Last Modified : Fri, 08 Nov 19

- 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

L/W | D | Date | Lectures on Mathematical Physics and its History |
---|---|---|---|

Part I: Complex algebra (15 Lectures) | |||

-/35 | M | 8/26 | Instruction begins |

1 | M | 8/26 | L1: Algebraic EquationAssignment: 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) |

2 | W | 8/28 | L2: Finding roots of polynomialsRead: 3.0, 3.1, 3.1.2 (pp. 71-81) |

3 | F | 8/30 | L3: 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 |

-/36 | M | 9/2 | Labor day: Holiday |

4 | W | 9/4 | L4: 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 |

5 | F | 9/6 | L5: Taylor seriesRead: 3.2.2 |

6/37 | M | 9/9 | L6: Analytic functions; Complex analytic functions; Brune ImpedanceResidue expansions of ratios of polynomials: \( Z(s)=N(s)/D(s) \) Read: 3.2.3, 3.2.4; 3.4--3.4.2 |

7 | W | 9/11 | L7: Analytic geomerty: Vectors and their dot \(\cdot\), cross \(\times\) and wedge \(\wedge\) products.More on colorized plots of complex mappings Assignment: AE2, Due 1 weekAE1 due Read: 3.5, 3.5.1; 3.10 (colorized plots, p. 143) video |

8 | F | 9/13 | L8: Analytic geometry of two linesInverse of 2x2 matrix Read: 3.5.2, 3.5.3 |

9/38 | M | 9/16 | L9: Gaussian Elimination; Permutation matricies Read: Sect. 3.5.4, A.2.3 |

10 | W | 9/18 | L10: Transmission and impedance matricies Formulation of a transmission line (Figs. 3.9, 3.11, 4.10) Assignment: AE3 AE2 due Read: 3.7+ |

11 | F | 9/20 | L11: 3.8: Fourier transforms of signalsRead: 3.8+ |

12/39 | M | 9/23 | L12: 3.9: Laplace transforms of systemsSystem postulates Read: 3.9+ |

13 | W | 9/25 | L13: 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 |

14 | F | 9/27 | NO Class Allen out of town |

15/40 | M | 9/30 | L15: Review for Exam I; Exam I, 7-10PM Rm 447AH Grade Distribution |

Part II: Scalar (ordinary) differential equations (10 Lectures) | |||

1 | W | 10/2 | L1: The fundamental theorems of scalar and complex calculus Assignment: DE1 Read: 4.2, 4.2.1 (p. 154) |

2 | F | 10/4 | L2: Complex differentiation and the Cauchy-Riemann conditionsProperties of complex analytic functions (Harmonic functions) Taylor series of complex analytic functions Read: 4.2.2 |

3/41 | M | 10/7 | L3: Brune impedance/admittance and complex analyticRatio 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+ |

4 | W | 10/9 | L4: Generalized impedanceBrune 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 |

5 | F | 10/11 | L5: Multi-valued complex analytic functionsBranch 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 indexRead: 4.4.2, 4.4.3 |

6/42 | M | 10/14 | L6: Three Cauchy integral theorems: CT-1, CT-2, CT-3How to calculate the residue Read: 4.5+ |

7 | W | 10/16 | L7: Inverse Laplace transform (\(t<0\)), Application of CT-3DE2 Due Assignment: DE3 Read: 4.7+ |

8 | F | 10/18 | L8: Inverse Laplace transform (\(t\ge0\)) CT-3 Read: 4.7.1 |

9/43 | M | 10/21 | L9: 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 |

10 | W | 10/23 | L10: Differences between the FT and LT; System postulates 3.9.1DE3 Due |

Part III: Vector Calculus (9 Lectures) | |||

1 | F | 10/25 | L1: Properties of Fields and potentialsRead: 5.1Assignment: VC1 |

2/44 | M | 10/28 | L2: 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 |

3 | W | 10/30 | L3: Field evolution for partial differential equations Read: 5.2+ |

4 | F | 11/1 | L4: Scalar wave equation (Acoustics)Read: 5.3+ |

5/45 | M | 11/4 | L5: Webster Horn equation Three examples of finite length horns Solution methods; Eigen function solutions Read: 5.4+, 5.6+ Assignment: VC2 VC1 Due |

6 | W | 11/6 | L6: Integral forms of \(\nabla()\), \(\nabla\cdot()\) and \(\nabla \times()\) Read: 5.7-5.7.4 |

7 | F | 11/8 | L7: Helmholtz decompositionRead: 5.7.5 |

8/46 | M | 11/11 | L8: second order operators DoG, GoD, gOd, DoC, CoG, CoCRead: 5.7.6 |

W | 11/13 | NO Lecture due to Exam II; Class time will be converted to optional Office hours, to review home work solutions and discuss exam | |

9/46 | W | 11/13 | Exam II @ 7-10 PM; Room: 447AH (Alt Hall) |

Part IV: Maxwell's equation and their solution | |||

1 | F | 11/15 | L1: Unification of Electricity and MagnitismRead: 5.8+, Symmetry in physics |

2/47 | M | 11/18 | L2: Derivation of the wave equation from 2 first-order equationsWebster Horn equation: vs separation of variables method; integration by partsRead: 5.8.2; Greenberg pp. ?? |

3 | W | 11/20 | L3: 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 |

4 | F | 11/22 | L4: Sturm-Liouville BV Theory Solutions for 1, 2, 3 dimensions (seperation of variables)Impedance Boundary conditions; The reflection coefficient and its properties;Read: 4.4.1VC2 Due |

-/47 | S | 11/23 | Thanksgiving Break |

-/49 | M | 12/2 | Instruction Resumes |

5/49 | M | 12/2 | L5a: WKB theory, Read: Greenberg, Ch. 20, 5.1-5.3 + Review p.290-1 ODE's with initial condition (vs. Boundary value problems)L5b: Fourier: Integrals, Transforms, Series, DFT; History: Newton, d'Alembert, Bernoullis, Euler |

6 | W | 12/4 | L6: The fundamental thm of vector calculus: \(\mathbf{F}(x,y,z) = \nabla{\phi(x,y,z)} + \nabla \times \mathbf{A}(x,y,z)\) Read: p. +++ |

7 | F | 12/6 | L:7 Differential & integral forms of Grad, Div, Curl; Conservation theorems (Gauss's and Stokes's Laws);incompressible: i.e., \(\nabla \cdot \mathbf{u} =0\) and irrotational \(\nabla \times \mathbf{w} =0\) vector fieldsRead: p. 224-5 |

8/50 | M | 12/9 | L8: Maxwell's Equations: Physics and Applications; Thoughts on quantum mechanics Read: p. 5.9-5.9.3 |

- | W | 12/11 | Instruction Ends |

- | R | 12/12 | Reading Day |

- | 12/12 | Review for Final: 2-4 PM Room 106B3 in Engineering Hall. | |

-/?? | R | TBD | Final Exam: TBD Room: 441 ( UIUC Final Exam Schedule) |

-/51 | F | 12/20 | Finals End |

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