Über diesen Kurs

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A course in single variable calculus

Ca. 22 Stunden zum Abschließen
Englisch

Was Sie lernen werden

  • 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

Kompetenzen, die Sie erwerben

Multivariable CalculusEngineering MathematicsCalculus Three
Zertifikat zur Vorlage
Erhalten Sie nach Abschluss ein Zertifikat
100 % online
Beginnen Sie sofort und lernen Sie in Ihrem eigenen Tempo.
Flexible Fristen
Setzen Sie Fristen gemäß Ihrem Zeitplan zurück.
Stufe „Anfänger“

A course in single variable calculus

Ca. 22 Stunden zum Abschließen
Englisch

von

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The Hong Kong University of Science and Technology

Lehrplan - Was Sie in diesem Kurs lernen werden

InhaltsbewertungThumbs Up97%(3,385 Bewertungen)Info
Woche
1

Woche 1

6 Stunden zum Abschließen

Vectors

6 Stunden zum Abschließen
15 Videos (Gesamt 133 min), 21 Lektüren, 5 Quiz
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
21 Lektüren
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
Levi-Civita Identities10m
The Levi-Civita Symbol and the Cross Product5m
Kronecker-Delta Identities5m
Levi-Civita and Kronecker-Delta Identities10m
Jacobi Identity5m
Lagrange's Identity in Three Dimensions5m
Examples of Scalar and Vector Fields5m
5 praktische Übungen
Diagnostic Quiz5m
Vectors15m
Analytic Geometry15m
Vector Algebra10m
Week One Assessment30m
Woche
2

Woche 2

5 Stunden zum Abschließen

Differentiation

5 Stunden zum Abschließen
13 Videos (Gesamt 122 min), 13 Lektüren, 4 Quiz
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 Lektüren
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 praktische Übungen
Partial Derivatives15m
The Del Operator15m
Vector Calculus Algebra15m
Week Two Assessment30m
Woche
3

Woche 3

5 Stunden zum Abschließen

Integration and Curvilinear Coordinates

5 Stunden zum Abschließen
12 Videos (Gesamt 117 min), 20 Lektüren, 5 Quiz
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 Lektüren
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 praktische Übungen
Multidimensional Integration15m
Polar Coordinates15m
Cylindrical and Spherical Coordinates15m
Vector Integration15m
Week Three Assessment30m
Woche
4

Woche 4

6 Stunden zum Abschließen

Fundamental Theorems

6 Stunden zum Abschließen
12 Videos (Gesamt 111 min), 18 Lektüren, 4 Quiz
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 Lektüren
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 Equation20m
Electric Field of a Point Charge10m
Magnetic Field of a Wire10m
Please Rate this Course1m
Acknowledgments1m
4 praktische Übungen
Gradient Theorem15m
Divergence Theorem15m
Stokes' Theorem15m
Week Four Assessment30m

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