MTH 254
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Homework
There are two different textbook options you may choose in order to complete your homework. You may choose either
- Gilbert Strang and Edwin Herman’s Calculus Volume 3
- James Stewart’s Calculus: Concepts and Contexts, 4th Edition
Select homework sets are provided below for either option you choose. The homework prompts listed are a starting point to practice the material we learned in class (or from the videos). Some people may feel they need more practice after working through these prompts, and that is great to have that self-awareness! In this case, try some of the even prompts between the assigned odd ones.
Strang and Herman’s Calculus Volume 3
- Introduction to 3D Coordinates: Section 2.2:
- Vectors: Section 2.1: ; then Section 2.2:
- The Dot Product: Section 2.3:
- The Cross Product: Section 2.4:
- Lines and Planes: Section 2.5:
- Functions & Surfaces: Section 2.6:
- Cylindrical & Spherical Coordinates: Section 2.7:
- Vector Functions & Space Curves: Section 3.1:
- Derivatives & Integrals of Vector Functions: Section 3.2:
- Arc Length & Curvature: Section 3.3:
- Velocity & Acceleration: Section 3.4:
- Functions of Several Variables: Section 4.1:
- Limits & Continuity: Section 4.2:
- Partial Derivatives: Section 4.3:
- Tangent Planes & Linear Approximations: Section 4.4:
- The Chain Rule: Section 4.5:
- Directional Derivatives & The Gradient: Section 4.6:
- Extrema: Section 4.7:
- Double Integrals Over Rectangles: Section 5.1:
- Iterated Integrals: Section 5.1:
- Double Integrals Over General Regions: Section 5.2:
- Double Integrals Over Polar Regions: Section 5.3:
- Triple Integrals: Section 5.4:
- Triple Integrals in Cylindrical & Spherical Coordinates: Section 5.5:
Stewart’s Calculus: Concepts & Contexts, 4th Edition 
- Introduction to 3D Coordinates: §9.1: 3 – 15 odd, 21, 25, 29, 31, 33, 35
- Vectors: §9.2: 3 – 25 odd, 33, 39 (describe in words and find a formula)
- The Dot Product: §9.3: 1, 9 – 23 odd, 29, 31, 37, 39, 43, 50a
- The Cross Product: §9.4: 1, 5 – 29 odd, 39
- Lines and Planes: §9.5: 1, 7 – 27 odd, 33 (verify with Desmos), 35 (verify with Desmos)
- Functions & Surfaces: §9.6: 1 – 27 odd, 29 (use Wolfram Alpha)
- Cylindrical & Spherical Coordinates: §9.7: 1 – 29 odd
- Vector Functions & Space Curves: §10.1: 1, 3, 5 – 11 odd (do these by hand and check on GeoGebra), 15, 17, 19 – 24 all, 27, 28, 43
- Derivatives & Integrals of Vector Functions: §10.2: 3 – 29 odd, 33 – 39 odd
- Arc Length & Curvature: §10.3: 1 – 9 odd, 10, 13, 14, 15, 17, 21 – 27 odd, 33, 36, 37
- Velocity & Acceleration: §10.4: 1, 2, 3 – 19 odd, 23, 26, 28, 33, 36, 37
- Functions of Several Variables: §11.1: 1, 5 – 25 odd, 35 – 43 odd
- Limits & Continuity: §11.2: 1 – 33 odd
- Partial Derivatives: §11.3: 1, 5, 7, 15, 17, 19, 21, 27, 31, 41, 47, 49, 55, 57, 61, 63, 65, 83
- Tangent Planes & Linear Approximations: §11.4: 3 – 13 odd, 17, 21 – 33 odd, 37, 39 – 43 odd
- The Chain Rule: §11.5: 3 – 11 odd, 15 – 33 odd, 37, 39
- Directional Derivatives & The Gradient: §11.6: 1 – 13 odd, 17 – 21 odd, 25, 29, 31, 37 – 41 odd, 45, 59
- Extrema: §11.7: 1 – 11 odd, 17, 19, 23, 27 – 3 odd, 39, 47
- Double Integrals Over Rectangles: §12.1: 1 – 9 all, 11 – 14 all
- Iterated Integrals: §12.2: 3 – 29 odd, 35, 37
- Double Integrals Over General Regions: §12.3: 3, 7 – 27 odd, 37, 41, 45, 47, 49, 55
- Double Integrals Over Polar Regions: §12.4: 1 – 35 odd
- Triple Integrals: §12.7: 3 – 15 odd, 19, 21, 27 – 35 odd
- Triple Integrals in Cylindrical & Spherical Coordinates: §12.8: 3, 5, 7, 11, 17, 19, 35, 37
Note Sheets
Below are a number of Guided Note Sheets. These are blank and constitute what will be covered during lecture.
- Introduction to 3D Coordinates
- Vectors
- The Dot Product Work
- The Cross Product
- Equations of Lines
- Equations of Planes
- Functions and Surfaces
- Spherical and Cylindrical Coordinates
- Vector Functions and Space Curves
- Derivatives and Integrals of Vector Functions
- Arc Length and Curvature
- Velocity and Acceleration
- Parametric Surfaces
- Functions of Several Variables
- Limits and Continuity
- Partial Derivatives
- Tangent Planes and Linear Approximations
- The Chain Rule
- Directional Derivatives and the Gradient Vector
- Extrema
- Double Integrals over Rectangles
- Iterated Integrals
- Double Integrals over General Planar Regions
- Double Integrals over Polar Regions
Mini Tests
There are four Mini Tests to be completed through the term. You may find them below.
<To Be Completed>
Reviews
Below are some reviews for both the midterm exam and the final exam. Use these reviews to study for the exam. These will not be collected or covered in class.
<To Be Completed>
Extra Credits
There are two extra credit opportunities available to you. Please complete these any time before the last week of instruction.
- Extra Credit 1: Women in Math: The Limit Does Not Exist
- Extra Credit 2: The Mathematics of the Three Waves of AI