Third semester of the 3-semester calculus sequence 103/104/201. Introduces mathematical methods needed to understand real world questions involving quantities changing over time in 3-space. Students must move beyond thinking about mathematics as a set of rules and algorithms to memorize. Instead they learn to approach problems with greater independence and maturity. Exams test for thorough conceptual understanding and computational fluency in standard cases. In other words, although demanding, the exams do not typically involve proofs, and there is little emphasis on exceptional cases.
The first part of the course introduces basic objects in space: lines, planes, curves, (quadric) surfaces, and basic properties like arc length, surface area and volume.
The second part moves on to quantities that change with position in 3-space, like temperature or population density, which can be described by functions of several variables. We study their graphs, level sets, rates of change (partial derivatives) and their extreme points (maxima/minima) using Lagrange multipliers and Taylor's theorem.
The third part is devoted to vector fields, quantities that change with both position in space and with time. Think of how storms move, how radio signals make cell phones work or how blood flows. Although we do not explicitly study such applications, we lay the mathematical foundation for more advanced courses in science, engineering, and economics. The course ends with the theorems of Green, Gauss, and Stokes.
Classes: meet 3 times per week, for 50 minutes. Generally offered MWF at 10, 11 and 12:30 in both Fall and Spring semesters. The course is organized into small precepts of 20 to 30 students. There is one course head who coordinates with all the instructors to write the exams. All students have the same homework assignments and take the same midterm and final exam. These exams count for most of your course grade. They are graded by all the instructors together to ensure uniformity across sections. In addition there are two to four take-home quizzes, the same for all sections.
Textbook: Thomas' Calculus Customized for Princeton University by Thomas, Weir, and Hass, Vol 2, (12th edition) Pearson: Addison Wesley.
General information about placement and contact information for the placement officer can be found on the math placement page.
Once you have tried the problems, you can check your answers:Quiz One Solutions, Midterm Exam Solutions, Quiz Two Solutions, Final Exam Solutions.