MathematicsAdvanced

Calculus 3: Multivariable Calculus

Study vectors, 3-D geometry, vector functions, partial derivatives, multiple integrals, and vector fields.

34 lessons34 quizzes34 video lessons

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Calculus 3: Multivariable Calculus
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About this course

This Calculus 3: Multivariable Calculus course follows the client-provided YouTube video list. Students can register for free and watch each lesson video without a subscription.

Quiz and transcript rule: quizzes unlock after the one-time $10 Quiz Proctor Fee is paid for this course. Students must complete all published Calculus 3 quizzes with a score of 90% or better for the course to appear as completed on their transcript.

One lesson at a time

Your learning journey

34 lessons · 34 assessments

01Calculus 3 Lecture 11.1: An Introduction to VectorsVideo lesson · Quiz

Use vectors and vector functions to describe position, motion, length, curvature, and moving frames.

02Calculus 3 Lecture 11.2: Vectors in 3-D Coordinate SystemVideo lesson · Quiz

Describe objects in three-dimensional space using coordinates, vectors, lines, planes, and surfaces.

03Calculus 3 Lecture 11.3: Using the Dot ProductVideo lesson · Quiz

Use the dot product to measure projection, angle, orthogonality, and work between vectors.

04Calculus 3 Lecture 11.4: The Cross ProductVideo lesson · Quiz

Use the cross product to create perpendicular vectors and measure parallelogram area.

05Calculus 3 Lecture 11.5: Lines and Planes in 3-DVideo lesson · Quiz

Describe objects in three-dimensional space using coordinates, vectors, lines, planes, and surfaces.

06Calculus 3 Lecture 11.6: Cylinders and Surfaces in 3-DVideo lesson · Quiz

Describe objects in three-dimensional space using coordinates, vectors, lines, planes, and surfaces.

07Calculus 3 Lecture 11.7: Using Cylindrical and Spherical CoordinatesVideo lesson · Quiz

Describe objects in three-dimensional space using coordinates, vectors, lines, planes, and surfaces.

08Calculus 3 Lecture 12.1: An Introduction To Vector FunctionsVideo lesson · Quiz

Use vectors and vector functions to describe position, motion, length, curvature, and moving frames.

09Calculus 3 Lecture 12.2: Derivatives and Integrals of Vector FunctionsVideo lesson · Quiz

Use vectors and vector functions to describe position, motion, length, curvature, and moving frames.

10Calculus 3 Lecture 12.3: Arc Length/Parameterization, TNB (Frenet-Serret) IntroVideo lesson · Quiz

Use vectors and vector functions to describe position, motion, length, curvature, and moving frames.

11Calculus 3 Lecture 12.3/12.5: TNB (Frenet-Serret) Frames, Curvature, Torsion, EncapsulationVideo lesson · Quiz

Use vectors and vector functions to describe position, motion, length, curvature, and moving frames.

12Calculus 3 Lecture 12.4: Velocity and Acceleration of Vector FunctionsVideo lesson · Quiz

Use vectors and vector functions to describe position, motion, length, curvature, and moving frames.

13Calculus 3 Lecture 13.1: Intro to Multivariable Functions (Domain, Sketching, Level Curves)Video lesson · Quiz

Study functions of several variables through limits, continuity, partial derivatives, gradients, tangent planes, and optimization.

14Calculus 3 Lecture 13.2: Limits and Continuity of Multivariable Functions (with Squeeze Th.)Video lesson · Quiz

Study functions of several variables through limits, continuity, partial derivatives, gradients, tangent planes, and optimization.

15Calculus 3 Lecture 13.3: Partial Derivatives (Derivatives of Multivariable Functions)Video lesson · Quiz

Study functions of several variables through limits, continuity, partial derivatives, gradients, tangent planes, and optimization.

16Calculus 3 Lecture 13.4: Finding Differentials of Multivariable FunctionsVideo lesson · Quiz

Study functions of several variables through limits, continuity, partial derivatives, gradients, tangent planes, and optimization.

17Calculus 3 Lecture 13.5: The Chain Rule for Multivariable FunctionsVideo lesson · Quiz

Study functions of several variables through limits, continuity, partial derivatives, gradients, tangent planes, and optimization.

18Calculus 3 Lecture 13.6: Finding Directional Derivatives and GradientsVideo lesson · Quiz

Study functions of several variables through limits, continuity, partial derivatives, gradients, tangent planes, and optimization.

19Calculus 3 Lecture 13.7: Finding Tangent Planes and Normal Lines to SurfacesVideo lesson · Quiz

Describe objects in three-dimensional space using coordinates, vectors, lines, planes, and surfaces.

20Calculus 3 Lecture 13.8: Finding Extrema of Functions of 2 Variables (Max and Min)Video lesson · Quiz

Study functions of several variables through limits, continuity, partial derivatives, gradients, tangent planes, and optimization.

21Calculus 3 Lecture 13.9: Constrained Optimization with LaGrange MultipliersVideo lesson · Quiz

Study functions of several variables through limits, continuity, partial derivatives, gradients, tangent planes, and optimization.

22Calculus 3 Lecture 14.1: INTRODUCTION to Double Integrals (Background Info)Video lesson · Quiz

Set up and evaluate multiple integrals over regions in rectangular, polar, cylindrical, and spherical coordinates.

23Calculus 3 Lecture 14.2: How to Solve Double/Repeated/Iterated IntegralsVideo lesson · Quiz

Set up and evaluate multiple integrals over regions in rectangular, polar, cylindrical, and spherical coordinates.

24Calculus 3 Lecture 14.3: Double Integrals over POLAR REGIONSVideo lesson · Quiz

Set up and evaluate multiple integrals over regions in rectangular, polar, cylindrical, and spherical coordinates.

25Calculus 3 Lecture 14.4: Center of Mass (and Moments of Mass and Inertia) for Lamina in 2-DVideo lesson · Quiz

Set up and evaluate multiple integrals over regions in rectangular, polar, cylindrical, and spherical coordinates.

26Calculus 3 Lecture 14.6: How to Solve TRIPLE INTEGRALS (Along with Center of Mass and Volume)Video lesson · Quiz

Set up and evaluate multiple integrals over regions in rectangular, polar, cylindrical, and spherical coordinates.

27Calculus 3 Lecture 14.7: TRIPLE Integrals Over Regions with CYLINDRICAL or SPHERICAL Coord.Video lesson · Quiz

Describe objects in three-dimensional space using coordinates, vectors, lines, planes, and surfaces.

28Calculus 3 Lecture 14.8: How to Change Variables in Multiple Integrals (Using the Jacobian)Video lesson · Quiz

Set up and evaluate multiple integrals over regions in rectangular, polar, cylindrical, and spherical coordinates.

29Calculus 3 Lecture 15.1: INTRODUCTION to Vector Fields (and what makes them Conservative)Video lesson · Quiz

Analyze vector fields using conservative fields, divergence, curl, line integrals, Green theorem, flux, and surface integrals.

30Calculus 3 Lecture 15.2: How to Find Divergence and Curl of Vector FieldsVideo lesson · Quiz

Analyze vector fields using conservative fields, divergence, curl, line integrals, Green theorem, flux, and surface integrals.

31Calculus 3 Lecture 15.3: How to Compute Line Integrals (Over Non-Conservative V.Fields)Video lesson · Quiz

Set up and evaluate multiple integrals over regions in rectangular, polar, cylindrical, and spherical coordinates.

32Line Integrals on CONSERVATIVE Vector Fields (Independence of Path): Calculus 3 Lecture 15.4Video lesson · Quiz

Set up and evaluate multiple integrals over regions in rectangular, polar, cylindrical, and spherical coordinates.

33Green's Theorem: Calculus 3 Lecture 15.5Video lesson · Quiz

Analyze vector fields using conservative fields, divergence, curl, line integrals, Green theorem, flux, and surface integrals.

34Surface And Flux Integrals, Parametric Surf., Divergence/Stoke's Theorem: Calculus 3 Lecture 15.6_9Video lesson · Quiz

Set up and evaluate multiple integrals over regions in rectangular, polar, cylindrical, and spherical coordinates.

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Notes & resources

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