
Stokes' Theorem in Two Dimensions5分钟
Test Stokes' Theorem10分钟
The Navier-Stokes Equation20分钟
Electric Field of a Point Charge10分钟
Magnetic Field of a Wire10分钟
Acknowledgments1分钟
4 个练习