Welcome to the course webpage for the Summer 2025 (Session 2) manifestation of MATH 22: Introduction to Calculus of Several Variables at the University of California, Santa Cruz.

The official syllabus for the course is located here. Much of the important information from the syllabus is summarized below.

Basic Course Information

• Prerequisites: MATH 11B or MATH 19B or MATH 20B or AM 15B or AP Calculus BC exam score of 4 or 5.
• Textbook: We will be using Active Calculus: Multivariable, by Steve Schlicker. In the spirit of reducing the cost of your education, I have chosen to use this free and open-source textbook. You can download the textbook for free or view the HTML version. This textbook is by no means traditional: as the title suggests, the student is expected to actively engage with the textbook. There are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts. Everyone will be expected to read the textbook and digest the material in a meaningful way outside of class. Class meetings will typically be reserved for discussing key ideas and completing the activities, either individually or in groups.
• Course Webpage: You're on it! Assigned readings and other assignments will typically be posted here. If there are any notes from our meetings, they will be posted here as well.
• Canvas: The Canvas webpage will be primarily used for hosting grades. Important links and due dates are also available there. I do not regularly check Canvas messages, so please contact me via email. Login here: https://canvas.ucsc.edu with your CruzID and Gold password.
• Edfinity: We will use the online homework management system Edfinity. You are required to enroll in our course at the following link: https://edfinity.com/join/K3LFRUY6. The cost is $35 per student. Note: I chose Edfinity as an alternative to WebAssign, which costs over $100 per student.
• Teaching Assistant: Our TA is Joseph Immel. You can contact him via email. Joseph will hold weekly office hours and discussion sections. You are highly encouraged to attend these!
  • TA e-mail:
  • TA Office Hours: 11:45AM-12:45PM
  • Office Hour Location: Cafe in Mchenry Library
  • Discussion Sections: 3:30PM-4:30PM T/Th
  • Section Location: Physical Sciences 130
  Sections and office hours begin the first week of class.
• Study Hall Tutoring: LSS is supporting our course through the Math Study Hall Program. You can sign-up for tutoring sessions on TutorHub. Our tutors are:
  • Tutor: Kate Wang
    e-mail:
  • Tutor: Megan Tallcott
    e-mail:
• Accessibility: I am strongly committed to making my course as accessible as possible. If you encounter materials that are not accessible to you, or experience a barrier to your participation, please bring this to my attention and I will gladly work with you to ensure accessibility. I am also happy to honor any accommodations letters from the Disability Resource Center (DRC) that you would like to confidentially bring to my attention.
• Course Content: Functions of several variables, continuity and partial derivatives, the chain rule, gradient and directional derivative, maxima and minima, including Lagrange multipliers, the double and triple integral and change of variables, surface area and volumes, and applications from biology, chemistry, earth sciences, engineering, and physics.
• Learning Outcomes: Upon successful completion of the course, students will be able to do the following within the topic of multivariable calculus:
  • Recall the basic definitions, theorems, and techniques of multivariable calculus.
  • Distinguish truth from falsehood and create examples and counterexamples.
  • Competently and confidently solve a variety of problems that require techniques from multivariable calculus.
  • Communicate mathematical ideas and arguments in clear, convincing, and concise language, both written and oral.
  In addition to mastering course content, students will further develop as independent, self-directed learners with the confidence to explore unfamiliar problems and ideas.

Assessments

• Assessment Distribution: Your final score in the course will be calculated as the weighted average of the following assessments.
  • Reading Assignments (15%)
  • Daily Assignments (15%)
  • Weekly Assignments (25%)
  • Edfinity Exercises (15%)
  • Midterm Exam (15%)
  • Final Exam (15%)
  • Discussion Sections (5%)
• Submitting Assignments: All reading assignments and weekly assignments must be submitted via Gradescope.
  
  • All Reading, Daily, and Weekly assignments must be submitted via Gradescope. When you submit your files, you will be prompted to select, for each specified problem or activity, the pages on which the associated work/solution are located. You are required to accurately identify the pages associated to each problem. If you fail to do so, you may receive a “No Pass” (if it is a daily or reading assignment) or you may receive no credit for each problem for which the pages are not correctly identified (if it is a weekly assignment).
  • Additionally, it is your responsibility to make sure your submission is legible and easy to read. If you submit work that is difficult or impossible to read, you will not receive credit for it, and you will not be allowed to resubmit.
    
  • There are numerous free smartphone apps that allow you to scan your work and save it as a PDF.
• Use of Generative AI: Use of generative AI (such as ChatGPT or Gemini) is permitted as a learning and study aid in this course, provided that their use aligns with the academic integrity policies at UCSC. All work submitted for grading must be your own original work. Any AI use on graded assignments must be documented and properly cited.
  Generative AI programs create responses to prompts by predicting what text comes next based on patterns in its training data. It does not understand math or reason logically. This means it can produce convincing “answers” that are completely wrong, especially in technical subjects like mathematics.
  Students must be aware that generative AI programs frequently generate misinformation and are generally unreliable for mathematical problem solving.
• Late Work Policy: I will not, under any circumstance, accept late submissions for reading assignments, daily assignments, or Edfinity exercises. Late submissions of weekly assignments and exams are only accepted, at my sole discretion, in extreme circumstances. Extreme circumstances must be adequately documented and confidentially brought to my attention as soon as possible.
• Letter Grades: Your final letter grade depends on your score. Final letter grades are assigned according to the following score ranges:
  

  A+	96-100	B+	86-89	C+	76-79	D+	66-69	F	0-59
  A	93-95	B	83-85	C	73-75	D	63-65
  A-	90-92	B-	80-82	C-	70-72	D-	60-62

  
  Score ranges may be adjusted (to your advantage) according to class performance. Scores falling in between two ranges will be rounded up. For example, according to the ranges above a final score of 75.1 will earn the letter grade C+ (rounded up), whereas a final score of 74.9 will earn the letter grade C (no rounding).