Calculus 4 Directory

 

 

Test

Examination Solutions

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á                     Final Examination Solutions


Handouts

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á                     Chain Rule

á                     Proof of Chain Rule in 2 Dimensions

á                     Implicit Function Theorem

á                     TaylorÕs Series

á                     Mixed Partials

á                     Tangent Planes

á                     Maxima and Minima of Functions of Several Variables

á                     Langrange Multiplier

á                     Meaning of Langrange Multipliers

á                     Hessians and Positive Definite Matrices

á                     Multiple Integration

á                     Multiple Integration Example

á                     Change of Variables

á                     Graphing Vector Fields

á                     Line Integrals

á                     Line Integral in Reverse Direction

á                     Line Integrals (Potential Function)

á                     Differential Forms

á                     Final Review

á                     Review 1 Fall 2006

á                     Review 2 Fall 2006



Homework

á                     Homework Assignments Calculus 4 2006-2007

á                     Homework Assignments Calculus 4 2006-2007 (pdf format)

á                     Tentative List of Assignments Calculus 4 2006-2007 Homework Assignments

á                     Honors Calculus 4 2005-2006 (N.B. Second Edition)

á                     List of Calculus 4 Homework Assignments From 2002-2003

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á                     Homework 1 Functions of several variables

á                     Homework 2 Limits, Partial Derivatives

á                     Homework 3 Tangent Planes, Chain Rule 

á                     Homework 4  Directional Derivative 

á                     Homework 5   Max/Min

á                     Homework 6 Constrained Max/Min

á                     Homework 7  Double Integration

á                     Homework 8 Applications of Double Integration

á                     Homework 9 Polar Coordinate Change of Variables

á                     Homework 10  Applications of Double Integration

á                     Homework 11 Surface Integrals

á                     Homework 12  Triple Integral

á                     Homework 13 Cylindrical and Spherical Change of Coordinates

á                     Homework 14 Change of Variables

 

 

Quiz Solutions

 

á                              Quiz 20 Surface Integral

á                              Quiz  21 Surface Integral

á                              Quiz 22  Surface Integral