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  • Advanced Engineering Mathematics: Syllabus: pdf-2018, pdf-2009; Listing: ECE-493, (Math-487) Campus: ECE/Math
  • Calendars: Class, Campus;
  • Time/place: Zoom and 1090 Lincoln Hall, MWF 10:00-10:50, ECE-493;
  • Matlab Tutorial pdf
  • Text: An Invitation to Mathematical Physics pdf; Greenberg: Advanced Eng Mathematics Greenberg
    * Office Hours: Tues 2:30-4:00PM Zoom; Friday 3-4:30PM, Zoom
  • Instructor: Prof. Jont Allen (netID jontalle; Office 3062ECEB); TA: TBD
  • COVID-19 on-campus testing twice per week is required for ALL faculty, staff, and students 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.
  • This week's Reading schedule; Final

ECE-493/MATH-487 Daily Schedule Spring 2020

Part I: Reading assignments: Complex algebra (15 Lec)
1L1: 1, 3.1 (p. 1-11) Intro + historyL2: 3.1,.1,.2 (p. 51-61) Roots of polynomials; Newton's method.L3: 3.1.3,.4 (p.61-64) Companion maxtrix
2L4: 3.2,.1,.2, B1, B3 EigenanalysisL5: 3.2.3 Taylor seriesL6: 3.2,.4,.5 Analytic Functions
3Labor dayL7: 3.4,.1,.2 Anal Geom, ResiduesL8: 3.5.1-.4 \(\cdot, \times, \wedge \) scalar products
4L9: 3.5.5, 3.6,.1-.5 Gauss Elim; Matrix algebra of systemsL10: 3.8,.1-.4 Thevenin parameters; Transmission lines; impedance matrixL11: 3.9,.1 \(\cal FT\) of signals
5L12: 3.10,.1-.3 \(\cal LT\) of systems + postulatesL13: 3.11,.1,.2 Complex analytic color maps; Riemann sphere; Bilinear transformL14: Review for Exam I
6 Exam I 
L/WDDateLectures on Mathematical Physics and its History
    Part I: Complex algebra (15 Lectures)
-/35M8/24 Instruction begins
1M8/24L1: Introduction + History
Assignment: HW0: pdf Evaluate your knowledge (not graded)
Assignment: NS1, Problems 1,2,4, 7; p. 36, Due 1 week:
2W8/26L2: Newton's method for finding roots of a polynomial \(P_n(s_k)=0\) (p.56).
3F8/28L3: The companion matrix and its characteristic polynomial
Working with Octave/Matlab: 3.1.4 (p. 63-64) zviz.m
3.11 Brief introduction to colorized plots of complex mappings (p. 123-125)
4/36M8/31L4: Eigenanalysis I: Eigenvalues and vectors of a matrix
Assignment: AE1 (p. 75-78) Probs: 1-11 (Due 1 wk)
NS1 due
5W9/2L5: Taylor series
6F9/4L6: Analytic functions; Complex analytic functions; Brune Impedance
Residue expansions of ratios of polynomials: \( Z(s)=N(s)/D(s) \)
-/37M9/7 Labor day: Holiday
7W9/9L7: Analytic geomerty: Vectors and their dot \(\cdot\), cross \(\times\) and wedge \(\wedge\) products. Residues.
Colorized plots of complex mappings
Assignment: AE2, Due 1 week
AE1 due
View: Mobius/bilinear transform video
8F9/11L8: Analytic geometry of two vectors (generalized scalar product)
Inverse of 2x2 matrix
9/38M9/14L9: Gaussian Elimination; Permutation matricies
10W9/16L10: Transmission and impedance matricies
Assignment: AE3
AE2 due
11F9/18L11: Fourier transforms of signals
12/39M9/21L12: Laplace transforms of systems;System postulates
13W9/23L13: Comparison of Laplace and Fourier transforms; Colorized plots; Probability -- basic definitions
AE3 due
14F9/25L14: Review for Exam I
15/40M9/28NO Class; Exam I, 7-10PM Rm ??447AH?? Exam 1 Grade Distribution F19
Part II: Reading assignments: Scalar differential equations (10 Lec)
6Exam I brief discussionL1: 4.1,4.2,.1 (p. 133) Fundmental Thms of \(\mathbb R, \mathbb C\) scalar calculusL2: 4.2.2 Cauchy-Riemann Eqs. CR-1, CR-2, CR-3, CR-4
7L3: 4.4 Brune impedance/admittanceL4: 4.4,.1,.2 Complex analytic ImpedanceL5: 4.4.3 Multi-valued functions, Branch cuts
8L6: 4.5,.1,.2 Cauchy's complex integration thms CT1, CT2, CT3L7: 4.7,.1,.2 Inv \({\cal LT} (t<0, t=0)\)L8: 4.7.3 Inv \({\cal LT} (t > 0) \)
9L9: 4.7.4 Properties of the \(\cal LT\)L10: 4.7.5 Solving LTI (simple) Diff. Eqs. with the \(\cal LT\) 

Edits 2 here

    Part II: Scalar (ordinary) differential equations (10 Lectures)
1W9/30L1: The fundamental theorems of scalar and complex calculus
Assignment: DE1
2F10/2L2: Complex differentiation and the Cauchy-Riemann conditions
Properties of complex analytic functions (Harmonic functions)
Taylor series of complex analytic functions
3/41M10/5L3: 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
4W10/7L4: 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
DE1 Due
5F10/9L5: 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
6/42M10/12L6: Three Cauchy integral theorems: CT-1, CT-2, CT-3
How to calculate the residue
7W10/14L7: Inverse Laplace transform (\(t<0\)), Application of CT-3
DE2 Due
Assignment: DE3
8F10/16L8: Inverse Laplace transform (\(t\ge0\)) CT-3
9/43M10/19L9: Properties of the Laplace transform
Linearity, convolution, time-shift, modulation, derivative etc
Differences between the FT and LT; System postulates
10W10/21L10: Solving differential equations: Train problem (DE3, problem 2, p. 167-8, Fig. 4.11)
DE3 Due
Part III: Reading assignments: Vector calculus (10 lectures)
10 L1: 5.1.1 (p. 171) Fields and potentials
11L2: 5.1.2,.3 \(\nabla(), \nabla \cdot(), \nabla \times(), \nabla \wedge(), \nabla^2() \)L3: 5.2 Field evolutionL4: 5.2.1 Scalar wave Eq.
12L5: 5.2.2,.3,5.4.1-.3 HornsL6: 5.5.1 Solution methodsL7: 5.6.1-.4 Integral forms of \(\nabla(), \nabla \cdot(), \nabla \times() \)
13L8: 5.6.5 Helmholtz decomposition thm
\( \vec{E} = -\nabla\phi +\nabla \times \vec A\ \)
L9: 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: \(\nabla \cdot \nabla \times()=0, \nabla \times \nabla ()=0 \)
Exam II
    Part III: Vector Calculus (10 Lectures)
1F10/23L1: Properties of Fields and potentials
Assignment: VC1
2/44M10/26L2: 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
3W10/28L3: Field evolution for partial differential equations
4F10/30L4: Scalar wave equation (Acoustics)
5/45M11/2L5: Webster Horn equation
Three examples of finite length horns
Solution methods; Eigen function solutions
Assignment: VC2; VC1 Due
6W11/4L6: Integral forms of \(\nabla()\), \(\nabla\cdot()\) and \(\nabla \times()\)
7F11/6L7: Helmholtz decomposition
8/46M11/9L8: second order operators DoG, GoD, gOd, DoC, CoG, CoC
9W11/11L9: review home work solutions and discuss exam II
 F11/13No Class: Exam II @ 7-10 PM; Room: ??447AH?? (Alt Hall) Exam2 Grade Distribution
Part IV: Reading assignments: Maxwell's equations + solutions (7 lectures)
13L1: 5.7 (p. 203) Unification of E&M: terminologyL2: 5.7.1 Maxwell's equationsL3: 5.7.2 Derivation of ME
14Thanksgiving Holiday
15L4: 5.8 Use of Helmholtz' Thm on MEL5: 5.8 Helmholtz solutions of MEL6: 5.8 Analysis of simple impedances (Inductors & capacitors)
16L7: TEM, TE, TM modes in waveguides (horns)L8: Wave-filters; Final ReviewThur: Optional Review for Final; Reading Day
    Part IV: Maxwell's equation with solutions
1/47M11/16L1: Unification of E & M; terminology (Tbl 5.4)
View: Symmetry in physics
2W11/18L2: Derivation of the wave equation from Eqs: EF and MF
Webster Horn equation: vs separation of variables method + integration by parts
3F11/20L3: Transmission line theory: Lumped parameter approximation:
Diffusion line, Telegraph equation, Wave equation (Parabolic, hyperbolic, elliptical)
-/47S11/21 Thanksgiving Break
-/49M11/30 Instruction Resumes
4M11/30L4: Helmholtz' Thm: The fundamental thm of vector calculus: \(\mathbf{F}(x,y,z) = \nabla{\phi(x,y,z)} + \nabla \times \mathbf{A}(x,y,z)\)
incompressible: i.e., \(\nabla \cdot \mathbf{u} =0\) and irrotational \(\nabla \times \mathbf{w} =0\) vector fieldsVC2 Due
5W12/2L5: Properties of 2d-order operators
6F12/4L6: Derivation of the vector wave equation
7/50M12/7L7: Physics and Applications; ME vs quantum mechanics
8W12/9L8: Sturm-Liouville Horn Theory Solutions for 1, 2, 3 dimensions (seperation of variables)
Impedance Boundary conditions; The reflection coefficient and its properties;
-R12/10 Reading Day
-R12/10Review for Final: 2-4 PM Room: 106B3 in Engineering Hall
  12/??Exam 3 grade distribution
- FFriday Dec 13 7-10 PM Final Exam: Room: 445AH ( UIUC Final Exam Schedule)
-/51F12/18 Finals End
 F12/18Final grade distribution; Letter Grade: 100-93 A+; 92=84 A; 83-79 A-; 78-75 B+


 ||- || F || 5/?? ||  Backup: Exam III 7:00-10:00+ PM on HW1-HW11atest>><<

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 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 (Prof's Discuression), count for 10%.

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