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Sasha Townsend

Sasha TownsendSasha TownsendSasha Townsend

Assistant Professor of Mathematics Tulsa Community College

Assistant Professor of Mathematics Tulsa Community College Assistant Professor of Mathematics Tulsa Community College

Calculus 3 - Course Information

This section includes recent syllabi for my online and face-to-face sections of Calculus III, as well as the SBG Course Standards, Grading Rubric, and Advice for Calculus III Students from this school year's students.

TTh Spring 2020 Syllabus (Face-to-face, using SBG) (pdf)Download
Spring 2020 Syllabus Addendum (Changes to the course due to COVID-19) (pdf)Download
Summer 2019 Syllabus (Online section) (pdf)Download
Calc3 SBG Course Standards and Grading Rubric (pdf)Download
Advice for Calculus III Students (From Fall 2019 Students) (pdf)Download
Advice for Calculus III Students (From MW Spring 2020 Students) (pdf)Download
Advice for Calculus III Students (From TTh Spring 2020 Students) (pdf)Download
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Materials for Analytic Geometry & Calculus III

A Work-in-Progress

I am currently revising my notes for this course, but I wanted to share those materials that I use in my course right now. Check out the links on this page to see recent syllabi, SBG course standards and rubric, course notes, completed course notes, and quiz keys from the most recent semester.

About Analytic Geometry & Calculus 3

Vision for this course

Multivariable calculus is an extension of differential and integral calculus to n-dimensions.  It reinforces the students' visualization skills and requires the student to think about how we interpret derivatives, integrals, and vector objects geometrically and in applications. The quizzes and notes below reflect that emphasis in our course. In class, I strive to show the students where each of the formulas come from, what they mean geometrically and in applications, and how to use the formulas and techniques, geometrically and in applications.


I view this course as less about the skill-building that is necessary in Calculus I and II. By the time a student has reached Calculus III, hopefully they understand single-variable limits, derivatives, antiderivatives, and integrals, and how they are interpreted geometrically and in applications. In Calculus III, we extend that understanding to n-dimensions. At this point, some students are comfortable with geometry but not computation, while others are comfortable computing but not comfortable with geometry. In this course, students are stretched to develop (1) their geometric intuition, (2) conceptual understanding, and (3) computational and procedural fluency. We focus on extension and application rather than skill-building here.


The quizzes aren't as straight-forward as they were in Calculus II, because in this course, many concepts, applications, and computations may comprise a single standard. A standard covering vector fields is necessarily more involved than a single standard devoted to integration by parts or volume using cylindrical shells. There are more ideas to connect. The computations themselves aren't difficult if the student is armed with excellent prerequisite skills, but keeping track of notation and the meaning of each mathematical object can be challenging. My goal is to help students meet that challenge. In chapter 16, we'll be able to compute quantities with calculus that would have been unimaginable back in algebra class, if we've done the work of understanding the foundation. It's like going hiking...We're working our way toward a beautiful view.


With these goals in mind, I allow one 8.5" by 11" hand-written, student-created formula sheet for vector identities, graphs of known functions, derivative and antiderivative rules for each quiz. Given our goals, this seems appropriate. (I allow two pages of notes for each unit exam in the online section of this course.) I use standards based grading in the face-to-face sections, and unit exams in the online sections. Lectures focus on derivations, computation, and meaning.


I hope you find multivariable calculus as beautiful as I do.

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Prerequisite Review Materials

There's so much that we're building upon in Calculus III. If you need review materials, please view the materials on the corresponding pages on this site.


If you're unable to find a resource because I haven't yet uploaded it, let me know, and I'll be happy to find and upload it, or direct you to other online resources.

Analytic Geometry & Calculus 3 (YouTube playlist)

In Spring 2020, I made videos for Calc III. They break the lesson up into small chunks. Some videos are long, because I'm showing you both the concepts and examples of how to solve related problems. 


While I don't expect you to watch every video from beginning to end, these resources are here to help you prepare. The videos help you solve the problems that I tend to put on quizzes and exams. I review the details. My students tend to need that review.


There are 106 videos posted here.

Unit 1 - Geometry of Space - Class Notes

Blank class notes and homework are shown below. Students are encouraged to use the class notes to organize their thinking and their study of the material we covered in class. Completed class notes are provided so that students can check their work. This is on the honor system; the expectation is that students will do their own work for  learning's sake and use the solutions to check their reasoning. Listed problems are selected from Thomas' Calculus Early Transcendentals, 13th edition.

U1 L1 Vectors and Vector Operations (with Assigned Problems) (12.1 and 12.2) (pdf)Download
U1 L2 Dot Product and Cross Product (with Assigned Problems) (12.3 and 12.4) (pdf)Download
U1 L3 Lines, Planes, and Distance (with Assigned Problems) (12.5) (pdf)Download
U1 L4 Cylinders and Quadric Surfaces (with Assigned Problems) (12.6) (pdf)Download
U1 L1 Completed Class Notes (12.1 and 12.2) (pdf)Download
U1 L2 Completed Class Notes (12.3 and 12.4) (pdf)Download
U1 L3 Completed Class Notes (12.5) (pdf)Download
U1 L4 Completed Class Notes (12.6) (pdf)Download

Unit 1 - Detailed Lesson Notes

This semester, I'm revising my notes to make them more detailed, so that students in my online courses have access to the same information I give students in my face-to-face classes. As I create these notes, I will post them here.

U1 L1 Lesson Notes - Vectors and Vector Operations in 2D and 3D (pdf)Download

Unit 2 - Vector-Valued Functions - Class Notes and Homework

Blank class notes and homework from Thomas' Calculus Early Transcendentals, 13th edition, are linked below. These are the notes covering vector-valued functions. Completed class notes are available for download as well. Listed problems are from Thomas' Calculus ET, 13th edition.

U2 L1 Introduction to Vector-Valued Functions (13.1 and 13.2) (pdf)Download
U2 L2 Unit Tangent, Unit Normal, Components of Acceleration, and Curvature (13.3 and 13.4) (pdf)Download
U2 L3 Frenet Frame, Binormal Vector, Torsion (13.5) (pdf)Download
U2 L1 Completed Class Notes (13.1 and 13.2) (pdf)Download
U2 L2 Completed Class Notes (13.3 and 13.4) (pdf)Download
U2 L3 Completed Class Notes (13.5) (pdf)Download
HW Help - Problem 13.2.17 (pdf)Download

Unit 3 - Multivariable Functions - Class Notes and Homework

Blank class notes and homework are linked below. The homework problems are selected from Thomas' Calculus Early Transcendentals, 13th edition. Completed class notes are available for download as well.

U3 L1 Introduction to Functions of Several Variables (14.1 and 14.2) (pdf)Download
U3 L2 Partial and Directional Derivatives (14.3 and 14.5) (pdf)Download
U3 L3 Chain Rules and Implicit Differentiation (14.4) (pdf)Download
U3 L4 Tangent Planes and Differentials (14.6) (pdf)Download
U3 L5 Optimization (14.7) (pdf)Download
U3 L1 Completed Class Notes (14.1 and 14.2) (pdf)Download
U3 L2 Completed Class Notes (14.3 and 14.5) (pdf)Download
U3 L3 Completed Class Notes (14.4) (pdf)Download
U3 L4 Completed Class Notes (14.6) (pdf)Download
U3 L5 Completed Class Notes (14.7) (pdf)Download

Unit 4 - Multiple Integration - Class Notes and Homework

Blank class notes and homework covering multiple integration are shown below. All textbook problems are assigned from Thomas' Calculus Early Transcendentals, 13th edition. Completed class notes are also linked below.

U4 L1 Area and Volume with Iterated Integrals (15.1-15.3) (pdf)Download
U4 L2 Double Integrals in Polar Coordinates (15.4) (pdf)Download
U4 L3 Surface Area (pdf)Download
U4 L4 Triple Integrals in Rectangular, Cylindrical, and Spherical Coordinates (15.5 and 15.7) (pdf)Download
U4 L5 Change of Variables and the Jacobian (15.8) (pdf)Download
U4 L1 Completed Class Notes (15.1-15.3) (pdf)Download
U4 L2 Completed Class Notes (15.4) (pdf)Download
U4 L3 Completed Class Notes (pdf)Download
U4 L4 Completed Class Notes (pdf)Download
U4 L5 Completed Class Notes (15.8) (pdf)Download

Unit 5 - Vector Analysis - Class Notes and Homework

The blank class notes and homework from the Thomas' Calculus Early Transcendentals, 13th edition, are shown below. 

After lecture, students are encourage to complete these class notes and practice problems in preparation for the corresponding quiz. 


Completed class notes are available for download here as well.

U5 L1 Vector Fields, Line Integrals, and the Fundamental Theorem of Line Integrals (16.1-16.3) (pdf)Download
U5 L2 Green's Theorem (16.4) (pdf)Download
U5 L3 Parametric Surfaces and Surface Integrals (16.5 and 16.6) (pdf)Download
U5 L4 The Divergence Theorem and Stokes's Theorem (16.7 and 16.8) (pdf)Download
U5 L1 Completed Class Notes (16.1 - 16.3) (pdf)Download
U5 L2 Completed Class Notes (16.4) (pdf)Download
U5 L3 Completed Class Notes (16.5 and 16.6) (pdf)Download
U5 L4 Completed Class Notes (16.7 and 16.8) (pdf)Download

Solutions to Quiz Problems (YouTube Playlist)

This semester, I wanted to provide solutions to the quiz problems in the form of a video, so that students could watch me working the problems, in addition to reviewing the quiz key and comparing it to the feedback I left them on their quizzes. The provided solutions videos to date are linked here. This is a playlist...If you click on the lines in the the top right-hand corner, you'll see a drop down menu with all of the videos posted on this playlist to date, listed by course standard.

Spring 2020 Quiz and Final Exam Keys

These are the quiz keys for the current semester. Remember, these are representative questions. Reassessments require exactly the same conceptual understanding, but the problems will tend to approach the concept in a different way. We didn't take a full set of in-class quizzes due to COVID-19. These are the keys to the quizzes that were taken this semester.

Calc3 Quiz 1 KEY Spring2020 (MW) (pdf)Download
Calc3 Quiz 1 KEY Spring2020 (TTh) (pdf)Download
Calc3 Quiz 2 KEY Spring2020 (MW) (pdf)Download
Calc3 Quiz 2 KEY Spring2020 (TTh) (pdf)Download
Calc3 Quiz 3 KEY Spring2020 (MW and TTh) (pdf)Download
Calc3 Quiz 4 KEY Spring2020 (MW) (pdf)Download
Calc3 Quiz 4 KEY Spring2020 (TTh) (pdf)Download
Calc3 Quiz 5 KEY Spring2020 (MW and TTh) (pdf)Download
Calc3 Quiz 6 KEY Spring2020 (MW) (pdf)Download
Calc3 Quiz 6 KEY Spring2020 (TTh) (pdf)Download
Calc3 Quiz 7 KEY Spring2020 (MW) (pdf)Download
Calc3 Quiz7 KEY Spring2020 (TTh) (pdf)Download
Calc3 Quiz 8 KEY Spring2020 (TTh) (pdf)Download
Calc3 Final Exam KEY Spring2020 (MW) (pdf)Download
Calc3 Final Exam KEY Spring2020 (TTh) (pdf)Download

Fall 2019 Quiz Keys

I use standards based grading in the face-to-face sections of this course. When using SBG, rather than assessing student understanding using tests, I use more frequent quizzes that cover the major topics (called standards) of our course. This course has about 30 standards. The online section covers exactly the same content, with the material assessed through unit exams and a comprehensive final rather than quizzes and a final. 


The students are given access to quiz keys so that they can see A-level work, and so that they can familiarize themselves with the format of the quizzes and exams. Students know that I won't simply ask them the same questions with different numbers. Students need a thorough understanding of each standard and the related concepts and techniques in order to be successful. 


The first 8 quiz keys have been posted here. The Fall 2019 Quiz 9 key will be posted at a later date. Quiz 10, which covers surface integrals, Stokes's theorem, and Gauss's divergence theorem, is administered as a take-home quiz before the final. The keys to in-class quizzes will be posted here.


Students are encouraged to create one-page 8.5" by 11" formula sheet for each quiz in Calculus III. 

Calc3 Quiz 1 KEY Fall2019 (pdf)Download
Calc3 Quiz 2 KEY Fall2019 (pdf)Download
Calc3 Quiz 3 KEY Fall2019 (pdf)Download
Calc3 Quiz 4 KEY Fall2019 (pdf)Download
Calc3 Quiz 5 KEY Fall2019 (pdf)Download
Calc3 Quiz 6 KEY Fall2019 (pdf)Download
Calc3 Quiz 7 KEY Fall2019 (pdf)Download
Calc3 Quiz 8 KEY Fall2019 (pdf)Download

Copyright © 2020 Sasha Townsend - All Rights Reserved.

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