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.) |
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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]) |
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Wed, Jan. 11 (HW1 Due) | Solution
of the Wave Equation by Separation of Variables : page
1--3. 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]) |
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3 | Mon. Jan. 16 Last day to withdraw without a W standing |
Solution
of the Wave Equation by Separation of Variables : page
3--5. (Optional: [BoyceDiPrima, Section 10.1, 10.5, 10.7]) |
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Wed. Jan.18 (HW2 Due) | Solution
of the Wave Equation by Separation of Variables : page
3--5. HW3 (Optional: [BoyceDiPrima, Section 10.1, 10.5, 10.7]) |
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4 | Mon, Jan.23 | - How to handle initial conditions: Solution of the Wave Equation by Separation of Variables : page 3--5: 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,) |
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Wed. Jan. 25 (HW3 Due) |
Fourier
Series : page 1--5. HW 4.
(Optional: [BoyceDiPrima, Section 10.2, 10.3]) |
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5 | Mon. Jan.30 | Orthogonality. Parseval relation. Fourier Series : page 1--2, 5-- 7, 12--13. (Optional: [BoyceDiPrima, Section 10.2, 10.3]) |
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Wed. Feb. 1 (HW4 Due) | Orthogonality. Parseval relation. Even and Odd functions
and their Fourier series. Fourier Series : page 1--2, 5-- 7, 12 -- 13. (Optional: [BoyceDiPrima, Section 10.2, 10.3, 10.4]) |
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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 |
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Last day to withdraw with a W standing (course cannot be dropped after this date) : Friday, February 10, 2012 |
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7 |
Mon. Feb. 13 |
The
Fourier Transform Page 1--2 (Reason for Fourier transform formula) |
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Wed. Feb. 15. (HW5 Due) | The
Fourier Transform Page 3 (Properties of Fourier transform: linearity, time-shifting, time reversal) |
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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 |
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Wed. Feb. 29 (HW6 Due) | The
Fourier Transform Fourier Inversion Duality Convolutions |
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10 |
Mon. Mar. 5 |
The
Fourier Transform Convolutions and Impulse (Delta function) |
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Wed. Mar. 7 (HW7 Due) | The Fourier
Transform Impulse (Delta function) |
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11 | Mon. Mar. 12 |
Discrete-Time
Fourier Series and Transforms * Discrete-time signals * Periodic (finite length) discrete-time signals * Discrete Fourier series (also Fourier inversion in this case) * Summation with discrete complex exponentials (examples with geometric sum) * Orthogonality for discrete complex exponentials. |
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Wed. Mar. 14 Midterm II | ||||
12 | Mon. Mar. 19 |
Discrete-Time
Fourier Series and Transforms - Properties of Discrete Fourier transform (aka Discrete Fourier series) and some examples. periodic convolution |
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Wed. Mar. 21 (HW 8 Due) | Discrete-Time
Fourier Series and Transforms - non-periodic discrete-time signals: important examples, convolution, |
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13 | Mon. Mar. 26 |
Discrete-Time
Fourier Series and Transforms -discrete-time Fourier transform for non-periodic signals: defintion, basic examples, some properties (convolution, n-difference). |
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Wed. Mar. 28 (HW9 Due) | Discrete-Time
Linear Time Invariant Systems and z-Transforms LTI system: - impulse response function. examples. z-transform: defintion, basic examples |
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14 | Mon. Apr. 2 |
Plan Discrete-Time Linear Time Invariant Systems and z-Transforms z-transform: basic examples, ROC, causality, stability, inverse z-transform, properties of z-transform |
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Wed. Apr. 4 (Last Class) | Plan Discrete-Time Linear Time Invariant Systems and z-Transforms z-transform: properties of z-transform |
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MATH267:201
Final Exam: Monday, April 16th at NOON |
Final Exam
12 noon -- 2:30pm (2 and 1/2 hours) AT HEBB TH |