Multivariable Calculus
Course facts
- Payment: Free, no certificate
- Credits: Non Credit
- Learning style: Self-paced, start anytime
- Resources: Exam Solutions; Exams; Lecture Notes; Lecture Videos; Problem Set Solutions; Problem Sets
MIT OpenCourseWare details
- As taught in: Fall 2010
- Department: Mathematics
| Course Details | ||||||
|---|---|---|---|---|---|---|
|
||||||
| Outcomes | ||||||
|
||||||
| Price & Terms | ||||||
|
||||||
| Technical | ||||||
|
||||||
| Specification | ||||||
|
||||||
Multivariable calculus for self-study: vectors, matrices, partial derivatives, multiple integrals, vector fields and the theorems of Green, Stokes and Gauss.
Pressure depends on volume and temperature, and electric and magnetic fields depend on three space variables and time, so describing the physical world needs calculus in more than one variable. This course, built for independent study, covers differential, integral and vector calculus for functions of several variables: vectors and matrices, parametric curves, partial derivatives, double and triple integrals, and vector calculus, ending with Green’s, Stokes’ and Gauss’ theorems.
What You Will Achieve
- Work fluently with vectors and matrices, including solving systems of linear equations
- Use gradients, directional derivatives and the chain rule for functions of several variables
- Solve optimization problems with and without constraints, including Lagrange multipliers
- Set up and compute multiple, line and surface integrals and apply Green’s, Stokes’ and Gauss’ theorems
Program Overview
Vectors, Matrices and Curves
The algebra and geometry of several dimensions.
- Vectors, determinants and planes
- Matrices and systems of equations
- Parametric equations for curves
Partial Derivatives
Rates of change when many variables change at once.
- Functions of two variables, tangent approximation and optimization
- Chain rule, gradient and directional derivatives
- Lagrange multipliers and constrained differentials
Multiple Integrals and Vector Calculus
Integration in the plane and in space, and the big theorems.
- Double integrals, vector fields, line integrals and Green’s theorem
- Triple integrals
- Flux and the divergence theorem
- Line integrals, Stokes’ theorem and physics applications
Course Completion
Job Outlook
Multivariable calculus is used in physics, every branch of engineering, economics, computer graphics, data science and machine learning.
Good for: Self-taught learners who want a complete course in multivariable calculus, laid out session by session with solutions to check their work.
Keep in mind: The lecture clips date from fall 2007, recorded in class with Professor Denis Auroux; recitation videos and worked examples add problem-solving help.
Bottom line: A complete self-study multivariable calculus course, with an exam and solutions at the end of each unit.
Frequently Asked Questions
How is the course organized?
Four units, each split into parts and each part into sessions meant for one sitting, with problems placed along the way and an exam covering the whole unit at the end of each.
Where does multivariable calculus show up in practice?
The course points to thermodynamics, where pressure depends on volume and temperature, electric and magnetic fields that vary in space and time, and fluid or heat flow.
What does the course build up to?
Green's, Stokes' and Gauss' theorems, which relate derivatives to integrals in more than one variable much as the Fundamental Theorem of Calculus does in one.
User Reviews
Write your review
You must be logged in to post a review.
Reviews can only be posted by registered learners. Log in or create a free account, then you will return here to post.
There are no reviews yet.