MIT OpenCourseWare

Browse materialsMIT 18.02 · Spring 2006

Multivariable Calculus

Subjects: Algebra · Calculus · Linear Algebra · Mathematics

Art: Max Brückner (1860 – 1934), Brückner Vielflache Tafel 07 · Public domain

Instructors: Prof. David Jerison, Prof. Arthur Mattuck
Term: Spring 2006
Level: Undergraduate
What's inside: 1 reading · 96 other files · 6 web pages
Materials open: MIT OCW

Other versions of this course

18.02SC · Fall 2010 · Study here
18.02 · Fall 2007 · Study here
18.02 · Spring 2006 · Study here (this version)

Start here

Start course: Lecture 1: Vectors in 2- and 3-space Dot Product Find a topic

Progress is saved in this browser.

Export or import progress

About this course

Source: MIT OpenCourseWare 18.02 Multivariable Calculus, Spring 2006, Prof. David Jerison, Prof. Arthur Mattuck — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Has MIT solutions 21 files in this course are named by MIT as solutions.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

How this course was organized

What's here, and what isn't

A lecture sequence of 35 items is confirmed. Assignment and exam materials exist too, but MIT's own order for them could not be verified, so they're shown as materials below rather than a sequence.

Not included here

1 item from the source could not be safely included:

Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence.

Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Readings

38 files in this section

18.02 Supplementary Notes and Problems

38 files

Assignments

12 problem sets

Exams

24 files

Study Materials

7 files

Other materials from this course

15 files

MIT OpenCourseWare, Prof. David Jerison, Prof. Arthur Mattuck, 18.02 Multivariable Calculus, Spring 2006.

License: CC BY-NC-SA 4.0 · Edition: Spring 2006 · Open the original course on OCW ↗

Organized by RedLectern, independent of MIT and not endorsed by MIT.

Per-resource rights are recorded on each resource; All-Rights-Reserved items are link-only, never mirrored.

Multivariable Calculus

Before you start

What's here, and what isn't

Not included here

Materials by section

Readings

18.02 Supplementary Notes and Problems

Assignments

Exams

Study Materials

Other materials from this course

Lecture 1: Vectors in 2- and 3-space Dot Product

Lecture 2: Determinants of Orders 2 and 3 Cross Product

Lecture 3: Matrices; Inverse Matrices

Lecture 4: Solving Systems of Linear Equations; Lines, Planes

Lecture 5: Parametric Curves; Velocity, Acceleration

Lecture 6: Kepler’s Second Law

Lecture 7: Level Curves, Partial Derivatives, Tangent Plane

Lecture 8: Max-Min Problems Least Squares Approximation

Lecture 9: 2nd Derivative Test; Boundaries and Infinity

Lecture 10: Differentials; Chain Rule

Lecture 11: Gradient, Directional Derivative

Lecture 12: Lagrange Multipliers

Lecture 13: Non-independent Variables

Lecture 14: Partial Differential Equations Review

Lecture 15: Double and Iterated Integrals

Lecture 16: Double Integrals in Polar Coordinates Applications

Lecture 17: Change of Variables

Lecture 18: Triple Integrals in Rectangular and Cylindrical Coordinates

Lecture 19: Spherical Coordinates Gravitational Attraction

Lecture 20: Line Integrals in the Plane

Lecture 21: Gradient Fields and Path Independence

Lecture 22: Conservative Fields and Potential Functions

Lecture 23: Green’s Theorem 2-dimensional Curl (Vorticity)

Lecture 24: Simply-connected Regions Review

Lecture 25: Flux Form of Green’s Theorem

Lecture 26: Vector Fields in 3-space; Surface Integrals and Flux

Lecture 27: Divergence (= Gauss’s) Theorem

Lecture 28: Divergence Theorem (cont.)

Lecture 29: Line Integrals in Space, Exactness, and Potentials

Lecture 30: Stokes’ Theorem

Lecture 31: Understanding Curl Review

Lecture 32: Topological Issues

Lecture 33: Conservation Laws; Heat/Diffusion Equation

Lecture 34: Course Review

Lecture 35: Course Evaluation Maxwell’s Equations