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Browse materialsMIT 18.02SC · 2. Partial Derivatives

Multivariable Calculus — 2. Partial Derivatives

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: 39 videos · 3 problem sets · 2 exams · 26 solutions · 45 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 24 Clip: Functions of Two Variables: Graphs Find a topic

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Materials by section

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

Session 24: Functions of Two Variables: Graphs

10 files

Session 25: Level Curves and Contour Plots

7 files

Session 26: Partial Derivatives

8 files

Session 27: Approximation Formula

10 files

Session 28: Optimization Problems

9 files

Session 29: Least Squares

11 files

Session 30: Second Derivative Test

19 files

Session 31: Example

Problem Set 4

Session 32: Total Differentials and the Chain Rule

11 files

Session 33: Examples

7 files

Session 34: The Chain Rule with More Variables

8 files

Session 35: Gradient: Definition, Perpendicular to Level Curves

8 files

Session 36: Proof

7 files

Session 37: Example

7 files

Session 38: Directional Derivatives

11 files

Problem Set 5

Session 39: Statement of Lagrange Multipliers and Example

11 files

Session 40: Proof of Lagrange Multipliers

Session 41: Advanced Example

7 files

Session 42: Constrained Differentials

8 files

Session 43: Clearer Notation

7 files

Session 44: Example

12 files

Problem Set 6

Practice Exam

Session 45: Review of Topics

15 files

Session 46: Review of Problems

Session 46: Review of ProblemsPNG image Open ↗

Multivariable Calculus — 2. Partial Derivatives

Materials by section

Session 24: Functions of Two Variables: Graphs

Session 25: Level Curves and Contour Plots

Session 26: Partial Derivatives

Session 27: Approximation Formula

Session 28: Optimization Problems

Session 29: Least Squares

Session 30: Second Derivative Test

Session 31: Example

Problem Set 4

Session 32: Total Differentials and the Chain Rule

Session 33: Examples

Session 34: The Chain Rule with More Variables

Session 35: Gradient: Definition, Perpendicular to Level Curves

Session 36: Proof

Session 37: Example

Session 38: Directional Derivatives

Problem Set 5

Session 39: Statement of Lagrange Multipliers and Example

Session 40: Proof of Lagrange Multipliers

Session 41: Advanced Example

Session 42: Constrained Differentials

Session 43: Clearer Notation

Session 44: Example

Problem Set 6

Practice Exam

Session 45: Review of Topics

Session 46: Review of Problems

Exam Materials

Session 24 Clip: Functions of Two Variables: Graphs

Session 24: Graphing Surfaces

Session 25 Clip: Level Curves and Contour Plots

Session 25: Level Curves

Session 25: Level Curves and Critical Points

Session 26 Clip: Partial Derivatives

Session 26: Partial Derivatives

Session 27 Clip: Approximation Formula

Session 27: Tangent Plane Approximation

Session 28 Clip: Optimization Problem

Session 29 Clip: Least Squares

Session 29: Least Squares

Session 30 Clip 1: Quadratic Example

Session 30 Clip 2: Second Derivative Test

Session 30: Second Derivative Test

Session 31 Clip: Example

Session 31: Max/Min

Session 32 Clip: Total Differentials and Chain Rule

Session 33 Clip: Examples

Session 34 Clip: Chain Rule with More Variables

Session 34: Total Differentials and the Chain Rule

Session 35 Clip: Definition, Perpendicular to Level Curves

Session 36 Clip: Proof

Session 37 Clip: Example

Session 37: Tangent Planes

Session 38 Clip: Directional Derivatives

Session 38: Gradient and Directional Derivative

Session 39 Clip: Lagrange Multipliers by Example

Session 39: Lagrange Multipliers

Session 40 Clip: Proof of Lagrange Multipliers

Session 41 Clip: Advanced Example

Session 41: Lagrange Multipliers (3 Variables)

Session 42 Clip: Constrained Differentials

Session 43 Clip: Clearer Notation

Session 43: The Chain Rule with Constraints

Session 44 Clip: Example

Session 44: Gradients - Composition

Session 45 Clip: Review of Topics

Session 46 Clip: Review of Problems