Last Modified : Sat, 18 Dec 21
ECE298-ComplexLinearAlg-F21
(Register here) University calendar; Academic calendar; Fall 2021
Summary of class status as of Oct 24, 2021
- Time and place: details
- 298CLA Echo 360 Lectures: All ONL, CLA
- 360 Viewing Live Streamed FAQ
- Professor: jontallen@illinois.edu; TA: Billy Walters [wcw5 @ illinois.edu]
- Syllabus: pdf; ICES Forms
- zoom link 1or link 2;Zoom: ID: 965 0165 0571, PW: 146870;
- Office Hours: MWF 11-12AM;
- Text: 298CLA.F21 Abridged text; Unabridged text; Hamming Digital filters
- Assignments: NS3: Lec 1-4; AE1: Lec 4-8; AE3: Lec 6-10; DE1: Lec 9-15; DE2: Lec 12-15; DE3: Lec 15-19;
*Gradescope entry code: 6P4PGW - Exams: Exam I: Lec 9; Final: Dec 14, 2021, 8:00-11:00 AM; Previous year's Grades: 2016, 2017, Spring 2019, Fall 2020 Spring 2021
- Mathematical notation by topic, alpha-order, use of Functions and their History, Mathematical vignettes.
- How to edit pdf files, such as homework or exams: xournalpp (PC-based pdf-editing) OR xodo.com: Web-based pdf-editing AND an incomplete Review of 8 pdf editors
- Tools: Octave, Latex, Matlab, Working with Octave/Matlab: 3.1.4 (p. 86) zviz.m
- This week's schedule
ECE 298 ComplexLinearAlg-F21 Schedule (Fall 2021)
| L | D | Date | Lecture and Assignment |
| Part I: Introduction to 2x2 matricies (8 Lectures) | |||
| 1 | M | 10/18 | Lecture: Introduction & Overview: (Read \(\S\)1 (Chap. 1, p. 1-17) & Intro + history; \(\S\)3.1 (p.69-73); Homework 1: NS-1: (not graded) pdf, NS1-sol.pdf,NS-3: Prob #3, #4 pdf, NS3-sol.pdf NS-1 & NS-3 Due on Lec 4 |
| 2 | W | 10/20 | Lecture: Roots of polynomials; Matlab Examples; Allm.zip; Read: \(\S\)3.1 (p. 73-82) Roots of polynomials+monics; Newton's method. |
| 3 | F | 10/22 | Lecture: Companion Matrix; Pell's equation: \(x^2_m-N y^2_n=1\) with \(x_n,y_n,n,N\in{\mathbb N}\), Fibonacci Series \(f_{n+1} = f_n + f_{n-1}\), with \(n,f_n \in{\mathbb N}\) (p. 57-64), move or merge with Lec 5: Companion matrix; (@39 mins): Pell & Fibonocci companion Matrix (p. 84-86) + solutions; Read: \(\S\)3.1.3,.4, (p.84-88) More on Monic roots; (Lec-3 video @23 mins) |
| 4 | M | 10/25 | Lecture: Eigen-analysis; Examples + analytic solution (Appendix B.3, p. 310) Next time merge Lec 4 & 5 too much overlap Read: \(\S\)3.2,.1,.2, B1, B3 Eigen-analysis, (p. 88-93) Homework 2: AE-1: Problems: pdf, Due on Lec 8; AE1-sol.pdf AE-1 Due on Lec 8 NS-1 Due |
| 5 | W | 10/27 | Lecture: Solution of Pell's and Fibinocci's Eqs., (p. 57-64); (See Lec 3 @44 min) Read: \(\S\)3.2.3;Eigen-analysis (Appendix B.3) |
| 6 | F | 10/29 | Lecture: Eigen-analysis; Taylor series (\(\S3.2.3\)) & Analytic functions (\(\S3.2.4\)); History: Beginnings of modern mathematics: Euler and Bernoulli, The Bernoulli family: natural logarithms; Euler's standard circular-function package (log, exp, sin/cos); Brune Impedance \(Z(s) = z_o{M_m(s)}/{M_n(s)}\) (ratio of two monics) and its utility in Engineering applications; Examples of eigen-analysis. Read: \(\S\)3.2,.3,.4, Eigen-analysis: Taylor series (\(\S3.2.3\), p. 93-8) & Analytic Functions (p. 98-100) Homework 3: AE-3: Problems: #1, 2, 3: 2x2 complex 2-port matrices; #4: FTA; #5-8: Complex algebra & scalar products; #9, 10: Schwarz Inequality AE3.pdf, Due on Lec 10, AE3-sol.pdf |
| 7 | M | 11/1 | Lecture: Fourier transforms for signals vs. Laplace transforms for systems: Read: \(\S\)3.9 (p. 152-6); Fourier Transform (wikipedia); Notes on the Fourier series and transform from ECE 310 pdf including tables of transforms and derivations of transform properties; Classes of Fourier transforms pdf due to various scalar products. Read: \(\S\)3.10 |
| 8 | W | 11/3 | Lecture: The important role of the Laplace transform re impedance: \(z(t) \leftrightarrow Z(s)\); Read: \(\S\)3.2.5,.3.10, Impedance (p. 100-1) & \(\cal LT \); Read: Hamming Digital filters: The idea of an Eigenfunction,; Impedance and Kirchhoff's Laws Fundamental limits of the Fourier vs. the Laplace Transform: \(\tilde{u}(t)\) vs. \(u(t)\) The matrix formulation of the polynomial and the companion matrix Complex-analytic series representations: (1 vs. 2 sided); RoC of \(1/(1-s), 1/(1-x^2), -\ln(1-s)\) 1) Series; 2) Residues; 3) pole-zeros; 4) Continued fractions; 5) Analytic properties AE-1 Due AE-3 Due Lec 10 |
| 9 | F | 11/5 | Exam 1: 1-4 PM: Via zoom (ONL) or 2015-ECEB (CLA); Exam Emailed via zoom or Download from Gradescope; Paper or pdf copy provided upon request. Topics: Homework 1-3: NS-1 & NS-3, AE-1, AE-3 (selected problems) Problems: FT vs LT; Residues; Power series, RoC; |
| Week | M | W | F |
|---|---|---|---|
| 45 | L10: Integration in complex plane: FTC & FTCC F21:L10-360 (no public), F21:L10-360 (?broken?), F21:L10-360 (@6:00min) ( login), (S21: L9-360 (@2m), F20: L9-360) | L11: 3.2,.4,.5 Complex Taylor series, Residues, Convolution; More on FTCC?: L11-360.F21 @1:00 (L10-360, S21, L10-360, F20 @4:00) | L12: 3.10,.1-.3 Complex analytic functions L12-360-F21: Audio OFF >@2:00 & ON@16:21 etc, (L11-360 @5m, S21; L11-360, F20) |
| 46 | L13: 3.11,.1,.2 Multi-valued functions; Domain coloring L13-360, F21, (L13-360, S21; L13-360, F20) | L14: 3.5.5, 3.6,.1-.5 1) Riemann's extended plane 2) Schwarz inequality; 3) Triangle inequality; L14-360, F21, (L14-360,F20) | L15: Cauchy's intergral thms CT-1,2,3; L15-360.F21 @3:30; L15-360.S21 (audio @18:00m); (L15-360, F20) |
| 47 | L16: Transmission line problem Lec16-360, F21 No Audio, (Lec16-360, S21; Lec16-360, F20) | L17: Wave function \(\kappa(s)\) when sound speed depends on frequency; L17-360,F21 Audio@2:45, Video@31:30; (Lec17-III-360, S21; Lec17-360, F20 @4min (Inv LT: \(t<0\))) | L18: LT (t>0) Lec18 360-F21 @3:00; Lec18 360-S21; Lec18 360-F20 |
| 48 | L19: S21: Review for Lec19-360-F21 @3:00; Final Exam (360-S21); | L20: LT Properties: (Lec20-III-360-F20) | Thur: Reading Day: Optional review for final Student Q&A 1-2 PM Review F20 |
| L | D | Date | Lecture and Assignment |
| Part II: Complex analytic analysis (6 Lectures) | |||
| 10 | M | 11/8 | Lecture: Fundamental theorem of real vs. complex calculus; Differentiation in the complex plane: Complex Taylor series; Cauchy-Riemann (CR) conditions and differentiation wrt \(s\) (p. 180-182) Discussion of Laplace's equation and conservative fields: (1, 2) |
| 11 | W | 11/10 | Lecture: Integration in the complex plane: FTC vs. FTCC; CR conditionsComplex analytic functions, e.g.: \(z(t) \leftrightarrow Z(s)\); FTC, FTCC (\(\S\)4.1, 4.2), Analytic vs complex analytic functions and Taylor formula and Taylor Series (p. 93-98); Calculus of the complex \(s=\sigma+j\omega\) plane: \(dF(s)/ds\); \(\int F(s) ds\) (Boas, p. 8); Text \(\S\)3.2.3: The convergent of the analytic power series (ROC): Residues; power series, RoC; LT; Read: \(\S\)3.2.6 (p. 101-3) |
| 12 | F | 11/12 | Lecture: Continue Lec 11 Homework 5: DE-2 Problems: Integration, differentiation wrt \(s\); Cauchy theorems; LT; DE-2 pdf, Due on Lec 15; DE2-sol.pdf DE-1 due on Lec15 |
| 13 | M | 11/15 | Lecture: Multi-valued functions: Visualizing complex valued functions Domain coloring, Branch cuts & points, Riemann Sheets, Colorized plots of rational functions; Software: Matlab: Working with Octave/Matlab: 3.1.4 (p. 86): zviz.m, zviz.zip, python Read: \(\S 3.11\) (p. 167) |
| 14 | W | 11/17 | Lecture: Riemann’s extended plane: The Riemann sphere (1851) pdf; Multi-valued functions; Branch points and cuts;Mobius Transformation: (youtube, HiRes), pdf description Mobius composition transformations, as matrices Read: \(\S 3.11.1\) (p. 170) |
| 15 | F | 11/19 | Lecture: Cauchy’s Integral theorems (CT-1,-2,-3) & Formula: Read: \(\S\)4.6.3 (p. 203-209) |
| Thanksgiving Break | |||
| 16 | M | 11/29 | Lecture: Scalar wave equation & WHEN (p. 246-248) Homework 6: DE-3: Problems: Inverse LT; Impedance; Transmission lines; DE3 pdf, Due on Lec 19; DE3-sol.pdf Read: \(\S 3.5.4, 5.2\) (p. 123-125 DE-1 & DE-2 due |
| 17 | W | 12/1 | Lecture: Train-mission problem (ABCD matrix method); More on the Cauchy Residue theorem; Read: \(\S\)4.8.3 (p. 224-226) |
| 18 | F | 12/3 | Lecture: Analysis of the wave propagation function \(\kappa(s)\in\mathbb{C}\) when speed of sound depends on frequency \(s=\sigma + \jmath\omega\). Examples of the inverse Laplace transform for \(F(s)=1/s, e^{-s T_o}/s, 1/s^2\) using the Cauchy residue theorem Read: \(\S\)3.1 (p. 69-73) |
| 19 | M | 12/6 | Lecture: Inverse Laplace transform via the Residue theorem \(t > 0\) and \(t < 0\); Case for causality Laplace Transform, Examples: Convolutions by the step function:LT \(u(t) \leftrightarrow 1/s\) vs. FT \(2\tilde{u}(t) \equiv 1+ \mbox{sgn}(t) \leftrightarrow 2\pi \delta(\omega) + 2/j\omega\) Read: \(\S\)5.7 (p. 216-220) DE-3 Due |
| 20 | W | 12/8 | Lecture: Properties of the Laplace Transform: Modulation, convolution; impedance/admittance, poles and zeros \(Z(s)=N(s)/D(s)\); Review DE3-sol.pdf, Full Solution to train problem. Read: \(\S\)5.7 (p. 220-222) |
| - | R | 12/9 | Reading Day Optional student 'Review Q&A session 9-11AM, 1-2PM |
| - | M | Final: Dec 14, 8-11:59 AM; Room 3017 Offical UIUC exam schedule: | |
| - | Letter grade statistics: F21, F20, F16; Comments by students for the class of Fall 2020, Spring 2021, and Fall 2017 |
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