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初級

A course in single variable calculus

完成時間大約為22 小時
英語(English)
字幕:英語(English)

您將學到的內容有

  • 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

您將獲得的技能

Multivariable CalculusEngineering MathematicsCalculus Three
可分享的證書
完成後獲得證書
100% 在線
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根據您的日程表重置截止日期。
初級

A course in single variable calculus

完成時間大約為22 小時
英語(English)
字幕:英語(English)

提供方

香港科技大学 徽標

香港科技大学

教學大綱 - 您將從這門課程中學到什麼

內容評分Thumbs Up97%(1,910 個評分)Info
1

1

完成時間為 6 小時

Vectors

完成時間為 6 小時
15 個視頻 (總計 133 分鐘), 20 個閱讀材料, 5 個測驗
15 個視頻
Course Overview2分鐘
Introduction1分鐘
Vectors | Lecture 18分鐘
Cartesian Coordinates | Lecture 210分鐘
Dot Product | Lecture 39分鐘
Cross Product | Lecture 410分鐘
Analytic Geometry of Lines | Lecture 510分鐘
Analytic Geometry of Planes | Lecture 612分鐘
Kronecker Delta and Levi-Civita Symbol | Lecture 716分鐘
Vector Identities | Lecture 812分鐘
Vector Triple Product | Tutorial7分鐘
Scalar and Vector Fields | Lecture 98分鐘
Matrix Addition and Multiplication9分鐘
Matrix Determinants and Inverses8分鐘
20 個閱讀材料
Welcome and Course Information1分鐘
How to Write Math in the Discussions using MathJax1分鐘
Associative Law5分鐘
Triangle Midpoint Theorem10分鐘
Newton's equation for the force between two masses10分鐘
Commutative and Distributive Properties10分鐘
Dot Product between Standard Unit Vectors5分鐘
Law of Cosines10分鐘
Do you know matrices?1分鐘
Commutative and Distributive Properties10分鐘
Cross Product Between Standard Unit Vectors5分鐘
Associative Property10分鐘
Parametric Equation for a Line5分鐘
Equation for a Plane10分鐘
Cross Product5分鐘
Kronecker Delta Identities5分鐘
Levi-Civita Identities5分鐘
Jacobi Identity5分鐘
Lagrange's Identity in Three Dimensions5分鐘
Examples of Scalar and Vector Fields5分鐘
5 個練習
Diagnostic Quiz5分鐘
Vectors15分鐘
Analytic Geometry15分鐘
Vector Algebra10分鐘
Week One Assessment30分鐘
2

2

完成時間為 5 小時

Differentiation

完成時間為 5 小時
13 個視頻 (總計 122 分鐘), 13 個閱讀材料, 4 個測驗
13 個視頻
Partial Derivatives | Lecture 1010分鐘
The Method of Least Squares | Lecture 1113分鐘
Chain Rule | Lecture 129分鐘
Triple Product Rule | Lecture 1310分鐘
Triple Product Rule: Example | Lecture 147分鐘
Gradient | Lecture 157分鐘
Divergence | Lecture 1612分鐘
Curl | Lecture 1712分鐘
Laplacian | Lecture 186分鐘
Vector Derivative Identities | Lecture 197分鐘
Vector Derivative Identities (Proof) | Lecture 2013分鐘
Electromagnetic Waves | Lecture 219分鐘
13 個閱讀材料
Computing Partial Derivatives10分鐘
Taylor Series Expansions10分鐘
Least-squares Method10分鐘
Chain Rule10分鐘
Triple Product Rule for a Linear Function10分鐘
Quadruple Product Rule10分鐘
Computing the Gradient10分鐘
Computing the Divergence5分鐘
Computing the Curl10分鐘
Computing the Laplacian10分鐘
Vector Derivative Identities10分鐘
The Material Acceleration10分鐘
Wave Equation for the Magnetic Field10分鐘
4 個練習
Partial Derivatives15分鐘
The Del Operator15分鐘
Vector Calculus Algebra15分鐘
Week Two Assessment30分鐘
3

3

完成時間為 5 小時

Integration and Curvilinear Coordinates

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

4

完成時間為 5 小時

Fundamental Theorems

完成時間為 5 小時
12 個視頻 (總計 111 分鐘), 18 個閱讀材料, 4 個測驗
12 個視頻
Gradient Theorem | Lecture 339分鐘
Conservative Vector Fields | Lecture 3413分鐘
Divergence Theorem | Lecture 3515分鐘
Divergence Theorem: Example I | Lecture 3612分鐘
Divergence Theorem: Example II | Lecture 3710分鐘
Continuity Equation | Lecture 389分鐘
Green's Theorem | Lecture 399分鐘
Stokes' Theorem | Lecture 405分鐘
Meaning of the Divergence and the Curl | Lecture 4110分鐘
Maxwell's Equations | Lecture 4211分鐘
Concluding Remarks1分鐘
18 個閱讀材料
Gradient Theorem10分鐘
Conservative Vector Fields10分鐘
Divergence Theorem for a Sphere10分鐘
Test the Divergence Theorem for a Cube10分鐘
Divergence Theorem for a Cube10分鐘
Test the Divergence Theorem for a Sphere10分鐘
Divergence Theorem for a Sphere10分鐘
Continuity Equation5分鐘
Electrodynamics Continuity Equation10分鐘
Test Green's Theorem for a Square10分鐘
Test Green's Theorem for a Circle10分鐘
Stokes' Theorem in Two Dimensions5分鐘
Test Stokes' Theorem10分鐘
The Navier-Stokes Equation2分鐘
Electric Field of a Point Charge5分鐘
Magnetic Field of a Wire5分鐘
Please Rate this Course1分鐘
Acknowledgments1分鐘
4 個練習
Gradient Theorem15分鐘
Divergence Theorem15分鐘
Stokes' Theorem15分鐘
Week Four Assessment30分鐘

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