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MATH 2934
Calculus III

Lecture Notes

The following are lecture notes designed for the Calculus III class at ATU. The topics follow the partition of the textbook "Calculus, Single and Multivariable" by Hughes-Hallett/Gleason et al. These notes have been improved and will continue to be. Please feel free to browse through them.

To Students: BEWARE! The notes posted here are those that I write for myself to bring to class so that if you miss class, you can see approximately what we covered. I will NOT be posting notes as they would appear in class. There will be many missing examples and explanations. This is not a replacement for coming to class and taking notes yourself.
§ 12.1 Functions of Two Variables
§ 12.2 Graphs of Functions of Two Variables
§ 12.3 Level Curves and Contour Diagrams
§ 12.4 Linear Functions in Two Variables
§ 12.5 Functions of Three Variables
§ 12.6 Limits and Continuity of Functions of Two Variables
§ 13.1 Introduction to Vectors
§ 13.2 Properties of Vector Arithmetic and Applications
§ 13.3 Multiplication of Vectors: The Scalar or Dot Product
§ 13.4 Multiplication of Vectors: The Vector or Cross Product
§ 14.1 The Partial Derivative
§ 14.2 Algebraic Rules for Computing Partial Derivatives
§ 14.3 Local Linearization of Multivariable Functions
§ 14.4 Directional Derivatives and Gradients of Functions of Two Variables
§ 14.5 Directional Derivatives and Gradients for Functions of Three Variables
§ 14.6 The Chain Rule of Functions of Two Variables
§ 14.7 Second Order Partial Derivatives
§ 14.8 Differentiability of Functions of Two Variables
§ 15.1 Local Extrema for Functions of Two variables
§ 15.2 Optimization: Finding Global Extrema
§ 15.3 Constraint Optimization: Lagrange's Multipliers
§ 16.1 The Definite Integral of f(x,y)
§ 16.2 Iterated Integrals
§ 16.3 Triple Integrals
§ 16.4 Double Integrals in Polar Coordinates
§ 16.5.1 Triple Integrals in Cylindrical Coordinates
§ 16.5.2 Triple Integrals in Spherical Coordinates
§ 16.6 Applications of Double Integrals to Probability
§ 16.7 Change of Variables in a Multiple Integral

Page created and maintained by Marcel B. Finan
Last updated:October 14, 2014