Math 50C --- Multivariable Calculus

Instructor: David Arnold

Compliments to Kristian Cozyris for the Easter Lily. You can download the Matlab 5.1 M-file lily.m and try it yourself. Compliments to Peter Gent for the Mystical Island. You can download the Matlab 5.1 M-file island.m and try it yourself.

What Is Multivariable Calculus?

The Math 50C course is the third in a sequence of three introductory calculus courses at College of the Redwoods. Math 50A and 50B, the first two courses in the three course calculus sequence, concentrate on functions mapping the real numbers into the real numbers; that is, functions of a single real variable. In Math 50C, topics in differentiation and integration are revisited, but the functions involved are no longer required to map the real numbers into the real numbers. For example, functions such as f(x,y) = xycos(xy), g(x,y,z) = xy + yz + xz, and F(x,y) = [-y,x] are typical of the functions used in multivariable calculus. The function f maps the plane to the real line, the function g maps three dimensional space to the real line, and the function F maps the plane to a two dimensional vector field.

Along the way, students in multivariable calculus will study

What Are The Prerequisites?

Students need to complete two courses in calculus -- differentiation and integration -- before enrolling in multivariable calculus. It is helpful (but not required) if you have completed a course in linear algebra. Linear algebra concepts are developed in the muultivariable calculus course as needed, so students should not feel that they are at a disadvantage if they have not completed a prior course in linear algebra.

Who Takes Multivariable Calculus?

Students in mathematics, science, and engineering usually complete the following core mathematics courses in their freshman and sophomore years.
 
First Semester Second Semester
Freshman Year Calculus I Calculus II
Sophomore Year Calculus III Differential Equations

Math and science students are also expected to fit in an introductory linear algebra course (Math 45, Fall only) during one of these first four semesters. Some schools actually require that you complete an introductory course in linear algebra before taking the third course in calculus or a course in differential equations (Math 55, spring only). You should also complete a one semester class in programming. We recommend Matlab Programming (Math 4, spring only).

Computing Resources

Multivariable calculus is taught in our phsyics laboratory where each student will have access to a computer during class for discovery and demonstration. Computers are also available in the computer laboratories (PS 116 and PS110) in the physical science building. Students will find Matlab and other software packages that will allow them to complete assignments and explore concepts at their own pace. You can also purchase the Student Edition of Matlab for home use. Be sure that you check the system requirements before purchasing the Matlab software.

Syllabus

Office hours, class management, materials needed, homework and test policies, grading, etc. All of these are available in the Syllabus online.

Homework Assignments

Activities and assignments for the semester will be accumulated on the Homework Page. This page will be under construction throughout the semester as new activities and assignments are added.

Sample Examinations

The examinations administered during past semesters can be found on the Examination Page. Although examinations this semester will not be identical to those found on the Examination Page, you can still find questions typical of those that you will encounter on upcoming quizzes and examinations.

Sample Activities

You can find a list of the Matlab Activities that will be used in this class on the Activities Page.