Calculus III (Multivariable Calculus)

Watch Calculus III (Multivariable Calculus)

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This course involves the study of functions of two or more variables using the principles of calculus. This is the third course of the calculus sequence required of engineering, physics, and mathematics majors.

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Seasons
Calculus III: The Cross Product (Level 9) | Torque Examples
47. Calculus III: The Cross Product (Level 9) | Torque Examples
 
This video goes over 3 torque examples. This video also ends the cross product series.
Calculus III: The Cross Product (Level 8) | Torque
46. Calculus III: The Cross Product (Level 8) | Torque
 
This video goes over a second application of the cross product and covers the basic concepts of torque which is also known as moment.
Calculus III: The Cross Product (Level 7) | Scalar Triple Product
45. Calculus III: The Cross Product (Level 7) | Scalar Triple Product
 
This video goes over the scalar triple product also known as the triple scalar product and its use in finding the volume of a parallelepiped and determining if 3 vectors are coplanar.
Calculus III: The Cross Product (Level 6) | Geometric Properties
44. Calculus III: The Cross Product (Level 6) | Geometric Properties
 
This video goes over various geometric properties of the cross product. Proofs of these properties are also presented as well as 2 examples.
Calculus III: The Cross Product (Level 5) | Algebraic Properties
43. Calculus III: The Cross Product (Level 5) | Algebraic Properties
 
This video goes over various algebraic properties of the cross product. Proofs of these properties are also presented as well as 4 examples.
Calculus III: The Cross Product (Level 4) | Examples II
42. Calculus III: The Cross Product (Level 4) | Examples II
 
This video goes over 8 examples illustrating how to find the cross product of two vectors in space by using both the geometric and component definition of the cross product.
Calculus III: The Cross Product (Level 3) | Examples I
41. Calculus III: The Cross Product (Level 3) | Examples I
 
This video goes over 5 examples illustrating how to find the cross product of two vectors in space by using both the geometric and component definition of the cross product.
Calculus III: The Cross Product (Level 2) | Component Definition
40. Calculus III: The Cross Product (Level 2) | Component Definition
 
This video introduces the third way of multiplying vectors called the cross product also known as the vector product and sometimes refereed to as the area product. This video will cover the component definition of the cross product. A review of determinants is also presented.
Calculus III: The Cross Product (Level 1) | Geometric Definition
39. Calculus III: The Cross Product (Level 1) | Geometric Definition
 
This video introduces the third way of multiplying vectors called the cross product also known as the vector product and sometimes refereed to as the area product. This video will cover the geometric definition of the cross product.
Calculus III: The Dot Product (Level 12 of 12) | Cauchy-Schwarz, Triangle Inequality
38. Calculus III: The Dot Product (Level 12 of 12) | Cauchy-Schwarz, Triangle Inequality
 
This video goes over the dot product also known as the scalar product. This video ends the dot product series by going over 3 proofs specifically the Cauchy-Schwarz Inequality, Triangle Inequality and the Parallelogram Law.
Calculus III: The Dot Product (Level 11 of 12) | Work, Examples VIII
37. Calculus III: The Dot Product (Level 11 of 12) | Work, Examples VIII
 
This video goes over the dot product also known as the scalar product. This video goes over how to find the work done by a constant force. 4 examples are also presented illustrating how to solve work problems.
Calculus III: The Dot Product (Level 10 of 12) | Direction Angles, Direction Cosines, Examples VII
36. Calculus III: The Dot Product (Level 10 of 12) | Direction Angles, Direction Cosines, Examples VII
 
This video goes over the dot product also known as the scalar product. This video covers direction angles and direction cosines. 3 examples are also covered illustrating how to solve problems involving direction angles and direction cosines.
Calculus III: The Dot Product (Level 9 of 12) | Examples VI
35. Calculus III: The Dot Product (Level 9 of 12) | Examples VI
 
This video goes over the dot product also known as the scalar product. This video goes over 3 examples illustrating how to find the scalar projection, vector projection, and orthogonal projection.
Calculus III: The Dot Product (Level 8 of 12) | Scalar, Vector and Orthogonal Projections
34. Calculus III: The Dot Product (Level 8 of 12) | Scalar, Vector and Orthogonal Projections
 
This video goes over the dot product also known as the scalar product. This video covers an application of the dot product specifically, the scalar projection, vector projection, and orthogonal projection.
Calculus III: The Dot Product (Level 7 of 12) | Examples V
33. Calculus III: The Dot Product (Level 7 of 12) | Examples V
 
This video goes over the dot product also known as the scalar product. This video goes over 3 challenging examples that require the use of dot product.
Calculus III: The Dot Product (Level 6 of 12) | Examples IV
32. Calculus III: The Dot Product (Level 6 of 12) | Examples IV
 
This video goes over the dot product also known as the scalar product. This video goes over 5 Intermediate level examples that require the use of dot product.
Calculus III: The Dot Product (Level 5 of 12) | Poof, Angle Between Vectors, Examples III
31. Calculus III: The Dot Product (Level 5 of 12) | Poof, Angle Between Vectors, Examples III
 
This video goes over the dot product also known as the scalar product. This video goes over a proof for the geometric definition of the dot product. This video also goes over 4 examples illustrating how to find the angle between two vectors.
Calculus III: The Dot Product (Level 4 of 12) | Examples II
30. Calculus III: The Dot Product (Level 4 of 12) | Examples II
 
This video goes over the dot product also known as the scalar product. This video goes over 5 examples illustrating how to solve problems that make use of the geometric and component definition of the dot product.
Calculus III: The Dot Product (Level 3 of 12) | Examples I
29. Calculus III: The Dot Product (Level 3 of 12) | Examples I
 
This video goes over the dot product also known as the scalar product. This video goes over 11 examples illustrating how to solve problems that make use of the geometric and component definition of the dot product.
Calculus III: The Dot Product (Level 2 of 12) | Component Definition, Properties
28. Calculus III: The Dot Product (Level 2 of 12) | Component Definition, Properties
 
This video goes over the dot product also known as the scalar product. In this video we will derive another method to compute the dot product between two vectors by using their components. We will also cover the properties of the dot product.
Calculus III: The Dot Product (Level 1 of 12) | Geometric Definition
27. Calculus III: The Dot Product (Level 1 of 12) | Geometric Definition
 
This video goes over the dot product also known as the scalar product. This video covers the geometric interpretation of the dot product by going over 5 distinct cases where the angle between the vectors varies.
Calculus III: Three Dimensional Vectors (Level 3 of 3) | Examples III
26. Calculus III: Three Dimensional Vectors (Level 3 of 3) | Examples III
 
This video covers Three Dimensional Vectors. This video goes over the various properties associated with three dimensional vectors. 4 intermediate examples including a static equilibrium problem are covered.
Calculus III: Three Dimensional Vectors (Level 2 of 3) | Examples II
25. Calculus III: Three Dimensional Vectors (Level 2 of 3) | Examples II
 
This video covers Three Dimensional Vectors. This video goes over the various properties associated with three dimensional vectors. 6 intermediate examples are covered illustrating how to solve problems that make use of vectors in space.
Calculus III: Three Dimensional Vectors (Level 1 of 3) | Properties, Examples I
24. Calculus III: Three Dimensional Vectors (Level 1 of 3) | Properties, Examples I
 
This video covers Three Dimensional Vectors. This video goes over the various properties associated with three dimensional vectors. 3 basic examples are also covered illustrating how to solve problems that make use of vectors in space.
Calculus III: Two Dimensional Vectors (Level 13 of 13) | Distance and Bearing
23. Calculus III: Two Dimensional Vectors (Level 13 of 13) | Distance and Bearing
 
This video is a review of Two Dimensional Vectors. This video goes over applications of vectors. 3 examples are covered illustrating how to solve distance and bearing problems.
Calculus III: Two Dimensional Vectors (Level 12 of 13) | Static Equilibrium
22. Calculus III: Two Dimensional Vectors (Level 12 of 13) | Static Equilibrium
 
This video is a review of Two Dimensional Vectors. This video goes over applications of vectors. 3 examples are covered illustrating how to solve static equilibrium problems.
Calculus III: Two Dimensional Vectors (Level 11 of 13) | Resultant Force
21. Calculus III: Two Dimensional Vectors (Level 11 of 13) | Resultant Force
 
This video is a review of Two Dimensional Vectors. This video goes over applications of vectors. 3 examples are covered illustrating how to find the resultant force.
Calculus III: Two Dimensional Vectors (Level 10 of 13) | Unit Vector Examples
20. Calculus III: Two Dimensional Vectors (Level 10 of 13) | Unit Vector Examples
 
This video is a review of Two Dimensional Vectors. This video goes over 6 examples that make use of unit vectors.
Calculus III: Two Dimensional Vectors (Level 9 of 13) | Unit, Standard, Direction
19. Calculus III: Two Dimensional Vectors (Level 9 of 13) | Unit, Standard, Direction
 
This video is a review of Two Dimensional Vectors. This video goes over unit vectors, standard unit vectors and direction of vectors.
Calculus III: Two Dimensional Vectors (Level 8 of 13) | Vector Properties
18. Calculus III: Two Dimensional Vectors (Level 8 of 13) | Vector Properties
 
This video is a review of Two Dimensional Vectors. This video goes over properties of vector operations. Properties are also proven geometrically and algebraically.
Calculus III: Two Dimensional Vectors (Level 7 of 13) | Vector Arithmetic Examples II
17. Calculus III: Two Dimensional Vectors (Level 7 of 13) | Vector Arithmetic Examples II
 
This video is a review of Two Dimensional Vectors. This video goes over 5 examples that make use of the algebraic definition of scalar multiplication and vector addition.
Calculus III: Two Dimensional Vectors (Level 6 of 13) | Vector Arithmetic - Algebraic
16. Calculus III: Two Dimensional Vectors (Level 6 of 13) | Vector Arithmetic - Algebraic
 
This video is a review of Two Dimensional Vectors. This video goes over how to algebraically find the scalar multiple of a vector and vector addition. The concept of parallel vector is also introduced along with 2 examples.
Calculus III: Two Dimensional Vectors (Level 5 of 13) | Vector Arithmetic Examples I
15. Calculus III: Two Dimensional Vectors (Level 5 of 13) | Vector Arithmetic Examples I
 
This video is a review of Two Dimensional Vectors. This video goes over 12 examples covering vector addition, vector subtraction and scalar multiplication. These problems are solved by using the geometric interpretation of these particular vector operations.
Calculus III: Two Dimensional Vectors (Level 4 of 13) | Vector Arithmetic - Geometric
14. Calculus III: Two Dimensional Vectors (Level 4 of 13) | Vector Arithmetic - Geometric
 
This video is a review of Two Dimensional Vectors. This video goes vector operations also known as vector arithmetic. Topics include: geometric interpretation of scalar multiplication of a vector, vector addition, and vector subtraction.
Calculus III: Two Dimensional Vectors (Level 3 of 13) | Examples
13. Calculus III: Two Dimensional Vectors (Level 3 of 13) | Examples
 
This video is a review of Two Dimensional Vectors. This video goes over 5 examples covering how to write the component form of a vector and sketching vectors in standard position.
Calculus III: Two Dimensional Vectors (Level 2 of 13) | Standard Position, Component Form
12. Calculus III: Two Dimensional Vectors (Level 2 of 13) | Standard Position, Component Form
 
This video is a review of Two Dimensional Vectors. Topics include vectors in a coordinate system, vectors in standard position, and component form of a vector.
Calculus III: Two Dimensional Vectors (Level 1 of 13) | Basics
11. Calculus III: Two Dimensional Vectors (Level 1 of 13) | Basics
 
This video is a review of Two Dimensional Vectors. This video goes over the basic concepts and terminology of vectors in a plane. Topics include: Vectors, Magnitude of a Vector, Equivalent Vectors, and Vector Notation. This video also goes over 2 examples.
Calculus III: Three Dimensional Coordinate Systems (Level 10 of 10) | Graphing Inequalities
10. Calculus III: Three Dimensional Coordinate Systems (Level 10 of 10) | Graphing Inequalities
 
This video concludes the exploration of a three dimensional Cartesian coordinate system. This video covers 2 examples illustrating the appropriate way of graphing equations in three dimensional space that are restricted to a given interval. In addition, this video goes over 5 examples illustrating how to graph inequalities in three dimensional space.
Calculus III: Three Dimensional Coordinate Systems (Level 9 of 10) | Sphere Examples III
9. Calculus III: Three Dimensional Coordinate Systems (Level 9 of 10) | Sphere Examples III
 
This video continues the exploration of a three dimensional cartesian coordinate system. This video covers two challenging examples that requires the use of the equation of a sphere. The first example involves finding the equation of a sphere that is constrained in the first octant. The second example involves finding an equation of a sphere by solving a system of equations.
Calculus III: Three Dimensional Coordinate Systems (Level 8 of 10) | Sphere Examples II
8. Calculus III: Three Dimensional Coordinate Systems (Level 8 of 10) | Sphere Examples II
 
This video continues the exploration of a three dimensional cartesian coordinate system.This video covers three intermediate examples that requires the use of the equation of a sphere. Two examples illustrate how to find the center and radius of a sphere by rewriting an equation into its standard form by completing the square.
Calculus III: Three Dimensional Coordinate Systems (Level 7 of 10) | Sphere Examples I
7. Calculus III: Three Dimensional Coordinate Systems (Level 7 of 10) | Sphere Examples I
 
This video continues the exploration of a three dimensional cartesian coordinate system.This video covers three basic examples that requires the use of the equation of a sphere.
Calculus III: Three Dimensional Coordinate Systems (Level 6 of 10) | Distance Formula Examples
6. Calculus III: Three Dimensional Coordinate Systems (Level 6 of 10) | Distance Formula Examples
 
This video continues the exploration of a three dimensional cartesian coordinate system.This video covers three slightly more challenging examples requiring the use of the distance formula in three dimensions.
Calculus III: Three Dimensional Coordinate Systems (Level 5 of 10) | Sphere Equation
5. Calculus III: Three Dimensional Coordinate Systems (Level 5 of 10) | Sphere Equation
 
This video continues the exploration of a three dimensional Cartesian coordinate system.This video covers two basic examples requiring the use of the distance formula in three dimensions. In addition, the equation of a sphere is also derived.
Calculus III: Three Dimensional Coordinate Systems (Level 4 of 10) | Midpoint, Distance Formulas
4. Calculus III: Three Dimensional Coordinate Systems (Level 4 of 10) | Midpoint, Distance Formulas
 
This video continues the exploration of a three dimensional cartesian coordinate system. This video goes over common formulas used in a three dimensional coordinate system, this video covers the midpoint formula and a derivation of the distance formula in three dimensions is also presented.
Calculus III: Three Dimensional Coordinate Systems (Level 3 of 10) | Planes, Cylinder
3. Calculus III: Three Dimensional Coordinate Systems (Level 3 of 10) | Planes, Cylinder
 
This video continues the exploration of a three dimensional Cartesian coordinate system. This video goes over 5 examples covering the proper way to graph equations in R cubed. Equations covered include planes, cylinder, and parabolic cylinder.
Calculus III: Three Dimensional Coordinate Systems (Level 2 of 10) | Equations
2. Calculus III: Three Dimensional Coordinate Systems (Level 2 of 10) | Equations
 
This video continues the exploration of a three dimensional Cartesian coordinate system. Basic equations of a two dimensional coordinate system are presented to illustrate the similarities to a three dimensional coordinate system. In addition, the equations of the coordinate planes are also discussed. This video concludes with an introduction to projections in three dimensional space.
Calculus III: Three Dimensional Coordinate Systems (Level 1 of 10) | Basics
1. Calculus III: Three Dimensional Coordinate Systems (Level 1 of 10) | Basics
 
This video is a review of number lines and coordinate systems. This video goes over the basic concepts and terminology of one dimensional, and two dimensional coordinate systems. This video concludes with an introduction to three dimensional coordinate systems as a starting point to successfully study multivariable calculus.
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