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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: Altgeld 445, 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 4036 ECEB; Friday 3-4:30PM, 4036 ECEB
  • Instructor: Prof. Jont Allen (netID jontalle; Office 3062ECEB); TA: TBD
  • This week's schedule; Final

ECE-493/MATH-487 Daily Schedule Fall 2019

L/WDDateLectures on Mathematical Physics and its History
    Part I: Complex algebra (15 Lectures)
-/35M8/26 Instruction begins
1M8/26L1: Algebraic Equation
Assignment: HW0: pdf Evaluate your present state of knowledge (not graded)
Assignment: NS1, Problems 1,2,4 7; p. 36, Due 1 week:
Read: Introduction, 1.1+ (pp. 13-35)
2W8/28L2: Finding roots of polynomials
Read: 3.0, 3.1, 3.1.2 (pp. 71-81)
3F8/30L3: Matrix formulation of polynomials
Working with Octave/Matlab: 3.1.4 zviz.m
Read: 3.1.3-3.1.4 (pp. 81-84), 3.10 (pp. 143-147):
Brief introduction to colorized plots of complex mappings
-/36M9/2 Labor day: Holiday
4W9/4L4: Eigenanalysis I: Eigenvalues and vectors of a matrix
Assignment: AE1 Probs: 1, 2, 3, 4, and 3 questions each from probs 5-11?; p. 95; Due 1 wk
NS1 due
Read: 3.2, 3.2.1; B.1 (p. 267-269), B.3
5F9/6L5: Taylor series
Read: 3.2.2
6/37M9/9L6: Analytic functions; Complex analytic functions; Brune Impedance
Residue expansions of ratios of polynomials: \( Z(s)=N(s)/D(s) \)
Read: 3.2.3, 3.2.4; 3.4--3.4.2
7W9/11L7: Analytic geomerty: Vectors and their dot \(\cdot\), cross \(\times\) and wedge \(\wedge\) products.
More on colorized plots of complex mappings
Assignment: AE2, Due 1 week
AE1 due
Read: 3.5, 3.5.1; 3.10 (colorized plots, p. 143) Mobius/bilinear transform video
8F9/13L8: Analytic geometry of two lines
Inverse of 2x2 matrix
Read: 3.5.2, 3.5.3
9/38M9/16L9: Gaussian Elimination; Permutation matricies
Read: Sect. 3.5.4, A.2.3
10W9/18L10: Transmission and impedance matricies
Formulation of a transmission line (Figs. 3.9, 3.11, 4.10)
Assignment: AE3
AE2 due
Read: 3.7+
11F9/20L11: 3.8: Fourier transforms of signals
Read: 3.8+
12/39M9/23L12: 3.9: Laplace transforms of systems
System postulates
Read: 3.9+
13W9/25L13: Comparison of Laplace and Fourier transforms (p. 134; 277-279)
What you need to know about probability (p. 142)
AE3 due
Read: 3.8, 3.9, 3.9.2
14F9/27NO Class Allen out of town
15/40M9/30L15: Review for Exam I; Exam I, 7-10PM Rm 447AH Exam 1 Grade Distribution
    Part II: Scalar (ordinary) differential equations (10 Lectures)
1W10/2L1: The fundamental theorems of scalar and complex calculus
Assignment: DE1
Read: 4.2, 4.2.1 (p. 154)
2F10/4L2: Complex differentiation and the Cauchy-Riemann conditions
Properties of complex analytic functions (Harmonic functions)
Taylor series of complex analytic functions
Read: 4.2.2
3/41M10/7L3: 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
Read: 4.4+
4W10/9L4: 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
Read: 4.4.1
5F10/11L5: 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
Read: 4.4.2, 4.4.3
6/42M10/14L6: Three Cauchy integral theorems: CT-1, CT-2, CT-3
How to calculate the residue
Read: 4.5+
7W10/16L7: Inverse Laplace transform (\(t<0\)), Application of CT-3
DE2 Due
Assignment: DE3
Read: 4.7+
8F10/18L8: Inverse Laplace transform (\(t\ge0\)) CT-3
Read: 4.7.1
9/43M10/21L9: Properties of the Laplace transform
Linearity, convolution, time-shift, modulation, derivative etc
Solving differential equations: Train problem (DE3, problem 2, p. 191, Fig. 4.10)
Read: 4.7.2, 4.7.3
10W10/23L10: Differences between the FT and LT; System postulates 3.9.1
DE3 Due
    Part III: Vector Calculus (9 Lectures)
1F10/25L1: Properties of Fields and potentials
Read: 5.1
Assignment: VC1
2/44M10/28L2: 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
Read: 5.1.1, 5.1.2
3W10/30L3: Field evolution for partial differential equations
Read: 5.2+
4F11/1L4: Scalar wave equation (Acoustics)
Read: 5.3+
5/45M11/4L5: Webster Horn equation
Three examples of finite length horns
Solution methods; Eigen function solutions
Read: 5.4+, 5.6+
Assignment: VC2
VC1 Due
6W11/6L6: Integral forms of \(\nabla()\), \(\nabla\cdot()\) and \(\nabla \times()\)
Read: 5.7-5.7.4
7F11/8L7: Helmholtz decomposition
Read: 5.7.5
8/46M11/11L8: second order operators DoG, GoD, gOd, DoC, CoG, CoC
Read: 5.7.6
 W11/13NO Lecture due to Exam II; Class time will be converted to optional Office hours, to review home work solutions and discuss exam
9/46W11/13 Exam II @ 7-10 PM; Room: 447AH (Alt Hall) Exam2 Grade Distribution
    Part IV: Maxwell's equation and their solution
1F11/15L1: Unification of Electricity and Magnitism
Read: 5.8+, Symmetry in physics
2/47M11/18L2: Derivation of the wave equation from 2 first-order equations
Webster Horn equation: vs separation of variables method; integration by parts
Read: 5.8.2; Greenberg pp. ??
3W11/20L3: Transmission line theory: Lumped parameter approximation:
Diffusion line, Telegraph equation, Wave equation (Parabolic, hyperbolic, elliptical)
Read: \(2^{nd}\) order PDE: Horns Sturm-Liouville (SL) Boundary Value (BV) problems;
Read: Greenberg pp. ???, 5.2
4F11/22L4: Sturm-Liouville BV Theory Solutions for 1, 2, 3 dimensions (seperation of variables)
Impedance Boundary conditions; The reflection coefficient and its properties;
Read: 4.4.1
VC2 Due
-/47S11/23 Thanksgiving Break
-/49M12/2 Instruction Resumes
5/49M12/2 L6: 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 fields
Read: 5.7.5 pages 228-230
6W12/4L:7 Second order operators
Read: 5.7.6 pages 229-233
7F12/6L:8 Derivation of the vector wave equation
Read: p. 233-234
8/50M12/9L8: Maxwell's Equations: Physics and Applications; Some thoughts on quantum mechanics
Read: p. 5.9 page 233-237
9W12/11L9: Maxwell's Equations: Physics and Applications; Some thoughts on quantum mechanics
Instruction ends
9W12/21Exam 3 grade distribution
9W12/22Final grade distribution; Letter Grade: 100-93 A+; 92=84 A; 83-79 A-; 78-75 B+
-R12/12 Reading Day
- 12/12Review for Final: 2-4 PM Room: 106B3 in Engineering Hall
- FFriday Dec 13 7-10 PM Final Exam: Room: 445AH ( UIUC Final Exam Schedule)
-/51F12/20 Finals End


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

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