MCS 222, Multivariable Calculus
(12:30-1:20 MTuThF in OHS 318 )

Syllabus: Here is the syllabus.

Office hours for the rest of the semester: These are held on Google Meets. The meeting code is aqc-ymhm-zfu.

• 2:30-4:00 Wed, 5/20
• 3-4:30 Fri, 5/22
• 3:30-5 Sun, 5/24
• 3-4:30 Mon, 5/25

Calculus tutoring center: Tutoring is available on Google Meets at 7-9 PM Sun-Thu. The meeting code is xvj-icfu-tkp. The tutoring center is primarily for single variable calculus students and lower, but some of the tutors may be qualified to help you with multivariable calculus questions too.

Online resources:

• Your class on Google Classroom
• Webwork is where you do your online homework. You can now access Webwork off campus directly.
• I use Moodle to post your grades periodically throughout the semester
• The grade calculator allows you o input your current running total and see what kind of score you need on the inal exam for each kind of letter grade. The calculator is a Google sheets document, so you need to be logged in to a Google account to access it. It is supposed to work with any Google account, not only your Gustavus account. Click Use Template in the upper right corner to start. You can also download an Excel version of the calculator if Google sheet does not want to cooperate.
• Here is a link to our textbook on the publisher's website.
• Here are the notes to help you read your textbook
  • 1.4. Cylindrical and Spherical Coordinates
  • 1.5. n-Dimensional Euclidean Space
  • 2.1. The Geometry of Real-Valued Functions
  • 2.2. Limits and Continuity
  • 2.3. Differentiation
  • 2.4. Introduction to Paths and Curves
  • 2.5. Properties of the Derivative
  • 2.6. Gradients and Directional Derivatives
  • 3.1. Iterated Partial Derivatives
  • 3.3. Extrema of Real-Valued Functions

Homework:

Assigned	Due	Read	Exercises
2/10		Historical Introduction, Prerequisites and Notation, 1.1	No homework yet
2/14	2/21	1.1	Webwork: Do HW0 and HW1. HW0 does not not count toward your grade. Offline: 1.1.12, 22, 23, 32
2/21	2/28	1.2	Webwork: Do HW2. Offline: 1.1.14, 20, 26, 31
2/28	3/6	1.3	Webwork: Do HW3. Offline: 1.2.26, 28, 30, 38
3/6	3/13	1.3, 4	Webwork: Do HW4. Offline: 1.3.23a, 24, 38, 46
3/13		1.4, 5	Homework holiday. Review for the upcoming exam.
4/3	4/10	2.1, 2	Webwork: Do HW5. Offline: 1.4.4, 10 and 1.5.2, 16
4/10	4/17	2.2, 3	Webwork: Do HW6. Offline: 2.1.8, 18, 22 and 2.2.20
4/17	4/24	2.3	Webwork: Do HW7. Offline: 2.2.22, 26, 32 Do 2.2.26 with a δ-ε argument. Hint: notice that |x| ≤ √x2+y2+z2 and the same is true for |y| and |z| and use these to show that √x2+y2+z2 is an upper estimate for |(xyz)/(x2+y2+z2)|, that is |(xyz)/(x2+y2+z2)| ≤ √x2+y2+z2.
4/24		2.3, 4	Homework holiday. Review for the upcoming exam.
5/1	5/8	2.4-6	Webwork: Do HW8. Offline: 2.3.4bc, 10bc, 22 and 2.4.24 In 2.3.4, C1 means that the first partial derivatives exist and are continuous at every point. The problem means to say f(0,0) is defined to be 0. Note that you will have to use the definition of the derivative to find the partial derivatives at the origin.
5/8	5/15	3.1, 3, 4	Webwork: Do HW9. Offline: 2.5.18, 22 and 2.6.14, 24
5/15	5/20	3.3, 5.1	Webwork: Do HW10. Offline: 3.1.32

Exam solutions:

• First hourly exam pdf
• Second hourly exam pdf
• Final exam pdf

Educational links:

• A serious paper on teaching/learning at the university level by Prof. Steven Zucker
• A more light-hearted, but very true guide on how to be on good terms with your professor (who assigns your grade) by Prof. Doug Andrews at Wittenberg University

Math links:

• Our own Problems of the Month are an excellent way to hone your reasoning skills. Most, if not all, of these problems require no knowledge of advanced math beyond what you already know to be solved. You can even earn a prize by submitting your solutions.
• Wolfram MathWorld is an interactive math encyclopedia.
• Wolfram Alpha gives you access to many features of Mathematica, an extremely powerful computer algebra program, without paying $$$ and learning Mathematica syntax. It does not only do algebra.
• Desmos is everyone's favorite graphing website for single variable functions.
• The following 3-D graphing app allows you to visualize the graph of a function of two variables.
• Math3d.org is another website that allows you to graph points, lines, vectors, functions, etc in R³.

Scholarship opportunities for prospective teachers:

• Knowles Teacher Initiative