Last Modified : October 19, 2012, at 06:02 AM
ECE 493 Adv Eng Math 11
- Advanced Engineering Mathematics; Syllabus: 2011, 2009, 2008, UIUC; Listing: Campus/ECE-493/MATH-487
- Calendars: Class, Campus; Time/place, Website, Contact, Text: etc B106-B6 Eng Hall
- Office Hours: Friday 1-2 Room 330M Everitt Lab (ECE Building); TA: Po-Sen Huang (huang146@illinois.edu)
- This week's schedule
ECE 493/MATH-487 Daily Schedule Spring 2011
| L/W | D | Date | Integrated Lectures on Mathematical Physics |
|---|---|---|---|
| 0/4 | M | 1/17 | MLK Day; no class |
| Part I: Complex Variables (10 lectures) | |||
| 1/4 | T | 1/18 | L1: T25. The frequency domain: Complex  as a function of complex frequency  ; e.g.,  ), phasors, Phasers and delay  ,  ,  T26. Singularities (i.e., poles, branch cuts and transformations);Mobius Transformation (youtube, HiRes), pdf description Read: [Ch. 21.1-21.4] HW0: Evaluate your present state of knowledge (not graded) HW8 Complex Functions and Laplace transforms (Solution) |
| 2 | R | 1/20 | L2: T 27. Differential calculus on  T 28. Cauchy-Riemann Eqs., Analytic functions, Harmonic functions Read: [21.5] and verify that you can do all the exercises on page 1113. |
| 3 | T | 1/25 | L3: Inverses of Analytic functions; T 29. Irrotational fields (e.g., velocity potential  ) [p.~829];T 28. Discussion on CR conditions: Computing  and  ;Analytic coloring, via matlab, using zviz.m; Read: [16.10] pp. 826-838; HW9 Analytic functions; 30. Integration of analytic functions; 33. Cauchy integral formula; Riemann Sheets and Branch cuts; Region of Convergence; inverse Laplace transforms; (Solution) |
| 4 | R | 1/28 | L4: T 30.Integral calculus on T 31.  on the unit circleContinue discussion of examples of analytic functions, 33. Cauchy integral formula, 37. inverse Laplace transforms, 38. Rational fraction expansions, conservative fields; Boas' method for computing  given  pdf from R.P. Boas, Invitation to Complex Analysis Random House 1987Read: [22.3] |
| 5 | T | 2/1 | L5:T 32.Cauchy's theorem; T 33.Cauchy's integral formula [23.5]; Read: [23.3, 23.5]; HW10 (Solution) |
| 6 | R | 2/3 | L6a: Contour integration and Inverse Laplace Transforms Examples of forward  and inverse  Laplace Transform pairs [e.g.,  ]L6b: Special functions and Pole-zero locations (stable/causal, allpass, minimum phase, positive real); Read: pp. 841-843 HW11; (Solution) |
| 7 | T | 2/8 | L7: Hilbert Transforms and the Cauchy Integral formula: The difference between the Fourier transform  and the Laplace  Review of Residues (Examples) and their use in finding solutions to integrals; T 34. Series: Maclaurin, Taylor, Laurent [24.3] T 36.Jordan's Lemma Read: [24.3] |
| 8 | R | 2/10 | L8: Cauer synthesis, Bode plots, Network theory (Brune Positive-real (PR) impedance functions) Schelkunoff on Impedance (BSTJ, 1938) (djvu(0.6M), pdf(17M) Δ) Inverse problems: Tube Area  given impedance  |
| 9/7 | T | 2/15 | L9: T 37. More on Inverse Transforms: Laplace and Fourier  ;The multi-valued  ,  and:  Analytic continuation T 35. Cauchy's Residue Theorem [24.5] Read: [24.2, 24.2] (power series and the ROC); HW12; (Solution) |
| 10 | R | 2/17 | L10: T 38. Rational Impedance (Pade) approximations:  Partial fraction:  and Continued fractions:  expansions Read: [24.5] |
| 0/8 | T | 2/22 | NO CLASS Optional office hours for review, during class time |
| 0/8 | T | 2/22 | Exam I Feb 22 Tuesday @ 7-9 PM; Place: 1MEB 135 |
| Part II: Linear (Matrix) Algebra (6 lectures) | |||
| 1 | R | 2/24 | L1: T 1. Basic definitions, Elementary operations; T 2. Cramer's Rule, Determininants, Inverse Matrix, Aug Matrix and Gauss Elimination; Vandermonde Review Exam I; Read: 8.1-2, 10.2; HW1, (Solution) |
| 2/9 | T | 3/1 | L2: T 3. Solutions to  by Gaussian elimination, T 4. Matrix inverse  ; Cramer's RuleRead: 8.3, 10.4 ; |
| 3 | R | 3/3 | L3: T 5. The symmetric matrix: Eigenvectors; T 6. Transformations (change of basis); Read: 10.6-10.8 HW2: Vector space; Schwartz and Triangular inequalities, eigenspaces (Solution) |
| 4/10 | T | 3/8 | L4: T 7. Vector spaces in  ; Innerproduct+Norms; Ortho-normal; Span and Perp ( ); Schwartz and Triangular inequalities Read: 9.1-9.6, 10.5, 11.1-11.3 |
| 5 | R | 3/10 | L5: Gram-Schmidt proceedure; Vector dot-product  , cross-product  , triple-products  ,  ;Read: 9.10, 11.4 ; Leykekhman Lecture 9 HW3 Rank-n-Span; Taylor series; Vector products and fields (Solution) |
| 0 | R | 3/11-3/12 | Engineering Open House |
| 6/11 | T | 3/15 | L6: T 5. Asymmetric matrix; T; 8. Optimal approximation and least squares; Singular Value Decomposition |
| Part III: Vector Calculus (5 lectures) | |||
| 1 | R | 3/17 | L1: T9. Partial differentiation [Review: 13.1-13.5;]; T 10. Vector fields, Path, volume and surface integrals HW3-b:;Symmetric and non-symmetric matrices, eigenvectors, Singular value decomposition (Solution) Read: 15 |
| 0/ | S | 3/18 | Spring Break |
| 0/13 | M | 3/28 | Instruction Resumes |
| 2 | T | 3/29 | L2: Vector fields:  , Change of variables under integration: Jacobians!! Read: 13.6 HW4: Key vector calculus topics (Solution) |
| 3 | R | 3/31 | L3: Gradient  , Divergence  , Curl  , Scaler (and vector) Laplacian  ;Vector identies in various coordinate systemsNotes (pdf, djvu) Read: 16.1-16.6 |
| 4/14 | T | 4/5 | L4: Integral and conservation laws: Gauss, Green, Stokes, Divergence Read: 16.8-16.10 |
| 5 | R | 4/7 | L5: Applications of Stokes and Divergence Thms: Maxwell's Equations; Potentials and Conservative fields; Review: all 16 |
| 0/15 | T | 4/12 | Exam II Apr 12 Tues @ 7-9 PM Room: 163 Everitt Lab |
| - | T | 4/12 | NO Lecture due to Exam I; Class time will be converted to optional Office hours, to review home work solutions and discuss exam |
| Part IV: Boundary value problems (6 lectures) | |||
| Outline: Ch. 17 Fourier Trans.; Ch. 18: Diffusion Eq.; Ch. 19: Wave Eq.; Ch. 20. Laplace's Eq. | |||
| 1 | R | 4/14 | L1: T 1. PDE: parabolic, hyperbolic, elliptical, discriminant Read: Chapter 18.3; Look at: Emmy Noether, Noether's Thm. I; Examples of Symmetry in physics HW6: Separation of variables, BV problems, symmetry (Solution) |
| 2/16 | T | 4/19 | L2: T 21. Special Equations of Physics: Diffusion (Ch. 18); Wave (Ch. 19); Laplace (Ch. 20) 18. Separation of variables; integration by parts Read: [20.2-3] |
| 3 | R | 4/21 | L4: T 16. Transmission line theory: Lumped parameter approximations 17.  order PDE: Lecture on: HornsRead:[17.7, pp.~ 887, 965, 1029, 1070, 1080] |
| 4/17 | T | 4/26 | L3: T 20. Sturm-Liouville BV Theory: Allen out of town; Prof. Levinson to lecture 23. Special functions by Power Series: Bessel, Legendre Polynomials, Riemann Zeta Read: 20 HW7: Sturm-Liouville, Boundary Value problems, Fourier and Laplace Transforms; (Solution); Hints for problems 3+5 and 4. |
| 5 | R | 4/28 | L5: T 24. Fourier: Integrals, Transforms, Series, DFT Read: 17.3-17-6 |
| 6/18 | T | 5/3 | L6: T Solutions to several geometries for the wave equation (Strum-Liouville cases) Read: Ch. 20, 5.1-5.3 + Review p.290-1; Study: the solution to HW7 T 40. ODE's with initial condition (vs. Boundary value problems) Di and Gilbert (1993) Redo HW0: |
| - | W | 5/4 | Instruction Ends |
| - | R | 5/5 | Reading Day |
| - | T | 5/10 | Exam III 7:00-10:00+ PM on HW1-HW11 (Room: EH 106B3) |
| -/19 | F | 5/13 | Finals End |
L= Lecture #
T= Topic #
W=week of the year, starting from Jan 1
D=day: T is Tue, W Wed, R Thur, S Sat, etc.
The somewhat random-ordered numbers in front of many (not all) topics, are the topic numbers defined
in the 2009 Syllabus:
ECE-493 is divided into 4 basic sections (I-IV), divided into 40 topics,
delivered as 24=4*6 lectures. There are two mid-term exams and one final.
There are 12 homework assignments, with a HW0 that does not count
toward your final grade. Each exam (I, II and Final) will count as 30% of your final grade,
while the Assignments (HW1-12) plus class participation, count for 10%.