Assignment schedule:

THESE WEBPAGES DESCRIBE HOW THIS COURSE WILL BE RUN.
Browse through all the options in the menu above. Visit this webpage regularly for updates

Homework: Typically there will be one homework per week. The HW will be posted here every Thursday (at the latest) and is due the following Thursday and must be handed in as soon as you enter the classroom before the lecture starts . In some occasions the HW will be posted a few days before Thursday so you are encouraged to start on it earlier. Late HW will not be accepted.

Midterm exams: There will be two midterm exams during the semester.

Matlab/Maple: In general you are not allowed to solve exercises with Matlab/Maple. However you should try to take profit of these tools by checking your results using Matlab/Maple. In some exercises I'll indicate if you may or must use Matlab/Maple.

 

Assignments: [bottom]

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Week#
 Topics: Boas_Index Sec.: Exercises: Due:

01
22/01

Special Functions:
Factorial function +
Gamma function +
Beta function

11.1-11.7

  HW#00:
  • Go over Matlab [PDF] tutorial [For students without previous knowledge on Matlab or if your did not take M342A with me (if you are an "expert" in Matlab just send me an email indicating so)]:
    Type in all instructions in Matlab (follow the whole tutorial) and submit to me by email a diary of it (to do the diary: do "diary FirstName_LastName_M342B.txt" as the first instruction and this will save all your inputs in that file)

 HW#01:
  • Sec. 11.3: 9, 10, 11, 12
  • Sec. 11.5: 1
  • Sec. 11.7: 2, 4, 9
  • Sec. 11.8: 3 and evaluate the integral to show that t = π √a/g
  • Boas_Chap_11
Th 29 Jan
02
27-29/01
Special Functions:
Stirling's asymptotic formula +
Simple pendulum +
Elliptic integrals +
Elliptic functions +
Full pendulum +
Error function

11.8-11.9 + 11.11-11.13
  HW#02:
  • Sec. 11.11: 3
  • Sec. 11.12: 1, 17, 22
  • Sec. 11.9: 2, 3, 4
  • Boas_Chap_11
Th 05 Feb
03
03-05/02
Fourier series:
Periodic Functions +
Average of a Function +
Fourier Coefficients +
Dirichlet Conditions +
Complex Form of Fourier Series +
Other Intervals +
Even and Odd Functions
7.1-7.9
 HW#03:
  • Sec. 7.5: 2, 7, 11
  • Sec. 7.8: 11 (only part (a))
  • Sec. 7.9: 6, 10
  • Read sections 7.10 and 7.11 and provide a detailed summary of the most important results/formulas
  • Boas_Chap_07
Th 12 Feb
04
10-12/02
Fourier Transforms

Series solutions to ODE:
Legendre Equation +
Leibniz' Rule +
Rodrigues' Formula +
Generating Function for Legendre Polynomials
7.12
12.1-12.5
  HW#04:
Th 19 Feb
05
17-19/02
Complete Set of Orthogonal Functions +
Generalized power series +
Bessel Functions of 1st and 2nd kind +
Recurrence relations for Bessel +
The lengthening pendulum
12.6-12.18
  HW#05:
  • Sec. 12.9: 3, 5, 11, 13, 15
  • bonus for extra credit: Sec. 12.9: 16
  • Sec. 12.11: 1, 5
  • Sec. 12.15: 1, 4
  • Sec. 12.16: 2, 6
  • Sec. 12.18: 10, 9 (don't do the quarter period)
  • Boas_Chap_12b
Tu 03 Mar
06
24-26/02
Orthogonality of Bessel functions +
Approximation of Bessel Functions +
Fuch's theorem +
Finding second solution to DE +
Sturm-Liouville
12-19-12.21
Sturm Liouville notes
    No HW this week just study HARD for MT#1
 
Th 05 Mar
 Midterm #1

Chap 11 +
Chap 7 +
Chap 12 +
Liouville
Th 05 Mar
07
03-05/03

MT#1 Review +
MT#1

     
08
10-12/03

Partial Differential Equations:
List of common PDEs +
Laplace's equation in a semi-infinite rectangular plate +
Laplace's equation in a rectangular plate +
13.1-13.3
  HW#06:
  • Sec. 13.2: 3, 10, 11
  • Sec. 13.3: 2, 3, 11
  • Extra credit: use the Matlab codes used in class to produce plots of the solutions
  • Boas_Chap_13a
Tu 24 Mar
09
17-19/03
Solving MT#1 +

Diffusion/Heat equation +
Schrödinger equation +
Wave equation
13.3-13.4
PDE notes
   
10
24-26/03
Steady state temperature in a cylinder +
Vibration of a circular Membrane +
Steady state temperature in a sphere
13.5-13.6
 HW#07:
  • Sec. 13.4: 2, 5
  • Sec. 13.5: 2, 3, 4
  • Sec. 13.6: 3, 4
  • Sec. 13.7: 7
  • Extra credit: use the Matlab codes used in class to produce plots of the solutions
Th 09 Apr
--
31/03-02/04

SPRING BREAK
 
NO CLASSES
 
Th 09 Apr
 Midterm #2

Chap 12 + Chap 13
  • In class AND Take home exam
  • Please arrive EARLY (3:45pm).
Th 09 Apr
11
07-09/04
Steady state temperature in a sphere +
Pattern formation

MT#2
13.7
Reaction-Diffusion notes
   
12
14-16/04
 Function of Complex Variable:
Analytic functions +
Contour integrals +
Laurent Series +
The Residue Theorem +
Methods for finding residues
Evaluation of integrals using residues
14.1-14.7
 HW#08:
  • Sec. 14.2: 22, 23
  • Sec. 14.3: 11, 14, 17
  • Sec. 14.6: 14, 24, 31
  • Sec. 14.7: 1, 12, 16, 30, 37
  • Boas_Chap_14
Th 23 Apr
13
21-23/04
 Residue theorem with poles at boundaries +
Branch cuts +
Examples

1D Dynamical Systems:
Flows on the line +
Fixed points and stability +
Perturbation around fixed points, stability +
Bifurcations:
Saddle-node bifurcation

1D Dynamical Systems notes
 HW#09:
Th 30 Apr
14
28-30/04
 Transcritical bifurcation +
Pitchfork bifurcation

2D Linear Dynamical Systems:
Definitions and examples +
Stability in 2D
2D Dynamical Systems notes
 HW#10:

  • Strogatz Chap 5: 1.4 + 1.6 + 1.7
  • Strogatz Chap 5: 2.2 + 2.3 + 2.4 + 2.7 + 2.8 + 2.13
  • Strogatz Chap 6: 1.8 + 3.1 + 3.4
    • [For 5.1.7 you might want to use pplane]
    [For 5.2.3, 5.2.4, 5.2.7, 5.2.8 do not forget to compute the eigenvalues and eigenvectors]
    [For 5.2.13 plot using pplane all the qualitative different cases for parameters of your choice]
  • Extra credit = 5.2.14

    • Exercises Strogatz Chap 5
    Exercises Strogatz Chap 6
Th 07 May
15
05-07/05
 Stability in 2D +
Classification of fixed points +
Linearization +
Stability +
Phase portrait analysis
Nonlinear 2D Dynamical Systems notes
   
Tu 12 May
 FINAL
The time for the final is 15:30-17:30.

ALL
Tu 12 May