Calculus of Several Variables
Course facts
- Payment: Free, no certificate
- Credits: Non Credit
- Learning style: Self-paced, start anytime
- Resources: Exam Solutions; Exams; Instructor Insights; Lecture Notes; Problem Set Solutions; Problem Sets
- Before you start: 18.01 Single Variable Calculus
MIT OpenCourseWare details
- As taught in: Fall 2010
- Department: Mathematics
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Several-variable calculus with a conceptual focus: vectors, derivatives, vector fields, multiple integrals, and Stokes and Gauss theorems.
Multivariable calculus can be taught for its uses in science or for its mathematical ideas, and this version takes the second path. Written for students with a more theoretical interest, it treats vectors, functions of several variables, parametrized curves, vector fields and multiple integrals with extra attention to the concepts. It closes on line and surface integrals, Stokes and Gauss theorems, and forms on n-dimensional space.
What You Will Achieve
- Work with vectors, dot products and cross products, and describe lines and planes
- Differentiate functions of several variables using partial derivatives and the chain rule
- Compute arc length and describe curves through parametrizations
- Apply gradient, divergence, curl, Green’s theorem, Stokes’ theorem and the divergence theorem
Program Overview
Vectors and n-Dimensional Space
The geometry that the rest of the course relies on.
- Dot product and cross product
- Planes and distances
- Cylindrical and spherical coordinates
Derivatives, Curves and Vector Fields
Differentiation for functions of several variables.
- Limits and the derivative
- Chain rule and implicit functions
- Parametrised curves, arclength and moving frames
- Taylor polynomials, maxima and minima
Integrals and the Big Theorems
Integration in several variables and how its results connect.
- Double and triple integrals
- Line and surface integrals
- Stokes theorem and Gauss theorem
- Forms on R n
Course Completion
Job Outlook
This conceptual treatment of calculus supports later study in mathematics and other theoretical subjects.
Good for: Learners drawn to the theory of calculus who want more conceptual depth than an applications-first course provides.
Keep in mind: Notes, problem sets and exams with solutions are published, but some problems come from the Colley textbook, so you may need a copy. No video is listed.
Bottom line: A complete, well-documented written course for anyone who wants several-variable calculus with its ideas up front.
Frequently Asked Questions
How does this differ from 18.02 Multivariable Calculus?
It covers the same topics with more focus on mathematical concepts. The instructor notes describe 18.02 as emphasizing applications to the sciences, especially physics.
Are practice exams and solutions available?
Yes. Three midterms and a final are published, each with a practice version and solutions to both, alongside twelve problem sets with solutions.
How much time did students spend each week?
About 12 hours, across three one-hour lectures, two one-hour recitations, problem sets and exam study, according to the published Instructor Insights.
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