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Browse materialsMIT 18.02SC · 4. Triple Integrals and Surface Integrals in 3-Space

Multivariable Calculus — 4. Triple Integrals and Surface Integrals in 3-Space

Subjects: Algebra · Calculus · Linear Algebra · Mathematics

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

About this course

Source: MIT OpenCourseWare 18.02SC Multivariable Calculus, Fall 2010, Prof. Denis Auroux — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: this unit's sessions in MIT's listing order. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 22, 2026. How RedLectern is built.

Instructor: Prof. Denis Auroux
Term: Fall 2010
Level: Undergraduate
What's inside: 45 videos · 5 problem sets · 2 exams · 27 solutions · 46 other files
Materials open: Videos here · files on MIT OCW

Other versions of this course

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

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Start course: Session 74 Clip: Triple Integrals Find a topic

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Materials by section

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

Session 74: Triple Integrals: Rectangular and Cylindrical Coordinates

12 files

Session 75: Applications and Examples

11 files

Session 76: Spherical Coordinates

8 files

Session 77: Triple Integrals in Spherical Coordinates

13 files

Session 78: Applications: Gravitational Attraction

9 files

Problem Set 10

Session 79: Vector Fields in Space

7 files

Session 80: Flux Through a Surface

8 files

Session 81: Calculating Flux; Finding ndS

10 files

Session 82: ndS for a Surface z = f(x, y)

9 files

Session 83: Other Ways to Find ndS

9 files

Session 84: Divergence Theorem

Session 85: Physical Meaning of Flux; Del Notation

Session 86: Proof of the Divergence Theorem

7 files

Session 87: Diffusion Equation

9 files

Problem Set 11

Session 88: Line Integrals in Space

11 files

Session 89: Gradient Fields and Potential Functions

11 files

Session 90: Curl in 3D

10 files

Session 91: Stokes' Theorem

11 files

Session 92: Proof of Stokes' Theorem

Session 93: Example

Session 94: Simply Connected Regions; Topology

9 files

Multivariable Calculus — 4. Triple Integrals and Surface Integrals in 3-Space

Materials by section

Session 74: Triple Integrals: Rectangular and Cylindrical Coordinates

Session 75: Applications and Examples

Session 76: Spherical Coordinates

Session 77: Triple Integrals in Spherical Coordinates

Session 78: Applications: Gravitational Attraction

Problem Set 10

Session 79: Vector Fields in Space

Session 80: Flux Through a Surface

Session 81: Calculating Flux; Finding ndS

Session 82: ndS for a Surface z = f(x, y)

Session 83: Other Ways to Find ndS

Session 84: Divergence Theorem

Session 85: Physical Meaning of Flux; Del Notation

Session 86: Proof of the Divergence Theorem

Session 87: Diffusion Equation

Problem Set 11

Session 88: Line Integrals in Space

Session 89: Gradient Fields and Potential Functions

Session 90: Curl in 3D

Session 91: Stokes' Theorem

Session 92: Proof of Stokes' Theorem

Session 93: Example

Session 94: Simply Connected Regions; Topology

Session 95: Stokes' Theorem and Surface Independence

Session 96: Summary of Multiple Integration

Problem Set 12

Practice Exam

Exam

Session 97: Curl and Physics

Session 98: Maxwell's Equations

Session 74 Clip: Triple Integrals

Session 74 Clip: Cylindrical Coordinates

Session 74: Volume in Cylindrical Coordinates

Session 75 Clip: Applications and Examples

Session 75: Average Height

Session 75: Moment of Inertia of a Cylinder

Session 76 Clip: Spherical Coordinates

Session 77 Clip: Triple Integrals in Spherical Coordinates

Session 77: Average Distance on a Sphere

Session 78 Clip: Gravitational Attraction

Session 78: Gravity and a Half-Sphere

Session 79 Clip: Vector Fields in Space

Session 80 Clip: Flux Through a Surface

Session 80: Flux Through Easy Surfaces

Session 81 Clip: Calculating Flux, Finding ndS

Session 81: Flux Through a Square

Session 81: Flux Through Surfaces

Session 82 Clip: ndS for a Surface z=f(x,y)

Session 83 Clip: Other Ways to Find ndS

Session 84 Clip: Divergence Theorem

Session 84: Flux

Session 84: Flux and the Divergence Theorem

Session 84: Extended Gauss' Theorem

Session 85 Clip: Physical Meaning of Flux, Del Notation

Session 85: Del and the Product Rule

Session 86 Clip: Proof of the Divergence Theorem

Session 87 Clip: Diffusion Equation

Session 88 Clip: Line Integrals in Space

Session 88: Line Integral on a Helix

Session 89 Clip: Gradient Fields and Potential Functions

Session 90 Clip: Curl in 3D

Session 90: Conservative Fields and Exact Differentials

Session 91 Clip: Stokes' Theorem

Session 91: Stokes' Theorem

Session 92 Clip: Proof of Stokes' Theorem

Session 93 Clip: Example

Session 93: Extended Stokes' Theorem

Session 94 Clip: Simply Connected Regions, Topology

Session 94: Simply Connected Regions

Session 94: More Stokes' Theorem