Calculus 3: Multivariable Calculus
Study vectors, 3-D geometry, vector functions, partial derivatives, multiple integrals, and vector fields.
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About this course
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.
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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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