Mathematics 114.01, Spring 1999
Syllabus

Day           Topic                           Reading                          







1/13    Organization, complex arithmetic     Section 17.1
1/15    Lab: Maple tutorial 

1/18    Martin Luther King Holiday
1/20    Geometry of complex plane            Section 17.2
1/22    Complex functions                    Section 17.4

1/25    Derivatives of complex functions 
        and the Cauchy-Riemann equations     Section 17.5
1/27    Complex transcendental functions     Sections 17.6 & 17.8
1/29    Lab: Complex transcendental functions               

2/1     Logarithms and hyperbolic functions  Sections 17.7 & 17.8
2/3     Complex line integrals               Section 18.1
2/5     Lab: Complex Line Integrals I

2/8     More on complex line integrals       Section 18.1
2/10    Cauchy Integral Theorem              Sections 18.2
2/12    Cauchy Integral Formula              Section 18.3

2/15    Applications of 
        Cauchy Integral Formula              Section 18.3
2/17    Taylor series expansions             Sections 17.6 and 18.4
2/19    Review, Take-home test handed out                           

2/22    Test #1 (in class)                                
2/24    Laurent series expansions            Section 18.4
2/26    Lab:  Isolated Singularities and Series Expansions 

3/1     The Residue Theorem                  Section 18.5
3/3     Application to real integrals        Section 18.7
3/5     Application to real integrals (cont.)Section 18.7
       
3/8     Overview of pdes         Introduction to Chapter 16
3/5     Fourier series                       Section 14.1
3/12    Lab: Fourier Series (optional)

3/22    The one-dimensional heat equation    Section 16.1
3/24    The one-dimensional wave equation    Section 16.3
3/26    Lab: The One-Dimensional Wave Equation                  

3/29    Complex Fourier series and 
        Fourier Transform                    Section 14.5
3/31    Fourier Transform                    Section 15.1
4/2     Lab: Fourier Transform I         

4/5     Review, Take-home test handed out                            
4/7     Test #2 (in-class)
4/9     Fourier Transform                    Sections 15.1 and 15.2

4/12    Laplace Transform and solution
        of differential equations            Section 3.2
4/14    Laplace Transform and solution 
        of partial differential equations    Section 16.6
4/16    Lab: Laplace Transform and solutions 
        of the one-dimensional heat equation

4/19    Fourier series revisited
4/21    The inverse Laplace transform        Section 18.6
4/23    Lab:  Using line integrals to calculate the inverse Laplace
              transform

4/26    Review
4/28    Evaluation