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Week | M | W | F |
---|---|---|---|
35 | L1: \(\S\)1, 3.1 (Read p. 1-17) Intro + history; | L2: \(\S\)3.1,.1,.2 (p. 69-84) Roots of polynomials; Newton's method. | L3: \(\S\)3.1.3,.4 (p.84-88) Companion matrix |
36 | Labor Day | L4: \(\S\)3.2.3 Taylor series | L5: Eigenanalysis: \(\S\)3.2,.1,.2; Pell & Fibonocci sol.; \(\S\)B1,B3 |
37 | L6: Impedance; residue expansions \(\S\)3.4.2 | L7: \(\S\)3.5, Anal Geom, Generalized scalar products \(\S3.5\) (p. 114-121), | L8: \(\S\)3.5.1-.4 \(\cdot, \times, \wedge \) scalar products |
38 | L9: \(\S\)3.5.5, \(\S\)3.6,.1-.5 Gauss Elim; Matrix algebra (systems) | L10: \(\S\)3.8,.1-.4 Thevenin parameters; Transmission lines; impedance matrix, | L11: \(\S\)3.9,.1 \({\cal FT}\) of signals |
39 | L12: \(\S\)3.10,.1-.3 \(\cal LT\) of systems + postulates | L13: \(\S\)3.11,.1,.2 Complex analytic color maps; Riemann sphere (pdf); Bilinear transform, | L14: Review for Exam I |
40 | Exam I; Any 3 hours between 10AM-2PM | Location 2017 ECEB | On paper; graded on Gradescope |
L/W | D | Date | Part I: Complex algebra (15 Lectures) |
Instruction begins | |||
1/35 | M | 8/26 | L1: Introduction + History; Assignment: HW0: (pdf); Evaluate your math knowledge (not graded); "What is a number?, Is 0 a number? is \(\jmath = \sqrt{-1}\) a number?; Apostol ``Number Theory Solutions; Definition of a number Assignment:'' NS1; Probs 1-4, 7 Due Lec 4:, |
2 | W | 8/28 | L2: Newton's method (p. 74) for finding roots of a polynomial \(P_n(s_k)=0\); IEEE URL & pdf; Chaotic convergence of NM; Example Code; Root derivation; Able's Thm: No closed form solution for \(P_n(s)\) for \(n \ge 5\), All m files: Allm.zip; Do Problem 2 in class. |
3 | F | 8/30 | L3: The companion matrix and its characteristic polynomial: Companion Matrix; The role of complex numbersl; Working with Octave/Matlab: \(\S\)3.1.4 (p. 86) zviz.m 3.11 (p. 167) Introduction to the colorized plots of complex mappings |
-/36 | M | 9/2 | Labor day: Holiday |
4/36 | W | 9/4 | L4: Taylor series and analysis of Newton's method Analysis; Text p. 97 |
5 | F | 9/6 | L5: Eigenanalysis I: Eigenvalues and vectors of a matrix; Text EigenAnalysis Assignment: NS2; Due Lec 7: |
6/37 | M | 9/9 | L6: Analytic functions; Text p. 99; Complex analytic functions; Brune Impedance Residue expansions of ratios of polynomials: \( Z(s)=N(s)/D(s) \); Causality and allowed poles and zeros |
7 | W | 9/11 | L7: Analytic geomerty: Vectors and their dot \(\cdot\), cross \(\times\) and wedge \(\wedge\) products. text p. 114-119; Residues. Colorized plots of complex mappings; View: Mobius/bilinear transform video, As geometry Assignment: NS3; Problems 1, 2 4, 5; Due Lec 10 |
8 | F | 9/13 | L8: Analytic geometry of two vectors (generalized scalar product) p. 121; Inverse of 2x2 matrix |
9/38 | M | 9/16 | L9:Gaussian Elimination; p. 125-128; Permutation matricies; Matrix Taxonomy Continued Fraction approximation (CFA) (Example: \(pi \approx\) 22/7); Hamming Correction code Assignment: AE1: #3,4,8,9,10,11; (Due 1 wk); AE1-Solution |
10 | W | 9/18 | L10: Transmission and impedance matricies; pp. 145-147; See Table 3.2 p. 147 for details |
11 | F | 9/20 | L11: Fourier transforms of signals; p. 152 Predicting tides, Part II Chaos |
12/39 | M | 9/23 | L12: Laplace transforms of systems; p. 157; System postulates p. 164-165 Assignment: AE3: # 2,3,7,9;, Due in 1 week; AE3-Solution |
13 | W | 9/25 | L13: Comparison of Laplace and Fourier transforms; p. 154 & 158; Colorized plots; p. 198-199; View: Mobius/bilinear transform video |
14 | F | 9/27 | L14: Review for Exam I; AE3 due |
15/40 | M | 9/30 | L15 Exam I; A paper copy of the exam will be provided. Open book. Exam1 Grade Stats F24, Exam1 Grade Stats F23, |
Week | M | W | F |
---|---|---|---|
40 | L15: Exam I | L16: 4.1,4.2,.1 (p. 178) Fundmental Thms of calculus & complex \(\mathbb R, \mathbb C\) scalar calculus (FTCC) (LEC-15-360.S20@8:00min), (LEC-15-zoom.S20) | L17: 4.2.2 Cauchy-Riemann Eqs. CR-1, CR-2, CR-3, CR-4 Lec16-360.F21; (LEC-16-360.S20) |
41 | L18: 4.4 Brune impedance/admittance LEC-17-360.F21, (LEC-17-360.S20) | L19: 4.4,.1,.2 Complex analytic Impedance; Lec-18-360.F21@0:25, (LEC-18-360.S20@2:50,, zoom) | L20: 4.4.3 Multi-valued functions, Branch cuts; LEC-19-360.S21@0:10, (LEC-19-360.S20@0:40,, zoom) |
42 | L21: 4.5,.1,.2 Cauchy's complex integration thms CT1, CT2, CT3; Lec-20-360.F21, (LEC-20-360.S20 @2:30, @15:45, @22:00) | L22: 4.7,.1,.2 Inv \({\cal LT} (t<0, t=0)\) Lec21-360-S21 @00:30, (LEC-21-360.S20,, zoom) | L23: 4.7.3 Inv \({\cal LT} (t > 0) \) LEC-22-360-S21@0:45, (LEC-22-360.S20) |
43 | L24: 4.7.4 Properties of the \(\cal LT\); Lec-23-360.F21@00:40, (LEC-23-360.S20,, zoom) | L25: 4.7.5 Solving LTI (simple) Diff. Eqs. with the \(\cal LT\) Lec-24-360.F21, Lec-24-360.S20 (LEC-24-360.S20, start @5:00 PM, zoom) |
L/W | D | Date | Part II: Scalar (ordinary) differential equations (10 Lectures) |
16/40 | W | 10/2 | L16: The fundamental theorems of scalar and complex calculus Assignment: DE1-F22.pdf Problems: 1.2, 1.5, 2.all, 4.all, 5.2, 6.all, 7.all, (Due 1 wk); DE1-sol.pdf |
17 | F | 10/4 | L17: Complex differentiation and the Cauchy-Riemann conditions; Life of Cauchy Properties of complex analytic functions (Harmonic functions);Taylor series of complex analytic functions |
18/41 | M | 10/7 | L18: Brune impedance/admittance and complex analytic Ratio of polynomials of similar degree: \( Z(s) = {P_n(s)}/{P_m(s)} \) with \(n,m \in {\mathbb N}\) \( Z(s) = {P_n(s)}/{P_m(s)} \) with \(n,m \in {\mathbb N}\) Basic properties of impedance functions (postulates) (e.g., causal, positive real) Complex analytic impedance/admittance is conservative (P3) Colorized plots of Impedance/Admittance functions; View: Mobius/bilinear transform video |
19 | W | 10/9 | L19: Generalized impedance Brune vs. generalized impedance/admittance functions (ratio of polynomials; branch cuts) Examples of Colorized plots of Generalized Impedance/Admittance functions; Calculus on complex analytic functions Assignment: Problems: 1.1-.2, 3.1-.4, 4.2-.4, 4.6; 6.4; 7.1-.3, 7.14, 7.19-.20, 9.1, 14.1; ;DE2-F22.pdf, (Due 2 wks); DE2-sol.pdf; |
20 | F | 10/11 | L20: Multi-valued complex analytic functions: Branch cuts and their properties (e.g., moving the branch cut); Examples of multivalued function; Colorized plots of multivalued functions: e.g.: \( F(s) = \sqrt{s e^{jk2\pi}} \) where \(k=\{0,1\}\in{\mathbb N}\) is the sheet index; Balakrishnan Lecture \(W(z)=\sqrt{z}\); More detailed lecture of multivalued \(f(z)\) |
21/42 | M | 10/14 | L21: Three Cauchy integral theorems: CT-1, CT-2, CT-3; How to calculate the residue \(R_k = \lim_{s \rightarrow s_k} (s-s_k)F(s)\), assuming a pole in \(F(s)\) at \(s_k\) |
22 | W | 10/16 | L22: Inverse Laplace transform (\(t<0\)), Application of CT-3 DE2 Due Assignment: DE3-F22.pdf, (Due 1 wk); DE3-sol.pdf |
23 | F | 10/18 | L23: No Class: Allen Out of Town Inverse Laplace transform (\(t\ge0\)) CT-3 Differences between the FT and LT; System postulates: P1, P2, P3, etc. \(\S 3.10.2\), p. 162-164; |
24/43 | M | 10/21 | L24: Properties of the Laplace transform: Linearity, convolution, time-shift, modulation, derivative etc; Introduction to the Train problem, and why it is important. |
25 | W | 10/23 | L25: Solving differential equations: Train problem (DE3, problem 2, p. 206) Fig. 4.11) DE3 Due date delayed to Mon 10/28/24 |
Week | M | W | F |
---|---|---|---|
43 | L26: 5.1.1 (p. 227) Fields and potentials (VC1 due L35); LEC-26-360.F21 @2:00 min, (LEC-25-zoom.S20) | ||
44 | L27: 5.1,.2,.3 (p. 229): \(\nabla()\), \(\nabla \cdot()\), \(\nabla \times()\), \(\nabla \wedge()\), \(\nabla^2() \): Differential and integral forms (LEC-26-360.S20@3:00), (zoom) | L28: 5.2 Field evolution \(\S\) 5.2 (pp. 242-245) Lec-27-360.F21; Cont of Lec 26, (LEC-27-360.S20@3:22), (zoom) | L29: 5.2: Field evolution \(\S\)5.2.1, 5.2.1.1, .2 (pp 242-246); & Scalar Wave Equation \(\S\)5.2.2 p. 246; Lec-28-360.F21@0:45, (LEC-28-360.S20@3:00min, Acoustics@24m) |
45 | L30: 5.2.2,.3,5.4.1-.3 (p. 248) Horns Lec29-360.F21 @0:15, (LEC-29-360.S20) | L31: 5.5.1 Solution methods; 5.6.1-.2 Integral forms of \(\nabla()\), \(\nabla \cdot()\), \(\nabla \times() \) Lec 30-360-Review of HWs, Lec 30-360.F21 @0:15, (LEC-30-360.S20) | L32: 5.6.3-.4 Integral forms of \(\nabla()\) \(\nabla \cdot()\), \(\nabla \times() \) (LEC-31-360.S20) |
46 | L33: 5.6.5 Helmholtz decomposition thm. \( \vec{E} = -\nabla\phi +\nabla \times \vec A \), ( \(\S\) 5.6.5, p. 270 ); LEC-32-360.F21 @1.45, (LEC-32-360.S20 @1:30) | L34: 5.6.6 2d-order scalar operators: \( \nabla^2 = \nabla \cdot \nabla() \), Vector operators: \( {\mathbf\nabla}^2 = \nabla \cdot \mathbf\nabla()\), \(\nabla \nabla \cdot()\), \(\nabla \times \nabla() \); Null operators: \(\nabla \cdot \nabla \times()=0\), \(\nabla \times \nabla ()=0 \) Lec-33-360.F21 @0:45, (LEC-33-360.S20); | L35: Unification of E & M; terminology (Tbl 5.4, p. 288); View: Symmetry in physics (LEC-34-360.S20) |
L/W | D | Date | Part III: Vector Calculus (10 Lectures) |
26/43 | F | 10/25 | L26: Properties of Fields and potentials Assignment: VC1.pdf, Due Lec-35; VC1-sol.pdf |
27/44 | M | 10/28 | L27: Gradient \(\nabla\), Divergence \(\nabla \cdot\), Curl \(\nabla \times\), Laplacian \(\nabla^2\); Integral vs differential definitions; Integral and conservation laws: Gauss, Green, Stokes, Divergence; Vector identies in various coordinate systems; Laplacian in \(N\) dimensions; Discussed Pages 119-121 \(P=M_o c_o^2\) & p. 280-285; |
28 | W | 10/30 | L28: Field evolution for partial differential equations \(\S\) 5.2; Text Appendix B, Eigen analysis methods; bubbles of air in water; Vector fields; Poincare Conjecture: Proved |
29 | F | 11/1 | L29: Review Field evolution \(\S\)5.2.1,.2 & Scalar wave equation & WHEN p. 248 (e.g., Acoustics) \(\S\)5.2.3 |
30/45 | M | 11/4 | L30: Webster Horn equation (p. 347-348) and Tesla inventions: Laser Diodes & how they work; |
31 | W | 11/6 | L31: Solution methods; Integral forms of \(\nabla()\), \(\nabla\cdot()\); (pp. 116/139, 120, 265-268) |
32 | F | 11/8 | L32: Integral form of curl: \(\nabla\times()\) and Wedge-product (p. 268-270) |
33/46 | M | 11/11 | L33: Helmholtz decomposition theorem for scalar and vector potentials (p. 270-274); Electrical (Stark) and Magnetic (Zemann) eigenvalue splitting; Prandt Boundary Layers |
34 | W | 11/13 | L34: Second order operators DoG, GoD, gOd, DoC, CoG, CoC; p. 274 |
35 | F | 11/15 | L35: Unification of E & M; terminology (Tbl 5.4); VC1 Due; Review for Exam II |
Week | M | W | F |
---|---|---|---|
47 | L36: Exam II: Open-Book @ 2-5 PM; `2015` ECEB | L37: 5.7.1-.3 Maxwell's equations (p. 277-280) LEC-35-360.F21 @1&36 min, (LEC-35-360.S20 @00:30) | L38: Derivation of ME \(\S\)5.7.4,.8, p. 281-5; LEC-36-360.F21 @1, (LEC-36-360.S20 @2) |
48 | Thanksgiving Holiday | ||
49 | L39: 5.8 Use of Helmholtz' Thm on ME LEC-37-360.F21,, (LEC-37-360.S20) | L40: 5.8 Helmholtz solutions of ME Lec-38-360.F21; (LEC-38-360.S20) \(\S5.6.5\) Tbl 5.3 | L41: 5.8 Analysis of simple impedances (Inductors & capacitors) Lec-29-360.F21, (LEC-39-360.S20) |
50 | L42: Stokes's Curl theorem & Gauss's divergence theorem; LEC-40-360.F21 @3:30, (LEC-40-360.S20) | L43: Review (LEC-41-360.S20) | Thur: Optional Review for Final; Reading Day |
L/W | D | Date | Part IV: Maxwell's equation with solutions |
36/47 | M | 11/18 | L36 Open-Book Exam II; 2-5 PM; 2015 ECEB Optional 10-11 AM: review for today's Midterm II |
37 | W | 11/20 | L37: Derivation of the wave equation from Eqs: EF and MF; Webster Horn equation: vs separation of variables method + integration by parts; Assignment: 493:/Assignments/VC2-F22.pdf |
38 | F | 11/22 | L38: Derivation of Maxwell's Equations \(\S\) 5.7.4 (p. 280),Transmission line theory: Lumped parameter approximation: 1D & 2D vs. 3D: \(\S 5.7.4 (p. 280)\) d'Alembert solution of wave Equation; Poynting vector; Problem of light bulb in series with a very long pair of wires (e.g., to the moon, or sun & further); Telegraph equation, Wave equation (Parabolic, hyperbolic, elliptical); Diffusion,, Role of the Mobius Transformation |
-/48 | S | 11/23 | Thanksgiving Break |
39/49 | M | 12/2 | L39: Helmholtz' Thm: The fundamental thm of vector calculus \(\mathbf{F}(x,y,z) = \nabla{\phi(x,y,z)} + \nabla \times \mathbf{A}(x,y,z)\); As applied to Maxwell's Equations. Recall: incompressible: \(\nabla \cdot \mathbf{u} =0\) and irrotational: \(\nabla \times \mathbf{w} =0\) VC2.pdf VC2-sol |
40 | W | 12/4 | L40: Properties of 2d-order operators \(\S5.6.5\) Table 5.3 p. 270; Oliver Heaviside and Maxwell's Equations, AIP, wikipedia, Nyquist proof of 4kTB noise floor L10: Summary |
41 | F | 12/6 | L41: Derivation of the vector wave equation; Discuss VC2 solutions |
42/50 | M | 12/9 | L42: Physics and Applications; MaxEq vs quantum` mechanics; Pauli-Heiseberg debate; Video demos re ME; |
43 | W | 12/11 | L43: Review of entire course (Summary) VC2 due; VC2-sol |
-/50 | R | 12/12 | Reading Day | |
R | 12/12 | Optional Q&A Review for Final (no Lec): 9-11 Room: ?3017? ECEB + Gradescope | ||
-/51 | R | 12/14 | Final: 8-11 AM | |
F | 12/15 | Finals End | ||
12/22 | Final grade analysis |
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