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MAT203 Advanced Vector Calculus

Schedule: MWTh@11AM or @1:30PM, Fall only. 

Course Type: Example-Based

Brief Course Description: Covers largely the same mathematical topics as MAT201, namely vectors, lines, planes, curves, and surfaces in 3-space and more generally in n-space; limits, continuity, optimization, differentiation and integration of functions of several variables; vector fields, line integrals, flux integrals and integration theorems generalizing the Fundamental Theorem of Calculus. The course requires greater independence, thorough conceptual understanding, and computational fluency.

Why take this course? Similar to MAT201 in content, MAT203 is more in-depth and theoretical, often generalizing from 3 dimensions to n-space.  MAT203 places greater emphasis on why than how; its homework and exam problems often require greater fluency in mathematical computations and sophistication in mathematical thinking. Assumes a strong interest in physics.

Prerequisites:  MAT104 or equivalent, and high level of mathematical interest and maturity.

Who takes this course? Most students in this course are first-year students with strong mathematical interest and maturity intending to major in physics, applied math, or engineering. 

Placement Information:  In addition to a strong background of single-variable calculus and precalclulus, students should have a serious interest in thinking rigorously about problems involving space and time. 

Work Load & Grading: Weekly precepts will cover more sophisticated examples to illustrate subtle aspects of definitions and interesting applications.  Weekly problem sets include supplementary problems not found in standard textbooks in order to help students develop independent and creative problem-solving skills. Students should read the textbook before each class and review lecture notes after each class. Homework should take at least 6 hours, although this can vary quite a lot depending on your background and goals. There are organized homework sessions with guidance from undergraduate course assistants before each problem set is due, but students should first work independently before seeking help from course assistants during homework sessions. To do well on math exams, you need to work through a lot of extra problems from past exams.   All in all, you should be ready to spend at least 10 hours per week working outside of class.  MAT203 is graded with a more generous curve than MAT201 in order to remove considerations of grades as a deciding factor between the two courses. 

FAQ: 

  • How much harder is MAT203 than MAT201?  MAT203 is more abstract and faster-paced than MAT201 and requires a great time commitment and enthusiasm.  MAT203 has significantly higher work load than MAT201.  For most students, MAT201 is an excellent course that provides enough challenge to be interesting and gives the background needed in upper division courses.
  • You think MAT203 is too hard after looking at the sample problems or attending the first couple classes.  MAT201 and MAT203 cover essentially the same topics, so it is quite easy to switch between the two courses in the first few weeks. It is not rare that after a week or two students decide to switch down to MAT104 to get a more thorough foundation for MAT201 or MAT203.  If the pace of 201/203 is overwhelming, consider this switch as soon as possible, as there is no overlap between MAT203 and MAT104, and it will be very difficult to catch up and do well in MAT104.  
  • You think MAT203 is not challenging enough.  Wait till you have had a quiz, which usually occurs in the 3rd week. Try some old quizzes for this course, but don’t just read the questions/solutions. Instead, see if you can produce correct solutions to most of the problems in the allotted time.  If you can do well on old exams, then you may consider taking MAT215 or MAT216 instead, especially if you are interested in math or physics as a major.  There is no overlap between MAT201 and MAT215/MAT216, so this course switch should take place as early as possible.
  • Can I take MAT203 and MAT204 in any order?  Yes.  MAT203 is only offered in the fall, and MAT204 only in the spring.   Most MAT203 students continue with MAT204 in the spring.  You can take them in either order, but we do recommend students take MAT203 first if possible. Students can substitute MAT201 for MAT203 or MAT202 for MAT204 to satisfy most programs or departments that require these courses.
File Attachments
MAT 203 Sample Problems

Remember

  • Your interests will naturally evolve over the course of your first year at Princeton. Keep an open mind and seek advice to help you reach your goals! 
  • Lots of help is available if you run into unexpected difficulty. Early action can make a big difference! It is easy to switch down to 201 after a few weeks.
  • Choose between 203 & 201 based on your interest, not on consideration of grades. The grading scheme takes into account that 203 is harder than 201.
  • Take the course that matches your current knowledge. Trying to jump ahead can actually slow you down. You can catch up later, over the summer, if necessary.