Last Modified : Tue, 18 Jan 11

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- Advanced Engineering Mathematics; Syllabus: 2009 Δ, 2008 Δ, UIUC; Listing: Campus/ECE-493/MATH-487
- Schedule: This week; Calendars: Class, Campus; Time/place, Website, Contact, Text: etc

L/W | D | Date | Integrated Lectures on Mathematical Physics |
---|---|---|---|

0/4 | M | 1/19 | MLK Day; no class |

Part I: Linear (Matrix) Algebra (5 lectures) | |||

1/4 | T | 1/20 | Lecture 1: Topic 1. Basic definitions, 2. Elementary operations;Read: 8.1-2, 10.2; Assignment: Flag terminology you don't understand in Class;HW0: Evaluate your present state of knowledge (not graded) |

2 | R | 1/22 | Lecture 2: 3. Solutions to {$Ax=b$}, 4. Matrix inverse {$x=A^{-1}b$};Read: 8.3, 10.4 |

3/5 | T | 1/27 | Lecture 3: 5. Matrix Algebra; 6. Transformations;Read: 10.6-10.8HW1 2. Cramer's Rule, Determininants, Inverse Matrix, Aug Matrix and Gauss Elimination; Vandermonde (Solution) Scores: 5x100 6x90 2x85 2x65 |

4 | R | 1/29 | Lecture 4: 7. Vector spaces in {$\mathbb{R}^n$};Read: 9.1-9.6, 10.5, 11.1-11.3 |

5/6 | T | 2/3 | Lecture 5: 5. Eigenvalues & vectors; 8. Optimal approximation and least squares;Read: 9.10, 11.4 HW2: Vector space; Schwartz and Triangular inequalities, eigenspaces (Solution) |

Part II: Vector Calculus (5 lectures) | |||

6 | R | 2/5 | Lecture 6: 9. Partial differentiation [Review: 13.1-13.5;]; 10. Vector fields, Path, volume and surface integralsRead: 15 |

7/7 | T | 2/10 | Lecture 7: Vector fields: {${\bf R}(x,y,z)$}, vector dot-product {$A \cdot B$}, cross-product {$A \times B$}, triple-products {$A \cdot A \times B$}, {$A \times (B \times C)$}; Change of variables under integration: Jacobians!! Read: 13.6 HW3: Rank-n-Span; Taylor series; Vector products and fields (Solution) |

8 | R | 2/12 | Lecture 8:Gradient {$\nabla$}, Divergence {$\nabla \cdot$}, Curl {$\nabla \times$}, Laplacian {$\nabla^2$};Read: 16.1-16.6 (not 16.7) |

9/8 | T | 2/17 | Lecture 9: Integral and conservation laws: Gauss, Green, Stokes, DivergenceLecture 9 NotesRead: 16.8-16.10HW4: Key vector calculus topics (Solution) |

10 | R | 2/19 | Lecture 10: Potentials and Conservative fields;Review: all 16 (not 16.7) |

T | 24 | ExamI Feb 24 Tues @ 7-9 PM Exam I grade distribution: [81,93 95, 102 109 103 105, 110 110 115 118, 122, 131, 143] | |

-/9 | T | 2/24 | NO Lecture due to Exam I; Class time will be converted to optional Office hours, to review home work solutions and discuss examRead: 17HW5: Not assigned |

Part III: Boundary value problems (6 lectures) | |||

11 | R | 2/26 | Lecture 11:15. PDE: parabolic, hyperbolic, elliptical, discriminantRead: 18-19 Emmy Noether, Noether's Thm. I; Examples of Symmetry in physics |

12/10 | T | 3/3 | Lecture 12:21. Special Equations of Physics: Wave, Laplace, Diffusion; 18.~Separation of variables; integration by parts Read: [18.3, 20.2-3];HW6: Separation of variables, BV problems, symmetry (Solution Ver-1.4) |

13 | R | 3/5 | Guest Lecture Prof. Levinson Lecture 13:20.Sturm-Liouville BV Theory;23. Special functions by Power Series: Bessel, Legendre Polynomials, Riemann Zeta Read: 18-20 |

14/11 | T | 3/10 | Lecture 14: 16. Transmission line theory: Lumped parameter approximations,17. {$2^{nd}$} order PDE from a pair of first order ODEs as unit-cell -> 0 Read:[17.7, pp.~ 887, 965, 1029, 1070, 1080]HW7-v1.2: Sturm-Liouville, Boundary Value problems, Fourier and Laplace Transforms; (Solution-3/18/09); Hints for problems 3+5 and 4. |

15 | R | 3/12 | Lecture 15:24.Fourier: Integrals, Transforms, Series, DFTRead: 17.3-17-6 |

16/12 | T | 3/17 | Lecture 16:25.Laplace and z Transforms19.The vector space {$\mathbb{C}$} Read: 5.1-1.3+Review p.290-1; Study: the solution to HW7 |

R | 3/19 | No Lecture: due to Exam II | |

A | 3/21 | Spring Break Starts | |

M | 3/30 | Instruction Resumes | |

Part IV: Complex Variables (10 lectures) | |||

17/14 | T | 3/31 | Lecture 17:The frequency domain: Complex {$Z(s) = R(s)+iX(s)$} as a function of complex frequency {$s=\sigma+i\omega$}; e.g., {$Z,s \in \mathbb{C}$}), phasors, Phasers and delay {$e^{-i\omega T}$}, {$\log(z)$}, {$\sum z^n$}27.Singularities (i.e., poles, branch cuts and transformations);Mobius Transformation (youtube, HiRes), complex color-coding Read: [Ch. 21.1-21.4]HW8-v1.01 Complex Functions and Laplace transforms (Solution) |

T | 3/31 | Exam II March 31 Tues @ 7-9 PM 441 Altgeld Hall A: 114-98; A-: 88 89 86; B+ 77 ;C+ 57 [114 111 109 108 105 103 99 98; 88 89 86; 77; 57] out of a maximum of 137 points | |

18 | R | 4/2 | Lecture 18:28.Differential calculus on {$\mathbb{C}$}29. Cauchy-Riemann Eqs., Analytic functions, Harmonic functions Read: [21.5] |

19/15 | T | 4/7 | Lecture 19: Inverses of Analytic functions;30. Irrotational fields (e.g., velocity potential {$\mathbf{u} = \nabla \phi(x,y,z)$}) [p.~829]; Discussion on CR conditions: Computing {$\Re f(z)$} and {$\Im f(z)$}; Analytic coloring; Read: [16.10] pp. 826-838;HW9 Analytic functions; Integration of analytic functions; Cauchy integral formula; Riemann Sheets and Branch cuts; Region of Convergence; inverse Laplace transforms; (Solution) |

20 | R | 4/9 | Lecture 20:31.Integral calculus on {$\mathbb{C}$} 32. {$\int z^{n-1} dz$} on the unit circle (Hardy spaces {${\cal H}^2$}) Continue discussion of examples of analytic functions,, Cauchy integral formula, inverse Laplace transforms, Rational fraction expansions, conservative fields; Read: [22.3] |

21/16 | T | 4/14 | Lecture 21: Special functions and Pole-zero locations (stable/causal, allpass, minimum phase, positive real); 33.Cauchy's theorem 34.Cauchy's integral formula [23.5] 36.Cauchy's Residue Theorem [24.5] Read: [23.5, 24.5];HW10 (ver 1.2) (Solution) |

22 | R | 4/16 | Lecture 22: Hilbert Transforms and the Cauchy Integral formula; Review of Residues (Examples) and their use in finding solutions to integrals; Topic 35.Series: Maclaurin, Taylor, Laurent [24.3]Topic 37.Jordan's Lemma Read: [24.3] |

23/17 | T | 4/21 | Lecture 23: Topic 38. More on Inverse Transforms: Laplace {${\cal L}^{-1}$} and Fourier {${\cal F}^{-1}$};The multi-valued {$ i^s $} and {$ \tanh^{-1}(log(s)) $}; Read:; |

24 | R | 4/23 | Lecture 24: 39. Rational Impedance (Pade) approximations: {$Z(s)={a+bs+cs^2}/({A+Bs})$}Partial fraction: {$Z(s) = \sum a_i/(s-s_i)$} and Continued fractions: {$Z(s)=s+a/(s+b/(s + c/(s+\cdots)))$} expansions Read: |

25 | T | 4/28 | Lecture 25: Guest Lecture: Prof. J. d'Angelo; Contour integration and Fourier TransformsHW11; (Solution) |

26 | R | 4/30 | Lecture 26: Inverse problems; Cauer synthesis, Bode plots, Network theory (Brune Positive-real (PR) impedance functions) Schelkunoff Impedance (1940?) Δ; 40.~ODE's with initial condition (vs. Boundary value problems) Di and Gilbert (1993) Δ |

27/19 | T | 5/5 | Last class; Review for FinalRedo HW0: |

- | W | 5/6 | Instruction Ends |

- | R | 5/7 | Reading Day |

- | F | 5/8 | Exam III 7:00-10:00+ PM on HW6-HW11: The Exam III score Distribution is trimodal: [74 76 76 77; 92 92 92 92 92; 104 105 106] out of 130. The top three top scores are JB, LM, VC. Nice job! Final scores to follow. |

-/20 | F | 5/15 | Finals End |

**L**= Lecture #**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 Δ:

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%.

- Spring 2009
*Website* - Professor: Jont B. Allen (ECE); NID: jontalle;
*Website*; TA: Hyunchul Park; NID: hpark48 - Time: 12-1:20 TR; Location: 441 Altgeld Hall
- Textbook: Greenberg; Homework; Exams: Exam 1, Exam 2; Final
- Useful online references: Math-Physics, verious items

All homework assigned on Tuesday will be due in class the following Tuesday. In 2009 there was no HW5 due to resource-constraints.

There are 3 exams total:

Exam I following *Sections I, II*, Exam II following *Section III*, Exam III following *Section IV*

The final is similar to the two midterms, and is only on the final 10 lectures on complex variables.

`Not proofed beyond here` |

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