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ECE 493/MATH487 {$\sqrt{Daily Schedule}$} (Spring 2009)
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: 8.12, 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: 10.610.8 HW1 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: 9.19.6, 10.5, 11.111.3 
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: 13.113.5;]; 10. Vector fields, Path, volume and surface integrals Read: 15 
7/7  T  2/10  Lecture 7: Vector fields: {${\bf R}(x,y,z)$}, vector dotproduct {$A \cdot B$}, crossproduct {$A \times B$}, tripleproducts {$A \cdot A \times B$}, {$A \times (B \times C)$}; Change of variables under integration: Jacobians !! Read: 13.6 HW3: RanknSpan; 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: 16.116.6 (not 16.7) 
9/8  T  2/17  Lecture 9: Integral and conservation laws: Gauss, Green, Stokes, Divergence Lecture 9 Notes Read: 16.816.10 HW4: 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 @ 79 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 exam Read: 17 HW5: Not assigned 
   Part III: Boundary value problems (6 lectures) 
11  R  2/26  Lecture 11:15. PDE: parabolic, hyperbolic, elliptical, discriminant Read: 1819 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, 20.23]; HW6: Separation of variables, BV problems, symmetry (Solution Ver1.4) 
13  R  3/5  Guest Lecture Prof. Levinson Lecture 13:20.SturmLiouville BV Theory; 23. Special functions by Power Series: Bessel, Legendre Polynomials, Riemann Zeta Read: 1820 
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 unitcell > 0 Read:[17.7, pp.~ 887, 965, 1029, 1070, 1080] HW7v1.2: SturmLiouville, Boundary Value problems, Fourier and Laplace Transforms; (Solution3/18/09); Hints for problems 3+5 and 4. 
15  R  3/12  Lecture 15:24.Fourier: Integrals, Transforms, Series, DFT Read: 17.3176 
16/12  T  3/17  Lecture 16:25.Laplace and z Transforms 19.The vector space {$\mathbb{C}$} Read: 5.11.3+Review p.2901; 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 colorcoding Read: [Ch. 21.121.4] HW8v1.01 Complex Functions and Laplace transforms (Solution) 
 T  3/31  Exam II March 31 Tues @ 79 PM 441 Altgeld Hall A: 11498; 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. CauchyRiemann 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. 826838; 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. {$\int z^{n1} dz$} 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 Polezero 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 multivalued {$ 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/(ss_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 Transforms HW11; (Solution) 
26  R  4/30  Lecture 26: Inverse problems; Cauer synthesis, Bode plots, Network theory (Brune Positivereal (PR) impedance functions) Schelkunoff Impedance (1940?); 40.~ODE's with initial condition (vs. Boundary value problems) Di and Gilbert (1993) 
27/19  T  5/5  Last class; Review for Final Redo HW0: 
  W  5/6  Instruction Ends 
  R  5/7  Reading Day 
  F  5/8  Exam III 7:0010:00+ PM on HW6HW11: 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 randomordered numbers in front of many (not all) topics, are the topic numbers defined
in the 2009 Syllabus: ECE493 is divided into 4 basic sections (IIV), divided into 40 topics,
delivered as 24=4*6 lectures. There are two midterm 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 (HW112) plus class participation, count for 10%.
General information
Assignments:
All homework assigned on Tuesday will be due in class the following Tuesday. In 2009 there was no HW5 due to resourceconstraints.
Exams
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.
