Course Resources Math 2110

Chapter 9 – Vectors and Geometry of Space

9.2 Vectors

• Position Vector Valued Functions

9.6 Functions and Surfaces

• Derivative of a position vector valued function
• Differential of a vector valued function
• Vector valued function derivative example

 

Chapter 10 – Vector Functions

10.3 Arc Length and Curvature

• Parameterization of a Reverse Path
• Constructing a unit normal vector to a curve

 

Chapter 11 – Partial Derivatives

11.3 Partial Derivatives

• Partial Derivatives: Introduction to partial derivatives

 

Chapter 12 – Multiple Integrals

12.1 Double Integrals over Rectangles

• Double Integral 1
• 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

12.7 Triple Integrals

• Triple Integrals 1
• Triple Integrals 2
• Triple Integrals 3

 

Chapter 13 – Vector Calculus

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

13.4 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

13.6 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

13.8 The Divergence Theorem

• 2 D Divergence Theorem
• Conceptual clarification for 2-D Divergence Theorem