John Trangenstein: Math 114 Applied Mathematical Analysis II

John Trangenstein : Math 114 Applied Mathematical Analysis II

Class hours: MWF 1:30-2:20 Physics 205
Office hours: MWF 11:30-12:30 Physics 024D
Weekly homework due in class on Mondays
Course grade depends on:

Homework (25%)
2 Midterms (25% each)
Final (25%)

First Midterm: Monday, February 21 (review session in class, February 18)
High = 75, low = 34, mean = 53, median = 52
Will add 25 to all scores in determining grade
Useful Formulas for Complex Variables

Second Midterm: Friday, March 25 (review session in class, March 23)
High = 80, low = 48, mean = 61, median = 61
Will add 20 to all scores in determining grade
Useful Formulas for Fourier Transforms

Final Exam: Thursday, May 5 2-5 pm (review sessions in class, April 22, 25, 27)
office hours Friday April 29 10--11:30, Monday May 2 1:30--3 and Wednesday May 4 1:30--3
High = 93, low = 55, mean = 75, median = 79
Will add 7 to all scores in determining grade
Useful Formulas for Partial Differential Equations
Homework: 10 sets, max possible total = 880
High = 836, low = 340
Took total score / 10 + 16 to figure final grade
Total score = normalized homework + midterm1 + midterm2 + final
High = 365, low = 273, median = 331, average = 323
A+ >= 358 (3 people)
A : 329 -- 346 ( 4 people)
A- : 321 (1 person)
B+ : 293 -- 297 (2 people)
B: 273 -- 277 (2 people)

Syllabus:

Chapter 20: Geometry and Arithmetic of Complex Numbers
- 20.1: Complex Numbers 1/12
- 20.2: Loci and Sets of Points in the Complex Plane 1/14
Chapter 21: Complex Functions
- 21.1: Limits, Continuity and Derivatives
- 21.2: Power Series
- 21.3: The Exponential Function and Trigonometric Functions
- 21.4: The Complex Logarithm
- 21.5: Powers
Chapter 22: Complex Integration
- 22.1: Curves in the Plane
- 22.2: The Integral of a Complex Function
- 22.3: Cauchy's Theorem
- 22.4: Consequences of Cauchy's Theorem
Chapter 23: Series Representations of Functions
- 23.1: Power Series Representations
- 23.2: The Laurent Expansion
Chapter 24: Singularities and the Residue Theorem
- 24.1: Singularities
- 24.2: The Residue Theorem
- 24.3: Some Applications of the Residue Theorem
Chapter 13: Fourier Series
- 13.1: Why Fourier Series
- 13.2: The Fourier Series of a Function
- 13.3: Convergence of Fourier Series
- 13.4: Fourier Cosine and Sine Series
- 13.5: Integration and Differentiation of Fourier Series
- 13.6: The Phase Angle Form of a Fourier Series
- 13.7: Complex Fouier Series and the Frequency Spectrum
Chapter 14: The Fourier Integral and Fourier Transforms
- 14.1: The Fourier Integral
- 14.2: Fourier Cosine and Sine Integrals
- 14.3: The Complex Fourier Integral and the Fourier Transform
- 14.4: Additional Properties and the Applications of the Fourier Transform
- Chapter 16: The Wave Equation
  - 16.1: The Wave Equation and Initial and Boundary Conditions
  - 16.2: Fourier Series Solutions of the Wave Equation
  - 16.3: Wave Motion Along Infinte and Semi-Infinite Strings
  - 16.4: Characteristics and d'Alembert's Solution
  - 16.5: Normal Modes of Vibration of a Circular Elastic Membrane
  - 16.6: Vibrations of a Circular Elastic Membrane, Revisited
  - 16.7: Vibrations of a Rectangular Membrane
- Chapter 17: The Heat Equation
  - 17.1: The Heat Equation and Initial and Boundary Conditions
  - 17.2: Fourier Series Solutions of the Heat Equation
  - 17.3: Heat Conduction in Infinite Media
  - 17.4: Heat Conduction in and Infinite Cylinder
  - 17.5: Heat Conduction in a Rectangular Plate
- Chapter 18: The Potential Equation
  - 18.1: Harmonic Functions and the Dirichlet Problem
  - 18.2: Dirichlet Problem for a Rectangle
  - 18.3: Dirichlet Problem for a Disk
  - 18.4: Poisson's Integral Formula for the Disk
  - 18.5: Dirichlet Problems in Unbounded Regions
  - 18.6: A Dirichlet Problem for a Cube
  - 18.7: The Steady-State Heat Equation for a Solid Sphere
  - 18.8: The Neumannn Problem
Homework:
- due January 21
  - Section 20.1: 2,4,8,13,14,16,17,28,29
  - Section 20.2: 1,7,10,14,31,32,39
- due January 28
  - 21.1: 2,7,14,16
  - 21.2: 2,9,12,15
  - 21.3: 5,6,12,15,18,20
  - 21.4: 5,8
  - 21.5: 2,12,17,25
- due February 4
  - 22.1: 1,6,8
  - 22.2: 1,2,10,14,19,24
  - 22.3: 4,10,13,16
  - 22.4: 1,5,23,24
- due February 11
  - 23.1: 10,14,20,26
  - 23.2: 4,5,8
- due February 18
  - 24.1: 12,14,15,20
  - 24.2: 1,10,11,24
  - 24.3: 17,30,35,36,53,61
- February 25: no homework due
- due March 7
  Computing Fourier Series in Maple
  Plotting Partial Sums of Fourier Series in Maple
  Fourier Series for Square Wave in Matlab: plot truncated series and phase spectrum
  Maple worksheet for Fourier series
  - 21.2: 12,13
  - 23.1: 11,16 (all terms, not just the first 3)
  - 13.2: 6,11,12
  - 13.3: 1,7,10,16
  - 13.4: 6,8
  - 13.5: 2
  - 13.6: 4,11,16
  - 13.7: 8
- due March 11
  - 14.1: 2,7
  - 14.2: 3,10,11
  - 14.3: 10,33
  - 14.4: 6
- due April 4
  - 16.1: 2,3,5
  - 16.2: 4,14,22
  - 16.3: 6,12
  - 16.7: 3
- due April 13
  - 17.1: 3
  - 17.2: 1,4,8,9,14,23,30
    Don't bother to graph the solutions, unless you want to.
  - 17.3: 6,8
  - 17.5: 2
- due April 27
  - 18.1: 1
  - 18.2: 4,6
  - 25.2: 1,15
  - find a linear fractional transformation that maps the upper half-plane into the unit disk
  - 25.3: 13
  - 25.4: 1
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