Calculus IV (Math 313)
Syllabus - Spring 2019

Sections MWF 8:00-8:50, DSC 110
Communication Office Hours: posted online, or by appointment
Announcements may be made via e-mail and the class web page:
Textbook Active Calculus 2018 Ed. and other online sources
Technology You will need to use software to complete assignments.
  • Bring a scientific calculator to class and tests.
  • We will use Wolfram Alpha, Geogebra, Sage, Jupyter, or other software packages. Demonstrations and instructions will be given.
Description Math 211/313 extends the concepts of calculus to higher dimensions.
  • Calc III will survey the following topics: multivariable functions, partial derivatives, function approximation, vector geometry, curves and surfaces, double/triple integrals, parametric equations, polar coordinates, length/area, sequences and series,
  • Calc IV will explore Calc III concepts deeper, while studying convergence, motion in space, optimization, applications of integration, vector fields, div/grad/curl
We will try to develop intuition via visualization and applications.
Prerequisites Calculus I and II
Final Exam
Guaranteed grades are A, B, C, D for 90, 80, 70, 60 respectively.
Class Structure This class will make limited use of traditional lecture. Each class period will consist of some subset of the following:
  • Instructor's introduction to a topic or software demo.
  • Working an example as a class.
  • Class Q&A, discussion.
  • Students working (often together) on a sequential problem set.
  • Student presentation of a solution.
  • Timed quiz.
Portfolio During the semester you will be proceeding through a sequential problem set. By the end of the semster, you should have created a beautiful portfolio of your mathematical work.
  • Class time will be reserved for working on these problems, but you will also need to spend significant time out of class. You are expected to keep up so that you can interact productively during class.
  • You may work together, ask questions, get feedback, etc. But your final written solutions should be your own, and represent your personal understanding of the problem. Your writeups should show a "signature" in notation, organization, word phrasing, etc. that demonstrates independent thought.
  • All final work must be typeset using a computer (Jupyter notebook); instruction will be given.
  • You are encouraged to use technology to do calculations or graphs. Only when explicitly stated do you need to do calculations by hand.
  • Some problems may require short computer programs or workspaces. Print out all supporting code, screenshots, inputs, and outputs.
  • Keep a loose leaf binder that can hold the final organized, labeled, and polished version of each problem.
  • There will be checkpoints roughly every 2 weeks, at which time you will submit a section of your portfolio for grading. Please ask for informal feedback often, and I can point out areas where your work needs to be improved.
  • Each problem will have a designated point value, and be graded on TRUTH, BEAUTY, and GOODNESS, according to the four P's of portfolio:
    • Perfect - is the work complete and correct?
    • Professional - is the presentation clear, orderly, neat, prepared according to instructions, with supporting work, references, and printouts? All steps must be documented using complete sentences or agreed upon notation. Ask yourself these questions:
      • Would I be proud to submit this work to my boss or client?
      • In 10 years will my future self understand what my present self did?
    • Punctual - was the item perfected by the checkpoint deadline?
    • Personal - does the work demonstrate independent process and understanding?

NOTE: Do not be surprised or disappointed that some problems do not have easy or obvious solutions. You may have to think deeply and try several things before discovering a solution. If you encounter a difficult problem, please don't give up. Struggling with a problem is the only way to really learn mathematics. Please come by my office to ask for help if you are stuck.

Participation You are expected to attend every class period, work diligently, and interact productively with your classmates.
  • When you must be absent, get notes from a classmate. You are responsible for all course material, as well as any in-class assignments that may be given.
  • Make arrangements with me if you have an excused absence, and miss a quiz or deadline.
  • Make regular visits to office hours to review your work and ask questions.
  • Prepare for class with assigned reading, problems, and videos.
  • During the semester, each student will be responsible for several problems to be presented in written form and/or on the board for the class.
  • Do not fall behind on your sequential problem set and portfolio construction.
  • You will be graded subjectively on your attendance, preparedness, presentation, questions, conscientiousness, attitude, and teamwork.
  • I encourage you to periodically ask me for feedback about your quality of participation.
Quizzes We will have in-class quizzes (maybe one a week), designed to make sure you become fluent in basic concepts and computational tasks.
  • Quiz topics (but not necessarily dates) will be announced in advance. They will reference the lectures, book, problem sets, or other examples. Once a topic has been announced, it is eligible for all subsequent quizzes.
  • Each quiz will be timed, and open-book, but not necessarily open-computer.
  • In-class quizzes may not be made up, but will not count against you if the absence is excused.
  • Each quiz is weighted 10 points.
Final Exam There will be no mid-term tests. The final exam is comprehensive, and will cover topics from quizzes and the sequential problem set. Consult the college exam schedule for date and time.
Academic Integrity