Math 312

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Ron Buckmire
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Math 312: Worksheets

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Date Topic
Week 1

Class 1

Wed Jan 21 Properties of Complex Numbers

Class 2

Fri Jan 23 Graphical Representation of Complex Numbers and Inequalities
Week 2

Class 3

Mon Jan 26 Polar and Exponential Forms of Complex Numbers

Class 4

Wed Jan 28  Roots of a Complex Numbers

Class 5

Fri Jan 30  Points Sets in the Complex Plane
Week 3

Class 6

Mon Feb 2  Complex Functions of a Complex Variable

Class 7

Wed Feb 4  Limits of Complex Functions and the Point at Infinity

Class 8

Fri Feb 6  Continuity, Differentiability, and Analyticity
Week 4

Class 9

Mon Feb 9 The Cauchy-Riemann Equations

Class 10

Wed Feb 11 Harmonic Functions and Laplace's Equation

Class 11

Fri Feb 13 Application of Complex Variables: Julia Sets (See links page)
Week 5

Class 12

Wed Feb 18 The Complex Exponential Function

Class 13

Fri Feb 20 The Complex Trigonometric and Hyperbolic Trigonometric Functions
Week 6

Class 14

Mon Feb 23 The Complex Logarithm

Class 15

Wed Feb 25 Branch Cuts

Class 16

Fri Feb 27 Application of Complex Variables: Boundary Value Problems
Week 7

Class 17

Mon Mar 1 Complex Exponents

Class 18

Wed Mar 3 Review for Exam 1

EXAM 1

Mon Mar 5 Exam 1
Week 8

Class 19

Mon Mar 8 Introduction to Complex Integration

Class 20

Wed Mar 10 Contour Integration

Class 21

Fri Mar 12 More Contour Integration
Week 9

Class 22

Mon Mar 22 Independence of Path

Class 23

Wed Mar 24 Applications of the Cauchy-Goursat Theorem

Class 24

Fri Mar 26 Understanding Contour Integration
Week 10

Class 25

Mon Mar 29 Cauchy's Integral Formula and Examples Galore

Class 26

Wed Mar 31 Applications and Implications of the CIF

Class 27

Fri Apr 2 Poles, Zeroes and Cauchy's Residue Theorem
Week 11

Class 28

Mon Apr 5 Cauchy's Second Residue Theorem and Introduction to Laurent Series

Class 29

Wed Apr 7 Using Laurent Series to Evaluate Residues

Class 30

Fri Apr 9 Application of Residues to Real Integrals
Week 12

Class 31

Mon Apr 12 More Applications of Residues

Class 32

Wed Apr 14 Cauchy Principal Value of Improper Integrals

Class 33

Fri Apr 16 Mappings Return: Introduction to Linear Fractional Transformations
Week 13

Class 34

Mon Apr 19 More Practice with LFTs

Class 35

Wed Apr 21 Review for Exam 2

Fri Apr 23 Exam 2

Last Updated April 14, 2004