Class:
Mon & Wed 9:00  10:30 at Buchanan A104
Office hours: Mon. Wed. 2pm 2:50pm at MATH 235 until
April 5. or by appointment (email at yhkim "at" math "dot"
ubc 'dot' ca)
First class: Wednesday,
Jan 04, 2012
Last class: Wednesday, Apr 04, 2012
Course Outline
Announcements:
HW assignments:
Your grade for the course will be computed roughly as follows:
Homework: 15%
Midterms: 35% (17.5% + 17.5%)
Final Exam: 50%
Important Notes:
Week  Date  Suggested reading of course material. (For optional reading, the sections in [BoyceDiPrima] are from the 9th edition.) 

1  
Wed. Jan. 4. (First Class) 
Complex Numbers and Exponentials HW1.  
2  Mon. Jan. 9. 
Review of
Ordinary Differential Equations , The RLC Circuit
(Optional: [BoyceDiPrima, Sections 3.3, 3.4, 3.5]) 

Wed, Jan. 11 (HW1 Due)  Solution
of the Wave Equation by Separation of Variables : page
13. HW2 . See also Solution of the Heat Equation by Separation of Variables Optional: Derivation of the Wave Equation, Derivation of the heat equation in 1D (Optional: [BoyceDiPrima, Section 10.1, 10.5, 10.7]) 

3  Mon. Jan. 16 Last day to withdraw without a W standing 
Solution
of the Wave Equation by Separation of Variables : page
35. (Optional: [BoyceDiPrima, Section 10.1, 10.5, 10.7]) 

Wed. Jan.18 (HW2 Due)  Solution
of the Wave Equation by Separation of Variables : page
35. HW3 (Optional: [BoyceDiPrima, Section 10.1, 10.5, 10.7]) 

4  Mon, Jan.23   How to handle initial conditions: Solution of the Wave Equation by Separation of Variables : page 35: The Third Step  Imposition of the Initial Conditions. Solution of the Heat Equation by Separation of Variables (Page 3. The Third Step Impositin of the initial condition.) (Optional: [BoyceDiPrima, Section 10.5, 10. 6 (pages 624 627) ]) Fourier Series : page 1. (Optional: [BoyceDiPrima, Section 10.2,) 

Wed. Jan. 25 (HW3 Due) 
Fourier
Series : page 15. HW 4.
(Optional: [BoyceDiPrima, Section 10.2, 10.3]) 

5  Mon. Jan.30  Orthogonality. Parseval relation. Fourier Series : page 12, 5 7, 1213. (Optional: [BoyceDiPrima, Section 10.2, 10.3]) 

Wed. Feb. 1 (HW4 Due)  Orthogonality. Parseval relation. Even and Odd functions
and their Fourier series. Fourier Series : page 12, 5 7, 12  13. (Optional: [BoyceDiPrima, Section 10.2, 10.3, 10.4]) 

6  Mon. Feb. 6 Midterm I  
Wed. Feb. 8  Periodic
Extensions *Self reading: Fourier Series page 7 9 Example 6 (this discusses Gibb's phenomenon), 7 and 8. The Fourier Transform page 1  2 

Last day to withdraw with a W standing (course cannot be dropped after this date) : Friday, February 10, 2012 


7 
Mon. Feb. 13 
The
Fourier Transform Page 12 (Reason for Fourier transform formula) 

Wed. Feb. 15. (HW5 Due)  The
Fourier Transform Page 3 (Properties of Fourier transform: linearity, timeshifting, time reversal) 

8 
Mon. Feb 20 (NO Class) 
Midterm Break  
Wed. Feb. 22 (NO Class) 
Midterm Break  
9 
Mon. Feb. 27 
The
Fourier Transform Scaling and Differentiation RLC circuit and Fourier transform motivation for Fourier inversion 

Wed. Feb. 29 (HW6 Due)  The
Fourier Transform Fourier Inversion Duality Convolutions 

10 
Mon. Mar. 5 
The
Fourier Transform Convolutions and Impulse (Delta function) 

Wed. Mar. 7 (HW7 Due)  The Fourier
Transform Impulse (Delta function) 

11  Mon. Mar. 12 
DiscreteTime
Fourier Series and Transforms * Discretetime signals * Periodic (finite length) discretetime signals * Discrete Fourier series (also Fourier inversion in this case) * Summation with discrete complex exponentials (examples with geometric sum) * Orthogonality for discrete complex exponentials. 

Wed. Mar. 14 Midterm II  
12  Mon. Mar. 19 
DiscreteTime
Fourier Series and Transforms  Properties of Discrete Fourier transform (aka Discrete Fourier series) and some examples. periodic convolution 

Wed. Mar. 21 (HW 8 Due)  DiscreteTime
Fourier Series and Transforms  nonperiodic discretetime signals: important examples, convolution, 

13  Mon. Mar. 26 
DiscreteTime
Fourier Series and Transforms discretetime Fourier transform for nonperiodic signals: defintion, basic examples, some properties (convolution, ndifference). 

Wed. Mar. 28 (HW9 Due)  DiscreteTime
Linear Time Invariant Systems and zTransforms LTI system:  impulse response function. examples. ztransform: defintion, basic examples 

14  Mon. Apr. 2 
Plan DiscreteTime Linear Time Invariant Systems and zTransforms ztransform: basic examples, ROC, causality, stability, inverse ztransform, properties of ztransform 

Wed. Apr. 4 (Last Class)  Plan DiscreteTime Linear Time Invariant Systems and zTransforms ztransform: properties of ztransform 

MATH267:201
Final Exam: Monday, April 16th at NOON 
Final Exam
12 noon  2:30pm (2 and 1/2 hours) AT HEBB TH 