RES.18-007 | Fall 2011 | Undergraduate

Calculus Revisited: Multivariable Calculus

Study Materials

Study Guides

The Study Guides include pre-tests, photographs of every chalkboard used in the videotapes, reading assignments in the supplementary notes and textbook, and exercises with solutions.

Part I: Vector Arithmetic
1 The “Game” of Mathematics (PDF - 1.8MB) (PDF - 3.7MB)
2 Three-Dimensional Vectors (PDF) (PDF - 2.8MB)
3 Three-Dimensional Vectors (PDF) (PDF - 2.1MB)
4 The Dot Product (PDF) (PDF - 2.9MB)
5 The Cross Product (PDF) (PDF - 2.1MB)
6 Equations of Lines & Planes (PDF) (PDF - 2.9MB)
Part II: Vector Calculus
1 Vector Functions of a Scalar Variable (PDF) (PDF - 2.4MB)
2 Tangential & Normal Vectors (PDF) (PDF - 2.8MB)
3 Polar Coordinates (PDF) (PDF - 2.6MB)
4 Vectors in Polar Coordinates (PDF) (PDF - 4.7MB)
Part III: Partial Derivatives
1 n-Dimensional Vector Spaces (PDF - 1.1MB) (PDF - 4.2MB)
2 Calculus of Several Variables (PDF) (PDF - 3.6MB)
3 Directional Derivatives (PDF) (PDF - 4.2MB)
4 The Chain Rule (PDF) (PDF - 2.7MB)
5 Integrals Involving Parameters (PDF) (PDF - 3.0MB)
6 Exact Differentials (PDF) (PDF - 4.2MB)
Part IV: Matrix Algebra
1 Linearity Revisited (PDF) (PDF - 2.3MB)
2 The “Game” of Matrices (PDF) (PDF - 3.1MB)
3 Inverting a Matrix (PDF) (PDF - 2.9MB)
4 Inverting More General Systems of Equations (PDF) (PDF - 1.5MB)
5 Maxima and Minima in Several Variables (PDF) (PDF - 3.8MB)
Part V: Multiple Integration
1 Double Multiple Sums (PDF - 1.1MB) (PDF - 2.3MB)
2 The Fundamental Theorem (PDF) (PDF 2.3MB)
3 Multiple Integration and the Jacobian (PDF) (PDF - 4.2MB)
4 Introduction to Line Integrals (PDF) (PDF - 2.2MB)
5 Green’s Theorem (PDF) (PDF - 1.7MB)

Supplementary Notes for Multivariable Calculus, Parts I through V

The Supplementary Notes include prerequisite materials, detailed proofs, and deeper treatments of selected topics.

  • Chapter 1: An Introduction to Mathematical Structure (PDF - 3.4MB)
  • Chapter 2: An Introduction to Vector Arithmetic (PDF - 2.1MB)
  • Chapter 3: An Introduction to Vector Calculus (PDF - 2.6MB)
  • Chapter 4: An Introduction to Functions of Several Real Variables (PDF - 5.4MB)
  • Chapter 5: Derivatives in n-Dimensional Spaces (PDF - 3.0MB)
  • Chapter 6: Matrix Algebra in the Study of Functions of Several Variables (PDF - 7.6MB)
  • Chapter 7: Applications of Linear Algebra to Non-Linear Functions (PDF - 2.1MB)

Textbook: The course makes reference to the out-of-print textbook cited below, but any newer textbook will suffice to expand on topics covered in the video lectures.

Thomas, George B. Calculus and Analytic Geometry. Addison-Wesley, 1968. ISBN: 9780201075250.

Course Info

As Taught In
Fall 2011
Learning Resource Types
Lecture Videos
Lecture Notes
Problem Sets with Solutions