Last Modified : Fri, 10 Jun 22
ECE493-F21
- Syllabus: pdf-2018, pdf-2009; Listing: ECE-493, (Math-487) Campus (Official): ECE, Math
- Calendars:\A Campus;
- Time/place: Zoom: ID: 965 0165 0571, PW: 146870;
- 360 recordings of all classes No logins required; Videos by course number: PUBLIC ACCESS to all ECE410 Lectures (videos): 2021, 2022
- Video Lectures ECE 493 Video
- Office Hours: F 11-11:59AM; Location TBD; Zoom: ID: 965 0165 0571, PW: 146870;
- Text: An Invitation to Mathematical Physics pdf, Greenberg: supplementary text
- Gradescope code: D5G555
- FAQ: 360 Documentation
- Instructor: Prof. Jont Allen (217)_369_7711c; (netID: jontalle@; Office 3062-ECEB); TA: Billy Walters [wcw5 @ illinois.edu]
- Extra hour credit ISUR mentoring includes $600 overhead
- Fantastic math videos, such as James Clerk Maxwell
- Matlab Tutorial pdf
- Homework must be submitted to gradescope Entry Code: D5G555
- How to electronically edit pdf files (homework and exams): xournalpp (PC-based pdf-editing) OR xodo.com: Web-based pdf-editing AND an incomplete Review of 8 pdf editors
- University guidlines
- COVID-19 on-campus testing twice per week is required for ALL students and 1 per week for staff, for those who are on-campus for any length of time.
Mandatory testing begins on August 10 for faculty and staff and on August 16 for students. See a list of on-campus testing sites here.
- COVID-19 on-campus testing twice per week is required for ALL students and 1 per week for staff, for those who are on-campus for any length of time.
- This week's Reading schedule; Final
ECE-493/MATH-487 Daily Schedule Fall 2021: An Introduction to Mathematical Physics and its History
| Week | M | W | F |
|---|---|---|---|
| 34 | L1: \(\S\)1, 3.1 (Read p. 1-17) Intro + history; L1.F21@5:00 min; (L1-Z.F20@8:27 min) The size of things; | L2: \(\S\)3.1,.1,.2 (p. 69-84) Roots of polynomials; Newton's method. L2.F21@11:30 min; (L2-360.F20@3:25 min) | L3: \(\S\)3.1.3,.4 (p.84-88) Companion matrix L4-Z.F20@0:30 (Eigen-analysis); @1:04 (Companion Matrix) L3.F21-360 (Audio died after 2 sec; (L3-Z.F20@10:35 min) |
| 35 | L4: Eigenanalysis: \(\S\)3.2,.1,.2; Pell & Fibonocci sol.; \(\S\)B1,B3 L4.F21-360; (L4-Z.F20@0:38) | L5: \(\S\)3.2.3 Taylor series L5-360.F21 @9:00, (L5-Z.F20) (L5@14:50) | L6: Impedance; residue expansions \(\S\)3.4.2 L6-360.F21; (L6-360.F20) |
| 36 | Labor day | L7: \(\S\)3.5, Anal Geom, Generalized scalar products (p. 112-121) L7-360.F21@5:15, (L7-360.F20@2:20 min) | L8: \(\S\)3.5.1-.4 \(\cdot, \times, \wedge \) scalar products (L8-360.F20, |
| 37 | L9: \(\S\)3.5.5, \(\S\)3.6,.1-.5 Gauss Elim; Matrix algebra (systems) L9-360.F21@3:30-Not Zoomed, (L9-360.F20@4:30min) | L10: \(\S\)3.8,.1-.4 Thevenin parameters; Transmission lines; impedance matrix, Screen_Shot-1, Screen_Shot-2, L10-360.F21@6:10, (L10-360.F20 No audio), | L11: \(\S\)3.9,.1 \({\cal FT}\) of signals L11-360.F21@13:05 min, (L11-360.F20@8:20 min) |
| 38 | L12: \(\S\)3.10,.1-.3 \(\cal LT\) of systems + postulates L12-360.F21@1:30m, (L12-360.F20), L12-Z.F20 | L13: \(\S\)3.11,.1,.2 Complex analytic color maps; Riemann sphere (pdf); Bilinear transform, L13-360.21, No Audio (L13-360.F20%red$@13min), L12-Z.F20 | L14: Review for Exam I; L14-360.F21; L14-360.F21, L14-360.F20@25min, L14-Z, L14-Z.F20 Exam_Review |
| 39 | Exam I; zoom+Gradescope (Code: D5G555) | ||
| L/W | D | Date | Part I: Complex algebra (15 Lectures) |
| Instruction begins | |||
| 1/34 | M | 8/23 | L1: Introduction + History; Map of mathematics; Understanding size requires an imagination Assignment: HW0: (pdf); Evaluate your knowledge (not graded); Assignment: NS1; Due Lec 4: NS2; Due Lec 7: NS3; Due Lec 13 |
| 2 | W | 8/25 | L2: Newton's method (p. 74) for finding roots of a polynomial \(P_n(s_k)=0\) Newton's method; All m files: Allm.zip |
| 3 | F | 8/27 | L3: The companion matrix and its characteristic polynomial:Working with Octave/Matlab: \(\S\)3.1.4 (p. 86) zviz.m or zvizMay31V4.m 3.11 (p. 167) Introduction to the colorized plots of complex mappings |
| 4/35 | M | 8/30 | L4: Eigenanalysis I: Eigenvalues and vectors of a matrix Singular-value analysis; Assignment: AE1, (Due 1 wk);Solution: AE1-sol Solution: NS1-sol, NS1 due |
| 5 | W | 9/1 | L5: Taylor series |
| 6 | F | 9/3 | L6: Analytic functions; Complex analytic functions; Brune Impedance Residue expansions of ratios of polynomials: \( Z(s)=N(s)/D(s) \) |
| -/36 | M | 9/6 | Labor day: Holiday |
| 7 | W | 9/8 | L7: Analytic geomerty: Vectors and their dot \(\cdot\), cross \(\times\) and wedge \(\wedge\) products. Residues. Colorized plots of complex mappings; View: Mobius/bilinear transform video, As geometry Assignment: AE2; NS2, AE1 due in 1 week; Sol: AE2-sol; Sol: NS2-sol |
| 8 | F | 9/10 | L8: Analytic geometry of two vectors (generalized scalar product) Inverse of 2x2 matrix |
| 9/37 | M | 9/13 | L9: Gaussian Elimination; Permutation matricies; Matrix Taxonomy |
| 10 | W | 9/15 | L10: Transmission and impedance matricies Assignment: AE3, Due in 1 week;AE2 dueSol: NS3-sol;Sol: AE3-sol |
| 11 | F | 9/17 | L11: Fourier transforms of signals; Predicting tides |
| 12/38 | M | 9/20 | L12: Laplace transforms of systems;System postulates |
| 13 | W | 9/22 | L13: Comparison of Laplace and Fourier transforms; Colorized plots; View: Mobius/bilinear transform video NS3, AE3 due |
| 14 | F | 9/24 | L14: Review for Exam I |
| -/39 | M | 9/27 | Exam I; The exam will be in ECEB-3017 from 9-12, no online local attendance.A paper copy of the exam will be provided. One student in China will be online. |
| Week | M | W | F |
|---|---|---|---|
| 39 | Exam I | L15: 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) | L16: 4.2.2 Cauchy-Riemann Eqs. CR-1, CR-2, CR-3, CR-4 Lec16-360.F21; (LEC-16-360.S20) |
| 40 | L17: 4.4 Brune impedance/admittance LEC-17-360.F21, (LEC-17-360.S20) | L18: 4.4,.1,.2 Complex analytic Impedance; Lec-18-360.F21@0:25, (LEC-18-360.S20@2:50,, zoom) | L19: 4.4.3 Multi-valued functions, Branch cuts; LEC-19-360.S21@0:10, (LEC-19-360.S20@0:40,, zoom) |
| 41 | L20: 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) | L21: 4.7,.1,.2 Inv \({\cal LT} (t<0, t=0)\) Lec21-360-S21 @00:30, (LEC-21-360.S20,, zoom) | L22: 4.7.3 Inv \({\cal LT} (t > 0) \) LEC-22-360-S21@0:45, (LEC-22-360.S20) |
| 42 | L23: 4.7.4 Properties of the \(\cal LT\); Lec-23-360.F21@00:40, (LEC-23-360.S20,, zoom) | L24: 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) |
| 15 | W | 9/29 | L15: The fundamental theorems of scalar and complex calculus Assignment: DE1-F21.pdf, (Due 1 wk); DE1-sol.pdf |
| 16 | F | 10/1 | L16: Complex differentiation and the Cauchy-Riemann conditions; Life of Cauchy Properties of complex analytic functions (Harmonic functions);Taylor series of complex analytic functions |
| 17/40 | M | 10/4 | L17: Brune impedance/admittance and complex analytic Ratio of polynomials of similar degree: \( Z(s) = {P_n(s)}/{P_m(s)} \) with \(n,m \in {\mathbb N}\) 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 |
| 18 | W | 10/6 | L18: 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: DE2-F21.pdf, (Due 1 wk); DE2-sol.pdf; |
| 19 | F | 10/8 | L19: 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 \(k\in{\mathbb N}\) is the sheet index; Balakrishnan Lecture \(F(s)=\sqrt{s}\) |
| 20/41 | M | 10/11 | L20: Three Cauchy integral theorems: CT-1, CT-2, CT-3 How to calculate the residue |
| 21 | W | 10/13 | L21: Inverse Laplace transform (\(t<0\)), Application of CT-3 DE2 Due Assignment: DE3-F21.pdf, (Due 1 wk); DE3-sol.pdf |
| 22 | F | 10/15 | L22: 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; |
| 23/42 | M | 10/18 | L23: Properties of the Laplace transform: Linearity, convolution, time-shift, modulation, derivative etc; Introduction to the Train problem and why it is important. |
| 24 | W | 10/20 | L24: Solving differential equations: Train problem (DE3, problem 2, p. 206) Fig. 4.11) DE3 Due |
| Week | M | W | F |
|---|---|---|---|
| 42 | L25: 5.1.1 (p. 227) Fields and potentials (VC-1); LEC-26-360.F21 @2:00 min, (LEC-25-zoom.S20) | ||
| 43 | L26: 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) | L27: 5.2 Field evolution \(\S\) 5.2 (p. 242) Lec-27-360.F21; Cont of Lec 26, (LEC-27-360.S20@3:22), (zoom) | L28: 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) |
| 44 | L29: 5.2.2,.3,5.4.1-.3 (p. 248) Horns Lec29-360.F21 @0:15, (LEC-29-360.S20) | L30: 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) | L31: 5.6.3-.4 Integral forms of \(\nabla()\) \(\nabla \cdot()\), \(\nabla \times() \) (LEC-31-360.S20) |
| 45 | L32: 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) | L33: 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); DE1,2,3 solutions.zip | L34: 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) |
| 25/42 | F | 10/22 | L25: Properties of Fields and potentials Assignment: VC1.pdf, Due Lec-37; VC1-sol.pdf |
| 26/43 | M | 10/25 | L26: 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 |
| 27 | W | 10/27 | L27: Field evolution for partial differential equations \(\S\) 5.2; bubbles of air in water; Vector fields; Poincare Conjucture: Proved |
| 28 | F | 10/29 | L28: Review Field evolution \(\S\)5.2.1,.2 & Scalar wave equation (e.g., Acoustics) \(\S\)5.2.3 |
| 29/44 | M | 11/1 | L29: Webster Horn equation Three examples of finite length horns; Solution methods; Eigen-function solutions (Tesla acoustic valve) |
| 30 | W | 11/3 | L30: Solution methods; Integral forms of \(\nabla()\), \(\nabla\cdot()\) and \(\nabla \times()\) |
| 31 | F | 11/5 | L31: Integral form of curl: \(\nabla \times()\) and Wedge-product (p. 269) |
| 32/45 | M | 11/8 | L32: Helmholtz decomposition theorem for scalar and vector potentials; (p. 270); Prandt Boundary Layers, |
| 33 | W | 11/10 | L33: Second order operators DoG, GoD, gOd, DoC, CoG, CoC |
| 34 | F | 11/12 | L34: Unification of E & M; terminology (Tbl 5.4); Review for Exam II |
| Week | M | W | F |
|---|---|---|---|
| 46 | Exam II @ 8-11 AM; Gradescope+Zoom + Room 3017 ECEB | L35: 5.7.1-.3 Maxwell's equations LEC-35-360.F21 @1&36 min, (LEC-35-360.S20 @00:30) | L36: Derivation of ME \(\S\)5.7.4,.8, p. 281-5; LEC-36-360.F21 @1, (LEC-36-360.S20 @2) |
| 47 | Thanksgiving Holiday | ||
| 48 | L37: 5.8 Use of Helmholtz' Thm on ME LEC-37-360.F21,, (LEC-37-360.S20) | L38: 5.8 Helmholtz solutions of ME Lec-38-360.F21; (LEC-38-360.S20) \(\S5.6.5\) Tbl 5.3 | L39: 5.8 Analysis of simple impedances (Inductors & capacitors) Lec-29-360.F21, (LEC-39-360.S20) |
| 49 | L40: Stokes's Curl theorem & Gauss's divergence theorem; LEC-40-360.F21 @3:30, (LEC-40-360.S20) | L41: Review (LEC-41-360.S20) | Thur: Optional Review for Final; Reading Day |
| L/W | D | Date | Part IV: Maxwell's equation with solutions |
| -/46 | M | 11/15 | Exam II; No Class Assignment: VC-1 Due Lec 37 |
| 35 | W | 11/17 | L35: Derivation of the wave equation from Eqs: EF and MF; Webster Horn equation: vs separation of variables method + integration by parts; |
| 36 | F | 11/19 | L36: 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 |
| -/47 | S | 11/22 | Thanksgiving Break |
| 37/48 | M | 11/29 | L37: 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: \(\nabla \times \mathbf{w} =0\) VC-1 Due; VC2.pdf VC-2: due Lec: 41; VC2-sol |
| 38 | W | 12/1 | L38: Properties of 2d-order operators; \(\S5.6.5\) Table 5.3 p. 270; OliverHeaviside, Nyquist proof of 4ktB noise floor (Add a HW problem on Thermal Noise in resistors), L10: Summary, |
| 39 | F | 12/3 | L39: Derivation of the vector wave equation |
| 40/49 | M | 12/6 | L40: Physics and Applications; ME vs quantum mechanics; Video demos re ME |
| 41 | W | 12/8 | L41: Review of entire course (very brief) VC-2 due; VC2-sol |
| - | R | 12/9 | Reading Day |
| - | R | 12/9 | Optional Q&A Review for Final (no lec): 9-11 Room: 3017 ECEB + Zoom + Gradescope |
| - | M | 12/13 | Final Exam: Zoom + Room: 3017 ECEB; UIUC Official Final Exam Schedule: If the class starts on Monday at 10:00 AM: The exam is scheduled for Dec 13, Monday, 1:00-5:00 PM |
| -/50 | F | 12/17 | Finals End |
| 12/24 | Final grade analysis |
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