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Course Resources
MATH 2110 -Calculus III
Resource List by Course Content
The resources listed on this page are meant only as general instruction materials. Students are expected to contact their instructors regarding the specific requirements for their classes.
*All video resources below link to Khan Academy unless otherwise noted
Matrices to solve a vector combination problem
Chapter 9 – Vectors and Geometry of Space
9.1 Three-Dimensional Coordinate Systems
9.2 Vectors
9.3 The Dot Product
9.4 The Cross Product
9.5 Equations of Lines and Planes
9.6 Functions and Surfaces
- Derivative of a position vector valued function
- Differential of a vector valued function
- Vector valued function derivative example
9.7 Cylindrical and Spherical Coordinates
Chapter 10 – Vector Functions
10.1 Vector Functions and Space Curves
10.2 Derivatives and Integrals of Vector Functions
10.3 Arc Length and Curvature
10.4 Motion in Space: Velocity and Acceleration
10.5 Parametric Surfaces
Chapter 11 – Partial Derivatives
11.1 Functions of Several Variables
11.2 Limits and Continuity
11.3 Partial Derivatives
- Partial Derivatives: Introduction to partial derivatives
- Partial Derivatives 2 : More on partial derivatives
11.4 Tangent Planes and Linear Approximations
11.5 The Chain Rule
11.6 Directional Derivatives and the Gradient Vector
11.7 Maximum and Minimum Values
11.8 Lagrange Multipliers
Chapter 12 – Multiple Integrals
12.1 Double Integrals over Rectangles
- Double Integral 1
- Double Integrals 2
- Double Integrals 3: Let's integrate dy first!
- Double Integrals 4: Another way to conceptualize the double integral.
- Double Integrals 5: Finding the volume when we have variable boundaries
- Double Integrals 6: Let's evaluate the double integrals with y=x^2 as one of the boundaries
12.2 Iterated Integrals
12.3 Double Integrals over General Regions
12.4 Double Integrals in Polar Coordinates
12.5 Applications of Double Integrals
12.6 Surface Area
12.7 Triple Integrals
12.8 Triple Integrals in Cylindrical and Spherical Coordinates
12.9 Change of Variables in Multiple Integrals
Chapter 13 – Vector Calculus
13.1 Vector Fields
13.2 Line Integrals
- (2^ln x)/x Antiderivative Example
- Introduction to the Line Integral
- Line Integral Example 1
- Line Integral Example 2 (part 1)
- Line Integral Example 2 (part 2)
- Line Integrals and Vector Fields
- Using a line integral to find the work done by a vector field example
- Scalar Field Line Integral Independent of Path Direction
- Vector Field Line Integrals Dependent on Path Direction
- Path Independence for Line Integrals
- Closed Curve Line Integrals of Conservative Vector Fields
- Example of Closed Line Integral of Conservative Field
- Second Example of Line Integral of Conservative Vector Field
13.3 The Fundamental Theorem for Line Integrals
13.4 Green’s Theorem
- Green's Theorem Proof Part 1
- Green's Theorem Proof (part 2)
- Green's Theorem Example 1
- Green's Theorem Example 2
13.5 Curl and Divergence
- Divergence 1: Introduction to the divergence of a vector field
- Divergence 2: The intuition of what the divergence of a vector field is
- Divergence 3: Analyzing a vector field using its divergence
- Curl 1: Introduction to the curl of a vector field
- Curl 2: The mechanics of calculating curl.
- Curl 3 : More on curl
13.6 Surface Integrals
- Introduction to Parametrizing a Surface with Two Parameters
- Determining a Position Vector-Valued Function for a Parametrization of Two Parameters
- Partial Derivatives of Vector-Valued Functions
- Introduction to the Surface Integral
- Example of calculating a surface integral part 1
- Example of calculating a surface integral part 2
- Example of calculating a surface integral part 3
- Surface Integral Example Part 1 - Parameterizing the Unit Sphere
- Surface Integral Example Part 2 - Calculating the Surface Differential
- Surface Integral Example Part 3 - The Home Stretch
- Surface Integral Ex2 part 1 - Parameterizing the Surface
- Surface Integral Ex2 part 2 - Evaluating Integral
- Surface Integral Ex3 part 1 - Parameterizing the Outside Surface
- Surface Integral Ex3 part 2 - Evaluating the Outside Surface
- Surface Integral Ex3 part 3 - Top surface : Parameterizing the top surface
- Surface Integral Ex3 part 4 - Home Stretch
- Conceptual Understanding of Flux in Three Dimensions
- Constructing a unit normal vector to a surface
- Vector representation of a Surface Integral
