Instructor: John Gemmer
Office: Manchester #388
E-mail: gemmerj@wfu.edu Office Hours: Tuesday 10-11, Wednesday 2-4, Thursday 1-3
Lecture: MWF: 12:00-12:50, Kirby Hall 10
Textbooks: See syllabus.
Course Handouts:
1. Syllabus: (.pdf)
2. Homework Policy: (.pdf)
3. Example Homework Solutions: (.pdf)
4. Latex Templates
5. Overleaf
5. Written Report Rubric (.pdf)
6. Presentation Rubric (.pdf)
Lecture Notes:
1. Lecture #1: (Algebra of Complex Numbers) (.pdf)
2. Lecture #2: (Point Representation) (.pdf)
3. Lecture #3: (Vectors and Polar Form) (.pdf)
4. Lecture #4: (Euler's Formula and Applications) (.pdf)
5. Lecture #5: (Powers and Roots) (.pdf)
6. Lecture #6: (Planar Sets) (.pdf)
7. Lecture #7: (The Riemann Sphere) (.pdf)
8. Lecture #8: (Functions of a Complex Variable) (.pdf)
9. Lecture #9: (Limits and Continuity) (.pdf)
10. Lecture #10: (Analyticity and the Cauchy Riemann Equations) (.pdf)
11. Lecture #11: (Harmonic Functions) (.pdf)
12. Lecture #12: (Polynomials and Rational Functions) (.pdf)
13. Lecture #13: (Transcendental Functions) (.pdf)
14. Lecture #14: (Logarithmic Functions) (.pdf)
16. Lecture #16: (Contours) (.pdf)
17. Lecture #17: (Contour Integrals) (.pdf)
18. Lecture #18: (Cauchy Integral Theorem) (.pdf)
19. Lecture #19: (Consequence of the Cauchy Integral Theorem) (.pdf)
20. Lecture #20: (Sequences and Series) (.pdf)
21. Lecture #21: (Taylor Series) (.pdf)
22. Lecture #22: (Laurent Series) (.pdf)
23. Lecture #23: (Residue Theorem) (.pdf)
24. Lecture #24: (Trigonometric Integrals) (.pdf)
25. Lecture #25: (Improper Integrals over R) (.pdf)
26. Lecture #26: (Improper Integrals with Trigonometry) (.pdf)
27. Lecture #27: (Improper Integrals with Branch Cuts) (.pdf)
Quiz Solutions:
1. Quiz #1 (.pdf).
2. Quiz #2 (.pdf).
3. Quiz #3 (.pdf).
4. Quiz #4 (.pdf).
5. Quiz #5 (.pdf).
6. Quiz #6 (.pdf).
Exam Solutions:
1. Exam #1 (.pdf)
2. Exam #2 (.pdf)
Homework Assignments:
1. Homework #1 (.pdf), (.tex), Solutions (.pdf).
2. Homework #2 (.pdf), (.tex), Solutions (.pdf).
3. Homework #3 (.pdf), (.tex), Solutions (.pdf).
4. Homework #4 (.pdf), (.tex), Solutions (.pdf).
5. Homework #5 (.pdf), (.tex), Solutions (.pdf).
6. Homework #6 (.pdf), (.tex), Solutions (.pdf).
7. Homework #7 (.pdf), (.tex), Solutions (.pdf).
8. Homework #8 (.pdf), (.tex), Solutions (.pdf).
9. Homework #9 (.pdf), (.tex), Solutions (.pdf).
10. Homework #10 (.pdf), (.tex), Solutions (.pdf).
Potential Projects:
1. Iterated maps: Julia and Mandlebrot sets (Section 2.7)
2. Applications in electrostatics, heat flow, and fluid mechanics (Section 7.6)
3. Fourier series and the Fourier transform (Sections 8.1-8.2)
4. Mobius transformations (Section 7.3-7.4)
5. Analytic continuation (Section 5.8)
6. Mathematical theory of convergence (Section 5.4)