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The following video provides an outline of all the topics you would expect to see in a typical Multivariable Calculus class (i.e., Calculus 3, Vector Calculus, Multivariate Calculus).
All the topics are covered in detail in our Online Calculus 3 Course.
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Calculus 3 Syllabus
Calculus 3 Overview
The following sections provide links to our complete lessons on all Calculus 3 topics.
Ready for Calc 3? Find out with our FREE Calculus 3 Readiness Test. It includes 20 Questions to help you find your strengths and weaknesses prior to taking a multivariable (Calc 3) course.
Vectors and The Geometry of Space
8 Videos 76 Examples 70 Practice Problems
- Three-Dimensional Coordinate Systems
- 3D Vector
- Dot Product in 3D
- Cross Product in 3D
- Vector Equation
- Quadric Surfaces
- Cylindrical and Spherical Coordinates
- Chapter Test
Vector Functions
7 Videos 41 Examples 57 Practice Problems
- Vector Valued Function
- Derivatives and Integrals of Vector Functions
- Arc Length Parameterization
- Calculate Curvature
- Unit Tangent Vectors
- Tangential & Normal Components Of Acceleration
- Chapter Test
Partial Derivatives
10 Videos 84 Examples 87 Practice Problems
- Functions of Several Variables
- Multivariable Limits
- Partial Derivatives
- Tangent Planes and Linear Approximations
- Multivariable Chain Rule
- Directional Derivatives and the Gradient Vector
- Saddle Points
- Extrema Of Multivariable Functions
- Lagrange Multipliers
- Chapter Test
Multiple Integrals
12 Videos 66 Examples 69 Practice Problems
- Double Integral
- Average Value Of A Double Integral
- Iterated Integral
- Double Integral Over General Regions
- Double Integral With Polar Coordinates
- Applications Of Double Integrals
- Surface Area
- Triple Integral
- Triple Integrals in Cylindrical Coordinates
- Triple Integrals in Spherical Coordinates
- Change Of Variables
- Chapter Test
Vector Calculus
12 Videos 73 Examples 70 Practice Problems
- Vector Fields
- Line Integrals
- Review of Line Integrals
- The Fundamental Theorem of Line Integrals
- Green’s Theorem
- Curl and Divergence
- Parametric Surfaces
- Surface Integrals
- Stokes’ Theorem
- Divergence Theorem
- Vector Calculus Review
- Chapter Test
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