Lecture Notes · Lecture Notes
MIT OpenCourseWare
Calculus of Several Variables
Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain
- Instructor
- Prof. James McKernan
- Term
- Fall 2010
- Level
- Undergraduate
- What's inside
- 1 lecture note · 74 other files · 4 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.022 Calculus of Several Variables, Fall 2010, Prof. James McKernan — 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.
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 34 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
8 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (6 items)
- Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence. (2 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Lecture Notes
34 files
- Lecture 1 · Vectors in R² and R³ Download
- Lecture 2 · Dot product Download
- Lecture 3 · Cross product Download
- Lecture 4 · Planes and distances Download
- Lecture 5 · n -dimensional space Download
- Lecture 6 · Cylindrical and spherical coordinates Download
- Lecture 7 · Functions Download
- Lecture 8 · Limits Download
- Lecture 9 · The Derivative Download
- Lecture 10 · More about derivatives Download
- Lecture 11 · Higher derivatives Download
- Lecture 12 · Chain rule Download
- Lecture 13 · Implicit functions Download
- Lecture 14 · Parametrised curves Download
- Lecture 15 · Arclength Download
- Lecture 16 · Moving frames Download
- Lecture 17 · Vector fields Download
- Lecture 18 · Div grad curl and all that Download
- Lecture 19 · Taylor polynomials Download
- Lecture 20 · Maxima and minima: I Download
- Lecture 21 · Maxima and minima: II Download
- Lecture 22 · Double integrals Download
- Lecture 23 · Inclusion-exclusion Download
- Lecture 24 · Triple integrals Download
- Lecture 25 · Change of coordinates: I Download
- Lecture 26 · Change of coordinates: II Download
- Lecture 27 · Line integrals Download
- Lecture 28 · Manifolds with boundary Download
- Lecture 29 · Conservative vector fields revisited Download
- Lecture 30 · Surface integrals Download
- Lecture 31 · Flux Download
- Lecture 32 · Stokes theorem Download
- Lecture 33 · Gauss theorem Download
- Lecture 34 · Forms on Rⁿ Download
Assignments
24 problem sets
- Problem set 1 Download
- Problem set 1 · Solutions Download
- Problem set 2 Download
- Problem set 2 · Solutions Download
- Problem set 3 Download
- Problem set 3 · Solutions Download
- Problem set 4 Download
- Problem set 4 · Solutions Download
- Problem set 5 Download
- Problem set 5 · Solutions Download
- Problem set 6 Download
- Problem set 6 · Solutions Download
- Problem set 7 Download
- Problem set 7 · Solutions Download
- Problem set 8 Download
- Problem set 8 · Solutions Download
- Problem set 9 Download
- Problem set 9 · Solutions Download
- Problem set 10 Download
- Problem set 10 · Solutions Download
- Problem set 11 Download
- Problem set 11 · Solutions Download
- Problem set 12 Download
- Problem set 12 · Solutions Download
Exams
16 files
- 1 · Practice exam Download
- 1 · Exam Download
- 1 · Practice exam solution Download
- 1 · Exam solution Download
- 2 · Practice exam Download
- 2 · Exam Download
- 2 · Practice exam solution Download
- 2 · Exam solution Download
- 3 · Practice exam Download
- 3 · Exam Download
- 3 · Practice exam solution Download
- 3 · Exam solution Download
- Practice final exam Download
- PDF - 1.3 Download
- Practice final exam solutions Download
- Final exam solutions Download
Other materials from this course
Course outline
Lecture Notes · Lecture Notes
Lecture 2: Dot product
Lecture Notes · Lecture Notes
Lecture 3: Cross product
Lecture Notes · Lecture Notes
Lecture 4: Planes and distances
Lecture Notes · Lecture Notes
Lecture 5: n -dimensional space
Lecture Notes · Lecture Notes
Lecture 6: Cylindrical and spherical coordinates
Lecture Notes · Lecture Notes
Lecture 7: Functions
Lecture Notes · Lecture Notes
Lecture 8: Limits
Lecture Notes · Lecture Notes
Lecture 9: The Derivative
Lecture Notes · Lecture Notes
Lecture 10: More about derivatives
Lecture Notes · Lecture Notes
Lecture 11: Higher derivatives
Lecture Notes · Lecture Notes
Lecture 12: Chain rule
Lecture Notes · Lecture Notes
Lecture 13: Implicit functions
Lecture Notes · Lecture Notes
Lecture 14: Parametrised curves
Lecture Notes · Lecture Notes
Lecture 15: Arclength
Lecture Notes · Lecture Notes
Lecture 16: Moving frames
Lecture Notes · Lecture Notes
Lecture 17: Vector fields
Lecture Notes · Lecture Notes
Lecture 18: Div grad curl and all that
Lecture Notes · Lecture Notes
Lecture 19: Taylor polynomials
Lecture Notes · Lecture Notes
Lecture 20: Maxima and minima: I
Lecture Notes · Lecture Notes
Lecture 21: Maxima and minima: II
Lecture Notes · Lecture Notes
Lecture 22: Double integrals
Lecture Notes · Lecture Notes
Lecture 23: Inclusion-exclusion
Lecture Notes · Lecture Notes
Lecture 24: Triple integrals
Lecture Notes · Lecture Notes
Lecture 25: Change of coordinates: I
Lecture Notes · Lecture Notes
Lecture 26: Change of coordinates: II
Lecture Notes · Lecture Notes
Lecture 27: Line integrals
Lecture Notes · Lecture Notes
Lecture 28: Manifolds with boundary
Lecture Notes · Lecture Notes
Lecture 29: Conservative vector fields revisited
Lecture Notes · Lecture Notes
Lecture 30: Surface integrals
Lecture Notes · Lecture Notes
Lecture 31: Flux
Lecture Notes · Lecture Notes
Lecture 32: Stokes theorem
Lecture Notes · Lecture Notes
Lecture 33: Gauss theorem
Lecture Notes · Lecture Notes
Lecture 34: Forms on Rⁿ
MIT OpenCourseWare, Prof. James McKernan, 18.022 Calculus of Several Variables, Fall 2010.
License: CC BY-NC-SA 4.0 · Edition: Fall 2010 · Open the original course on OCW ↗
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