Partial Differential Equations and Complex Variables
|
|
- Fay Gardner
- 5 years ago
- Views:
Transcription
1 EE-22, Spring 29 p. /25 EE 22 Partial Differential Equations and Complex Variables Ray-Kuang Lee Institute of Photonics Technologies, Department of Electrical Engineering and Department of Physics, National Tsing-Hua University, Hsinchu, Taiwan Course info: rklee
2 EE-22, Spring 29 p. 2/25 EE 22 Time: M7M8R6 (3:2PM-5:PM, Monday; 2:AM-3:PM, Thursday) Teaching Method: in-class lectures with examples. I would try to write in the black board, not the slides. Evaluation:. Four Homeworks, 4%; 2. Midterm 3%; Tentatively scheduled on 4/27, covering Ch.2 of the textbook. 3. Final exam 3%: Tentatively scheduled on 6/5, covering Ch.3 - Ch.8 of the textbook. 4. Bonus: just rise your hand in the classroom, 2%.
3 EE-22, Spring 29 p. 3/25 Textbook and Reference Books [Note]: Class handouts; Prof. S.D. Yang s note: sdyang/courses/pde.htm [Textbook]: E. Kreyszig, "Advanced Engineering Mathematics", 9th Ed., John Wiley & Sons, Inc., (26). [Ref.]: Stanley J. Farlow, "Partial Differential Equations for Scientists and Engineers", Dover Publications, (993); (for PDE, but optional). [Ref.num]: Matthew P. Coleman, "An Introduction to Partial Differential Equations with MATLAB", Chapman & Hall/Crc Applied Mathematics & Nonlinear Science (24); (optional).
4 EE-22, Spring 29 p. 4/25 Syllabus: for PDE. Introduction to PDE and Complex variables, (2/23, 2/26). 2. Diffusion-type problems: [Textbook] Ch.2, [Ref.] Ch.2. Derivation of the Heat equation, (3/2). Boundary conditions for Diffusion-type problems, (3/5). Separation of variables, (3/9). Solving nonhomogeneous PDEs, (3/2). Integral transforms, (3/6, 3/9). The Fourier transform, (3/23). The Laplace Transform, (3/26). 3. Hyperbolic-type problems: [Textbook] Ch.2, [Ref.] Ch.3. -D Wave equation, (4/2, 4/6). D Alembert solution of the Wave equation, (4/9). Sturm-Liouville problems, (4/3). 2-D Wave equation in Cartesian and polar coordinates, (4/6, 4/2). Laplace s equation in Cartesian, polar, and spherical coordinates, (4/23).
5 EE-22, Spring 29 p. 5/25 Syllabus: for Complex variables. Midterm, (4/27). 2. Introduction to Numerical PDE (4/3): [Ref.num]. 3. Complex variables: [Textbook]Ch.3-Ch.8. Complex numbers and functions, (5/4). Cauchy-Riemann equations, (5/7, 5/). Complex integration, (5/4, 5/8). Complex power & Taylor series, (5/2, 5/25). Laurent series & residue, (5/28, 6/, 6/4). Conformal mapping, (6/8, 6/). Applications: real integrals by residual integration, potential theory, (6/5, 6/8). 4. Final exam, (6/5).
6 EE-22, Spring 29 p. 6/25 Related courses. Applied Mathematics (Phys.), 2. Complex Analysis (Math.), 3. Numerical Mehtods for Parital Differential Equations (Math.), 4. Numerical Analysis (EE), 5. Computational Methods for Optoelectronics (IPT), 6....
7 EE-22, Spring 29 p. 7/25 Partial Differential Equations A(x,y) 2 u x + B(x,y) 2 u 2 x y + u u C(x,y) 2 = f(x,y,u, y2 x, u y ),
8 EE-22, Spring 29 p. 8/25 Vector calculus: scalar and vector fields scalar fields: Ψ, f, V, ρ vector fields: A, F, E, H, D, B, J
9 EE-22, Spring 29 p. 9/25 Vector calculus: Gradient For the measure of steepness of a line, slope. the gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change. f(x, y, z) = f xî + f y ĵ + f ˆk, z f(ρ, θ, z) = f ρ êρ + ρ f(r, θ, φ) = f r êr + r f θ êθ + f z êz, f θ êθ + r sin θ f φêφ, in Cartesian coordinates in cylindrical coordinates in spherical coordinates
10 EE-22, Spring 29 p. /25 Maxwell s equations with total charge and current Gauss s law for the electric field: E = ρ ǫ S E d A = Q ǫ, Gauss s law for magnetism: B = S B d A =, (83-879) Faraday s law of induction: E = κ t B C E d l = κ t Φ B, Ampére s circuital law: B = κµ (J + ǫ E) t C B d l = κµ (I + ǫ t Φ E)
11 EE-22, Spring 29 p. /25 Wave equations For a source-free medium, ρ = J =, 2 ( E) = µ ǫ t 2 E, ( E) 2 2 E = µ ǫ t 2 E. When E =, one has wave equation, 2 E = µ ǫ 2 t 2 E which has following expression of the solutions, in D, with v 2 = µ ǫ = c 2. E = ˆx[f + (z vt) + f (z + vt)], plane wave solutions: E + = E cos(kz ωt), where ω k = c.
12 Cavity modes EE-22, Spring 29 p. 2/25
13 EE-22, Spring 29 p. 3/25 More PDEs Diffusion equation: Schrödinger equation: i 2 Ψ(x,t) = t 2m 2 A(x,t) = κ t x 2A(x,t) Nonlinear Schrödinger equation: i 2 Ψ(x,t) = t 2m 2 x2ψ(x,t) + V (x)ψ(x,t) 2 x 2Ψ(x,t)+V (x)ψ(x,t)+γ Ψ(x,t) 2 Ψ(x,t)
14 EE-22, Spring 29 p. 4/25 Diffusion equation z U(z, t) = i 2 2 U(z, t) t2 Z Y X.75 Intensity [a.u.] Time 5 5 Distance
15 EE-22, Spring 29 p. 5/25 Laplacian eq. in a disk Eigenmodes of Laplacian equations, [ 2 x x 2 ]u(x, y) = f(x, y). Mode λ =. Mode 3 λ = Mode 6 λ = Mode λ =
16 EE-22, Spring 29 p. 6/25 FFT method for wave equation u tt = u xx + u yy, < x, y <, t >, u = on the boundary t = t = t = t =.5.5
17 EE-22, Spring 29 p. 7/25 Mach-Zehnder structure by BeamProp
18 EE-22, Spring 29 p. 8/25 Soliton collisions U(t =, x) = sech(x + x ) + sech(x x )
19 EE-22, Spring 29 p. 9/25 FDTD: example From:
20 EE-22, Spring 29 p. 2/25 FDTD: example From:
21 EE-22, Spring 29 p. 2/25 Metallic Waveguide Examples in "Field and Wave Electromagnetics," 2nd ed., by David K. Cheng, pp ; simulated by ToyFDTD
22 EE-22, Spring 29 p. 22/25 Fields profile in 2D, H x (x,z), H z (x,z), and E y (x,z) g933326,
23 EE-22, Spring 29 p. 23/25 Optimization of SHG pulse A z B z = η A 2 T + iξ 2 A T 2 iρ A B, = η B 2 T + iξ 2 A 2 T 2 i kb iρ A 2,
24 EE-22, Spring 29 p. 24/25. Office hours: 3:-5:PM, Thursday at Room 523, EECS bldg I should reply every Website: For more information and course slides: rklee 4. TA hours: at Room 52, EECS bldg. (2 2 hours per week to be confirmed) (a) I-Hong Chen, 2nd-year PhD student, ehome4829@gmail.com (b) Chih-Yao Chen, 2nd-year Master student, hihittttt@yahoo.com.tw
25 EE-22, Spring 29 p. 25/25 Enjoy this Course!! 2> ω a > Frequency (ωd/2πc) x j M Γ X M -5 5 x i
Computational Methods for Optoelectronics
IPT 526 Computational Methods for Optoelectronics Ray-Kuang Lee Department of Electrical Engineering and Institute of Photonics Technologies National Tsing-Hua University, Hsinchu, Taiwan e-mail: rklee@ee.nthu.edu.tw
More informationVibrating-string problem
EE-2020, Spring 2009 p. 1/30 Vibrating-string problem Newton s equation of motion, m u tt = applied forces to the segment (x, x, + x), Net force due to the tension of the string, T Sinθ 2 T Sinθ 1 T[u
More informationUNIVERSITY OF TORONTO - FACULTY OF APPLIED SCIENCE AND ENGINEERING Department of Electrical and Computer Engineering
UNIVERSITY OF TORONTO - FACULTY OF APPLIED SCIENCE AND ENGINEERING Department of Electrical and Computer Engineering MAT290H1F: ADVANCED ENGINEERING MATHEMATICS - COURSE SYLLABUS FOR FALL 2014 COURSE OBJECTIVES
More informationMAE502/MSE502 Partial Differential Equations in Engineering. Spring 2012 Mon/Wed 5:00-6:15 PM
MAE502/MSE502 Partial Differential Equations in Engineering Spring 2012 Mon/Wed 5:00-6:15 PM Instructor: Huei-Ping Huang, hp.huang@asu.edu (Huei rhymes with "way") Office: ERC 359 Office hours: Monday
More informationIntroduction. EE 2FH3 Winter 2014 (Prof. Mohamed H. Bakr) ELECTROMAGNETICS I
Introduction EE 2FH3 Winter 2014 (Prof. Mohamed H. Bakr) ELECTROMAGNETICS I Room: ITB-A219 ext. 24079 E-mail: mbakr@mail.ece.mcmaster.ca Main Topics * Vector Calculus * Electrostatics * Magnetostatics
More informationMAE/MSE502 Partial Differential Equations in Engineering. Spring 2019 Mon/Wed 6:00-7:15 PM Classroom: CAVC 101
MAE/MSE502 Partial Differential Equations in Engineering Spring 2019 Mon/Wed 6:00-7:15 PM Classroom: CAVC 101 Instructor: Huei-Ping Huang, hp.huang@asu.edu Office: ERC 359 Office hours: Monday 3-4 PM,
More informationB.Sc. in Electronics and Communication Engineering, Cairo University, Cairo, Egypt with Distinction (honors), 1992
EE3FK4 Electromagnetics II Dr. Mohamed Bakr, ITB A219, ext. 24079 mbakr@mail.ece.mcmaster.ca http://www.ece.mcmaster.ca/faculty/bakr/ ece3fk4/ece3fk4_main_2008.htm Lecture 0 0-1 Info About Myself B.Sc.
More informationPhys 631 Mathematical Methods of Theoretical Physics Fall 2018
Phys 631 Mathematical Methods of Theoretical Physics Fall 2018 Course information (updated November 10th) Instructor: Joaquín E. Drut. Email: drut at email.unc.edu. Office: Phillips 296 Where and When:
More informationTake-Home Exam 1: pick up on Thursday, June 8, return Monday,
SYLLABUS FOR 18.089 1. Overview This course is a review of calculus. We will start with a week-long review of single variable calculus, and move on for the remaining five weeks to multivariable calculus.
More informationMTH5201 Mathematical Methods in Science and Engineering 1 Fall 2014 Syllabus
MTH5201 Mathematical Methods in Science and Engineering 1 Fall 2014 Syllabus Instructor: Dr. Aaron Welters; O ce: Crawford Bldg., Room 319; Phone: (321) 674-7202; Email: awelters@fit.edu O ce hours: Mon.
More informationWelcome to Math 257/316 - Partial Differential Equations
Welcome to Math 257/316 - Partial Differential Equations Instructor: Mona Rahmani email: mrahmani@math.ubc.ca Office: Mathematics Building 110 Office hours: Mondays 2-3 pm, Wednesdays and Fridays 1-2 pm.
More informationIntroduction to Optoelectronic Engineering,
EE 3130 Introduction to Optoelectronic Engineering, Ray-Kuang Lee Institute of Photonics Technologies, Department of Electrical Engineering, and Department of Physics, National Tsing-Hua University e-mail:
More informationMath Partial Differential Equations
Math 531 - Partial Differential Equations to Partial Differential Equations Joseph M. Mahaffy, jmahaffy@sdsu.edu Department of Mathematics and Statistics Dynamical Systems Group Computational Sciences
More informationECE 3110 Electromagnetic Fields I Spring 2016
ECE 3110 Electromagnetic Fields I Spring 2016 Class Time: Mon/Wed 12:15 ~ 1:30 PM Classroom: Columbine Hall 216 Office Hours: Mon/Wed 11:00 ~ 12:00 PM & 1:30-2:00 PM near Col 216, Tues 2:00 ~ 2:45 PM Other
More informationEEE321 Electromagnetic Fileds and Waves. Prof. Dr. Hasan Hüseyin BALIK. (1 st Week)
EEE321 Electromagnetic Fileds and Waves Prof. Dr. Hasan Hüseyin BALIK (1 st Week) Outline Course Information and Policies Course Syllabus Vector Operators Coordinate Systems Course Information (see web
More informationEE 230 -ELECTROMAGNETIC THEORY
Karabuk University Department of Electrical and Electronics Engineering Spring Semester 2014-2015 EE 230 -ELECTROMAGNETIC THEORY 2013/2014 Spring Instructor :Assoc. Prof. Dr. Habibe Uslu :Asst. Prof. Dr.
More informationPHYS F212X FE1+FE2+FE3
Syllabus for PHYS F212X FE1+FE2+FE3 General Physics II College of Natural Science and Mathematics University of Alaska Fairbanks Fall 2016 (8/29/2016 to 12/14/2016) Course Information: PHYS F212X FE1+FE2+FE3
More informationEET 492: Electromagnetic Fields and Waves. Fall Syllabus
EET 492: Electromagnetic Fields and Waves Fall 2007 Syllabus Lecturer Information: Name: Dr. Zhaoxian Zhou Office: TEC 326 Phone: (601)266 4482 Email: Zhaoxian.Zhou@usm.edu Web Page: www.usm.edu/zxzhou
More informationElectromagnetic Theory (Hecht Ch. 3)
Phys 531 Lecture 2 30 August 2005 Electromagnetic Theory (Hecht Ch. 3) Last time, talked about waves in general wave equation: 2 ψ(r, t) = 1 v 2 2 ψ t 2 ψ = amplitude of disturbance of medium For light,
More informationFall 2016 Spring 2017
BE 603: Partial differential equations (Spring 2017) Instructor: TA: Andy Fan (fana@bu.edu) TBD Class: Time is TBD (Spring 2016 only) Recitation: Should be on Fri afternoons (Spring 2016 only) Office Hours:
More informationCLASSICAL ELECTRODYNAMICS I Physics 6/75203 SPRING 2013
INSTRUCTOR: CLASSICAL ELECTRODYNAMICS I Physics 6/75203 SPRING 2013 Dr. Mark Manley manley@kent.edu 220 Smith Hall http://www.kent.edu/cas/physics/people/manley.cfm 330-672-2407 CLASS HOURS: 1:10-2:00
More informationSyllabus for Applied Mathematics Graduate Student Qualifying Exams, Dartmouth Mathematics Department
Syllabus for Applied Mathematics Graduate Student Qualifying Exams, Dartmouth Mathematics Department Alex Barnett, Scott Pauls, Dan Rockmore August 12, 2011 We aim to touch upon many topics that a professional
More informationNirma University Institute of Technology
Nirma University Institute of Technology Department of Mathematics & Humanities Template B. Tech. Electrical Engineering Semester: III Academic Year: 28-19 Term: Odd 28 Course Code & Name : MA04, Mathematics
More informationJoel A. Shapiro January 20, 2011
Joel A. shapiro@physics.rutgers.edu January 20, 2011 Course Information Instructor: Joel Serin 325 5-5500 X 3886, shapiro@physics Book: Jackson: Classical Electrodynamics (3rd Ed.) Web home page: www.physics.rutgers.edu/grad/504
More informationPartial Differential Equations - part of EM Waves module (PHY2065)
Partial Differential Equations - part of EM Waves module (PHY2065) Richard Sear February 7, 2013 Recommended textbooks 1. Mathematical methods in the physical sciences, Mary Boas. 2. Essential mathematical
More informationAP Physics C Syllabus
Course Overview AP Physics C Syllabus AP Physics C will meet for 90 minutes on block scheduling and for 45 minutes on regular scheduling. Class activities will include lecture, demonstration, problem solving
More informationSan Jose State University Department of Mechanical and Aerospace Engineering ME 230, Advanced Mechanical Engineering Analysis, Fall 2015
San Jose State University Department of Mechanical and Aerospace Engineering ME 230, Advanced Mechanical Engineering Analysis, Fall 2015 Instructor: Office Location: Younes Shabany TBD Telephone: (408)
More informationECE 4800 Fall 2011: Electromagnetic Fields and Waves. Credits: 4 Office Hours: M 6-7:30PM, Th 2-3:30, and by appointment
ECE 4800 Fall 2011: Electromagnetic Fields and Waves Instructor: Amar S. Basu Office: 3133 Engineering Email: abasu@eng.wayne.edu Phone: 313-577-3990 Lecture Times: M W 7:30PM - 9:20PM, Class Dates: 9/7/11
More informationFinal Exam May 4, 2016
1 Math 425 / AMCS 525 Dr. DeTurck Final Exam May 4, 2016 You may use your book and notes on this exam. Show your work in the exam book. Work only the problems that correspond to the section that you prepared.
More informationIntroduction of Partial Differential Equations and Boundary Value Problems
Introduction of Partial Differential Equations and Boundary Value Problems 2009 Outline Definition Classification Where PDEs come from? Well-posed problem, solutions Initial Conditions and Boundary Conditions
More informationMath 4263 Homework Set 1
Homework Set 1 1. Solve the following PDE/BVP 2. Solve the following PDE/BVP 2u t + 3u x = 0 u (x, 0) = sin (x) u x + e x u y = 0 u (0, y) = y 2 3. (a) Find the curves γ : t (x (t), y (t)) such that that
More informationPARTIAL DIFFERENTIAL EQUATIONS. MTH 5230, Fall 2007, MW 6:30 pm - 7:45 pm. George M. Skurla Hall 116
PARTIAL DIFFERENTIAL EQUATIONS MTH 5230, Fall 2007, MW 6:30 pm - 7:45 pm George M. Skurla Hall 116 Ugur G. Abdulla Office Hours: S311, TR 2-3 pm COURSE DESCRIPTION The course presents partial diffrential
More informationAND NONLINEAR SCIENCE SERIES. Partial Differential. Equations with MATLAB. Matthew P. Coleman. CRC Press J Taylor & Francis Croup
CHAPMAN & HALL/CRC APPLIED MATHEMATICS AND NONLINEAR SCIENCE SERIES An Introduction to Partial Differential Equations with MATLAB Second Edition Matthew P Coleman Fairfield University Connecticut, USA»C)
More informationECE 341 Electromagnetic Fields I, Fall 2016
COLORADO STATE UNIVERSITY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING (1) Course Details: ECE 341 Electromagnetic Fields I, Fall 2016 COURSE SYLLABUS Instructor: BRANISLAV M. NOTAROS, Professor,
More information2.20 Fall 2018 Math Review
2.20 Fall 2018 Math Review September 10, 2018 These notes are to help you through the math used in this class. This is just a refresher, so if you never learned one of these topics you should look more
More informationMathematical Methods for Physics
Mathematical Methods for Physics Peter S. Riseborough June 8, 8 Contents Mathematics and Physics 5 Vector Analysis 6. Vectors................................ 6. Scalar Products............................
More informationChemistry 565 / 665 BIOPHYSICAL CHEMISTRY. - Spring
Chemistry 565 / 665 BIOPHYSICAL CHEMISTRY - Spring 2003 - LECTURE: LECTURER: OFFICE HOURS: 9:55 10:45 a.m. MTRF, B383 Chemistry Prof. Silvia Cavagnero Office: 8108 New Chemistry Building (will be 5341
More informationIPT 5340 (PHYS 6840) Quantum Optics. Ray-Kuang Lee. Institute of Photonics Technologies Department of Electrical Engineering and Department of Physics
IPT5340, Spring 09 p. 1/35 IPT 5340 (PHYS 6840) Quantum Optics Ray-Kuang Lee Institute of Photonics Technologies Department of Electrical Engineering and Department of Physics National Tsing-Hua University,
More informationEngineering Electromagnetics- 1 Lecture 1: Introduction and Class outline
Engineering Electromagnetics- 1 Lecture 1: Introduction and outline ksyoung@skku.edu School of Information and Communication Engineering Sungkyunkwan University Course Information meets at 3:00 pm or 4:30
More informationLahore University of Management Sciences. MATH 210 Introduction to Differential Equations
MATH 210 Introduction to Differential Equations Fall 2016-2017 Instructor Room No. Office Hours Email Telephone Secretary/TA TA Office Hours Course URL (if any) Ali Ashher Zaidi ali.zaidi@lums.edu.pk Math.lums.edu.pk/moodle
More informationIntroduction. Outline. EE3321 Electromagnetic Field Theory. Welcome! About this class Rules and syllabus Let s get started! 9/19/2018. E t.
D v B 0 B E t D H J t D B E H Introduction EE3321 Electromagnetic Field Theory Outline Welcome! About this class Rules and syllabus Let s get started! Slide 2 1 Welcome Course Information http://emlab.utep.edu/ee3321emf.htm
More informationContact Hours Face to Face: 1.5 hr lecture; 1.5 hr tutorial Online: hr (pace depends on student) lecture video and assessment
Academic Year 2018/19 Semester 2 Course Coordinator Dr. Koh Teck Seng Course Code PH2102 Course Title Electromagnetism Pre-requisites (MH1801 & MH2800 & PH1106) OR (MH1802 & MH1803 & MH2802 & PH1106) OR
More information8.03 Lecture 12. Systems we have learned: Wave equation: (1) String with constant tension and mass per unit length ρ L T v p = ρ L
8.03 Lecture 1 Systems we have learned: Wave equation: ψ = ψ v p x There are three different kinds of systems discussed in the lecture: (1) String with constant tension and mass per unit length ρ L T v
More informationPhysics Summer 1996
http://physics.syr.edu/courses/phy212.96summer/ Syracuse University - Department of Physics Physics 212 - Summer 1996 Textbook: Halliday/Resnick/Walker. Fundamentals of Physics. Chapters 23-42. Scheduling
More informationPHYSICS PHYSICS FOR SCIENTISTS AND ENGINEERS. Course Outline - Spring 2009
PHYSICS 2220 - PHYSICS FOR SCIENTISTS AND ENGINEERS Course Outline - Spring 2009 INSTRUCTOR: Dr. Bradley W. Carroll OFFICE: SL 211 TELEPHONE: 626-7921 E-MAIL: bcarroll@weber.edu HOMEPAGE: TEXTBOOK: http://physics.weber.edu/carroll/phys2220/
More informationAPPM 2350 Final Exam points Monday December 17, 7:30am 10am, 2018
APPM 2 Final Exam 28 points Monday December 7, 7:am am, 28 ON THE FONT OF YOU BLUEBOOK write: () your name, (2) your student ID number, () lecture section/time (4) your instructor s name, and () a grading
More information21 Laplace s Equation and Harmonic Functions
2 Laplace s Equation and Harmonic Functions 2. Introductory Remarks on the Laplacian operator Given a domain Ω R d, then 2 u = div(grad u) = in Ω () is Laplace s equation defined in Ω. If d = 2, in cartesian
More informationMATH20411 PDEs and Vector Calculus B
MATH2411 PDEs and Vector Calculus B Dr Stefan Güttel Acknowledgement The lecture notes and other course materials are based on notes provided by Dr Catherine Powell. SECTION 1: Introctory Material MATH2411
More informationMath 240: Syllabus and Vector Functions
Math 240: Syllabus and Vector Functions Ryan Blair University of Pennsylvania Wednesday January 11, 2012 Ryan Blair (U Penn) Math 240: Syllabus and Vector Functions Wednesday January 11, 2012 1 / 19 Outline
More informationThe purpose of this lecture is to present a few applications of conformal mappings in problems which arise in physics and engineering.
Lecture 16 Applications of Conformal Mapping MATH-GA 451.001 Complex Variables The purpose of this lecture is to present a few applications of conformal mappings in problems which arise in physics and
More informationMathematics of Physics and Engineering II: Homework problems
Mathematics of Physics and Engineering II: Homework problems Homework. Problem. Consider four points in R 3 : P (,, ), Q(,, 2), R(,, ), S( + a,, 2a), where a is a real number. () Compute the coordinates
More informationMathematics of Chemistry: Techniques & Applications (CHEM-UA 140)
Mathematics of Chemistry: Techniques & Applications (CHEM-UA 140) Professor Mark E. Tuckerman Office: 1166E Waverly Phone: 8-8471 Email: mark.tuckerman@nyu.edu Class Time & Location: Tuesday, Thursday:
More informationMath 3B: Lecture 1. Noah White. September 23, 2016
Math 3B: Lecture 1 Noah White September 23, 2016 Syllabus Take a copy of the syllabus as you walk in or find it online at math.ucla.edu/~noah Class website There are a few places where you will find/receive
More informationAP Physics C Electricity and Magnetism
AP Physics C Electricity and Magnetism Course overview This is a calculus based course in physics. The course is the equivalent of an introductory engineering course in Physics. The main objective of the
More informationCourse Syllabus: Continuum Mechanics - ME 212A
Course Syllabus: Continuum Mechanics - ME 212A Division Course Number Course Title Academic Semester Physical Science and Engineering Division ME 212A Continuum Mechanics Fall Academic Year 2017/2018 Semester
More informationSyllabus: for Complex variables
EE-2020, Spring 2009 p. 1/42 Syllabus: for omplex variables 1. Midterm, (4/27). 2. Introduction to Numerical PDE (4/30): [Ref.num]. 3. omplex variables: [Textbook]h.13-h.18. omplex numbers and functions,
More informationImportant Dates. Non-instructional days. No classes. College offices closed.
Instructor: Dr. Alexander Krantsberg Email: akrantsberg@nvcc.edu Phone: 703-845-6548 Office: Bisdorf, Room AA 352 Class Time: Tuesdays and Thursdays 7:30 PM - 9:20 PM. Classroom: Bisdorf / AA 467 Office
More informationPDEs in Spherical and Circular Coordinates
Introduction to Partial Differential Equations part of EM, Scalar and Vector Fields module (PHY2064) This lecture Laplacian in spherical & circular polar coordinates Laplace s PDE in electrostatics Schrödinger
More informationGRADUATE MATHEMATICS COURSES, FALL, 2016
GRADUATE MATHEMATICS COURSES, FALL, 2016 Math 8007: Introduction to Methods in Applied Mathematics I Prof. I. Klapper Modeling and understanding our world through mathematical description and analysis
More informationRequired Textbook. Grade Determined by
Physics 273 Honors (Spring 2015) (4 Credit Hours) Fundamentals of Physics II Syllabus available on BlackBoard http://webcourses.niu.edu/ under Course information Name: Prof. Omar Chmaissem (sha-my-sim)
More informationF. Elohim Becerra Chavez
F. Elohim Becerra Chavez Email:fbecerra@unm.edu Office: P&A 19 Phone: 505 277-2673 Lectures: Monday and Wednesday, 5:30-6:45 pm P&A Room 184. Textbook: Many good ones (see webpage) Lectures follow order
More informationLecture 14.1 :! Electromagnetic Fields
Lecture 14.1 :! Electromagnetic Fields Lecture Outline:! LR Circuits! E & B Transformations! The Displacement Current!! Textbook Reading:! Ch. 33.10-34.3 April 14, 2015 1 Announcements Leo Anthony Soderberg
More informationUNIVERSITY OF TORONTO Department of Electrical and Computer Engineering ECE320H1-F: Fields and Waves, Course Outline Fall 2013
UNIVERSITY OF TORONTO Department of Electrical and Computer Engineering ECE320H1-F: Fields and Waves, Course Outline Fall 2013 Name Office Room Email Address Lecture Times Professor Mo Mojahedi SF2001D
More informationTENTATIVE CONTENTS OF THE COURSE # EE-271 ENGINEERING ELECTROMAGNETICS, FS-2012 (as of 09/13/12) Dr. Marina Y. Koledintseva
TENTATIVE CONTENTS OF THE COURSE # EE-271 ENGINEERING ELECTROMAGNETICS, FS-2012 (as of 09/13/12) Dr. Marina Y. Koledintseva Part 1. Introduction Basic Physics and Mathematics for Electromagnetics. Lecture
More informationMATH 251 Ordinary and Partial Differential Equations Summer Semester 2017 Syllabus
MATH 251 Ordinary and Partial Differential Equations Summer Semester 2017 Syllabus Course Description: Ordinary and Partial Differential Equations. First and second order equations; series solutions; Laplace
More informationENGINEERING MATHEMATICS I. CODE: 10 MAT 11 IA Marks: 25 Hrs/Week: 04 Exam Hrs: 03 PART-A
ENGINEERING MATHEMATICS I CODE: 10 MAT 11 IA Marks: 25 Hrs/Week: 04 Exam Hrs: 03 Total Hrs: 52 Exam Marks:100 PART-A Unit-I: DIFFERENTIAL CALCULUS - 1 Determination of n th derivative of standard functions-illustrative
More informationPhysics 9, Introductory Physics II Spring 2010
Physics 9 page 1/6 Physics 9, Introductory Physics II Spring 2010 - Course Description - Instructor: Dr. Derrick Kiley Office: AOB 176; Office Phone 209 228-3076 E-mail Address: dkiley@ucmerced.edu. Course
More informationMath 7824 Spring 2010 Numerical solution of partial differential equations Classroom notes and homework
Math 7824 Spring 2010 Numerical solution of partial differential equations Classroom notes and homework Jan Mandel University of Colorado Denver May 12, 2010 1/20/09: Sec. 1.1, 1.2. Hw 1 due 1/27: problems
More informationMATH-UA 263 Partial Differential Equations Recitation Summary
MATH-UA 263 Partial Differential Equations Recitation Summary Yuanxun (Bill) Bao Office Hour: Wednesday 2-4pm, WWH 1003 Email: yxb201@nyu.edu 1 February 2, 2018 Topics: verifying solution to a PDE, dispersion
More informationAdvanced Engineering Mathematics Course Number: Math Spring, 2016
Advanced Engineering Mathematics Course Number: Math 401-501 Spring, 2016 Instructor: Dr. Prabir Daripa Office: Blocker 629D Email: daripa@math.tamu.edu Lecture: TTh 12:45 pm - 2:00 pm. Classroom: Blocker
More informationPHY General Physics II
Do you want to print this page? HOME Introduction Textbook Syllabus Staff Grading Homework Notes HELP Labs physics.syr.edu/courses/phy212.98summer/ Last modified: Tue Aug 4 20:48:22 1998 PHY 212 - General
More informationSCIENCE DEPT CHAIR: Mr. Scheidt AS 212B
PHS224 GENERAL PHYSICS II 4 HOURS CREDIT SEMESTER: FALL 2009 INSTRUCTOR: Dr. George Saum Office: Room 16 A & S Bldg. Phone: 573-518-2174 Lab: A & S 112 Office Hours:: 12:00 MTWF 10:00 R SCIENCE DEPT CHAIR:
More informationELECTROMAGNETIC THEORY
Phys 311 Fall 2014 ELECTROMAGNETIC THEORY Phys 311 Fall 2014 Instructor: Office: Professor David Collins WS 228B Phone: 248-1787 email: Office Hours: dacollin@coloradomesa.edu MT 9:00 9:50am, MWF 2:00
More informationSyllabus for OPTI 6101/8101 PHYS 6210 Fall 2010 Mathematical Methods for Optical Science and Engineering Theoretical Physics
Syllabus for OPTI 6101/8101 PHYS 6210 Fall 2010 Mathematical Methods for Optical Science and Engineering Theoretical Physics Instructor: Greg Gbur Office: Grigg 205, phone: 687-8137 email: gjgbur@uncc.edu
More informationAE 200 Engineering Analysis and Control of Aerospace Systems
Instructor Info Credit Class Days / Time Office Location: ENG 272C Office Hours: Monday 4:00pm 6:30pm Email: kamran.turkoglu@sjsu.edu 3 units Tuesday, 6:00pm 8:45pm Classroom CL 222 Prerequisites TA: Contact
More informationMath 251 Midterm II Information Spring 2018
Math 251 Midterm II Information Spring 2018 WHEN: Thursday, April 12 (in class). You will have the entire period (125 minutes) to work on the exam. RULES: No books or notes. You may bring a non-graphing
More informationGuide for Ph.D. Area Examination in Applied Mathematics
Guide for Ph.D. Area Examination in Applied Mathematics (for graduate students in Purdue University s School of Mechanical Engineering) (revised Fall 2016) This is a 3 hour, closed book, written examination.
More informationThis exam will be over material covered in class from Monday 14 February through Tuesday 8 March, corresponding to sections in the text.
Math 275, section 002 (Ultman) Spring 2011 MIDTERM 2 REVIEW The second midterm will be held in class (1:40 2:30pm) on Friday 11 March. You will be allowed one half of one side of an 8.5 11 sheet of paper
More informationECE 2112 ELECTROMAGNETIC THEORY C-term 2018
Worcester Polytechnic Institute Department of Electrical and Computer Engineering ECE 2112 ELECTROMAGNETIC THEORY C-term 2018 Professor: Dr. Reinhold Ludwig Office: AK 229, Tel.: 508-831-5315 Office hours:
More informationWelcome to Physics 331: Introduction to Numerical Techniques in Physics
Welcome to Physics 331: Introduction to Numerical Techniques in Physics Instructor: Joaquín Drut Lecture 1 Logistics Phys 331 Introduction to Numerical Techniques in Physics Spring 2016 Course information
More informationCHAPTER 2. COULOMB S LAW AND ELECTRONIC FIELD INTENSITY. 2.3 Field Due to a Continuous Volume Charge Distribution
CONTENTS CHAPTER 1. VECTOR ANALYSIS 1. Scalars and Vectors 2. Vector Algebra 3. The Cartesian Coordinate System 4. Vector Cartesian Coordinate System 5. The Vector Field 6. The Dot Product 7. The Cross
More informationClass Meeting # 1: Introduction to PDEs
MATH 18.152 COURSE NOTES - CLASS MEETING # 1 18.152 Introduction to PDEs, Spring 2017 Professor: Jared Speck Class Meeting # 1: Introduction to PDEs 1. What is a PDE? We will be studying functions u =
More informationAppendix: Orthogonal Curvilinear Coordinates. We define the infinitesimal spatial displacement vector dx in a given orthogonal coordinate system with
Appendix: Orthogonal Curvilinear Coordinates Notes: Most of the material presented in this chapter is taken from Anupam G (Classical Electromagnetism in a Nutshell 2012 (Princeton: New Jersey)) Chap 2
More informationMAT389 Fall 2016, Problem Set 4
MAT389 Fall 2016, Problem Set 4 Harmonic conjugates 4.1 Check that each of the functions u(x, y) below is harmonic at every (x, y) R 2, and find the unique harmonic conjugate, v(x, y), satisfying v(0,
More informationPHYS4210 Electromagnetic Theory Spring Final Exam Wednesday, 6 May 2009
Name: PHYS4210 Electromagnetic Theory Spring 2009 Final Exam Wednesday, 6 May 2009 This exam has two parts. Part I has 20 multiple choice questions, worth two points each. Part II consists of six relatively
More informationSYLLABUS. Course Applications Course Applications Indiv. study S L P S L P
1. Data about the program of study SYLLABUS 1.1 Institution The Technical University of Cluj-Napoca 1.2 Faculty Electrical Engineering 1.3 Department Electrotechnics and Measurements 1.4 Field of study
More informationPhysics 202, Lecture 8. Exam 1
Physics 202, Lecture 8 Today s Topics More on Exam 1: logistics and mini-review Current And Resistance (Ch. 27) Current: Macroscopic and Microscopic Resistance: Macroscopic and Microscopic Electrical Power
More informationNotes 19 Gradient and Laplacian
ECE 3318 Applied Electricity and Magnetism Spring 218 Prof. David R. Jackson Dept. of ECE Notes 19 Gradient and Laplacian 1 Gradient Φ ( x, y, z) =scalar function Φ Φ Φ grad Φ xˆ + yˆ + zˆ x y z We can
More informationCoordinate systems and vectors in three spatial dimensions
PHYS2796 Introduction to Modern Physics (Spring 2015) Notes on Mathematics Prerequisites Jim Napolitano, Department of Physics, Temple University January 7, 2015 This is a brief summary of material on
More informationLecture 3- Vectors Chapter 3
1 / 36 Lecture 3- Vectors Chapter 3 Instructor: Prof. Noronha-Hostler Course Administrator: Prof. Roy Montalvo PHY-123 ANALYTICAL PHYSICS IA Phys- 123 Sep. 21 th, 2018 2 / 36 Course Reminders The course
More informationUNIVERSITY of LIMERICK OLLSCOIL LUIMNIGH
UNIVERSITY of LIMERICK OLLSCOIL LUIMNIGH Faculty of Science and Engineering Department of Mathematics and Statistics END OF SEMESTER ASSESSMENT PAPER MODULE CODE: MA4006 SEMESTER: Spring 2011 MODULE TITLE:
More informationMathematics Qualifying Exam Study Material
Mathematics Qualifying Exam Study Material The candidate is expected to have a thorough understanding of engineering mathematics topics. These topics are listed below for clarification. Not all instructors
More informationPhysics 9, Introductory Physics II Fall 2011
Physics 9 page 1/6 Physics 9, Introductory Physics II Fall 2011 - Course Description - Instructor: Dr. Derrick Kiley Office: AOB 177; Office Phone 209 228-3077 E-mail Address: dkiley@ucmerced.edu. Course
More informationJoel A. Shapiro January 21, 2010
Joel A. shapiro@physics.rutgers.edu January 21, 20 rmation Instructor: Joel Serin 325 5-5500 X 3886, shapiro@physics Book: Jackson: Classical Electrodynamics (3rd Ed.) Web home page: www.physics.rutgers.edu/grad/504
More informationGIST 4302/5302: Spatial Analysis and Modeling
GIST 4302/5302: Spatial Analysis and Modeling Spring 2016 Lectures: Tuesdays & Thursdays 12:30pm-1:20pm, Science 234 Labs: GIST 4302: Monday 1:00-2:50pm or Tuesday 2:00-3:50pm GIST 5302: Wednesday 2:00-3:50pm
More informationPhysics 170 Lecture 5. Dot Product: Projection of Vector onto a Line & Angle Between Two Vectors
Phys 170 Lecture 5 1 Physics 170 Lecture 5 Dot Product: Projection of Vector onto a Line & Angle etween Two Vectors Phys 170 Lecture 5 2 Mastering Engineering Introduction to M.E. and Assignment 1 moved
More informationToday s Topics. The Physics 202 Team Course Formality and Overview. Physics 202 Homepage
Today s Topics The Physics 202 Team Course Formality and Overview Ch. 21.1-21.5: Electric Charge, Coulomb's Law Text: Giancoli, Physics for Scientists and Engineers, 4th ed., Volume II. Physics 202 Homepage
More informationIntroduction to PDEs and Numerical Methods Lecture 1: Introduction
Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen Introduction to PDEs and Numerical Methods Lecture 1: Introduction Dr. Noemi Friedman, 28.10.2015. Basic information on the course Course
More informationLecture 3- Vectors Chapter 3
1 / 36 Lecture 3- Vectors Chapter 3 Instructor: Prof. Noronha-Hostler Course Administrator: Prof. Roy Montalvo PHY-123 ANALYTICAL PHYSICS IA Phys- 123 Sep. 21 th, 2018 2 / 36 Course Reminders The course
More informationLecture 1. EE70 Fall 2007
Lecture 1 EE70 Fall 2007 Instructor Joel Kubby (that would be me) Office: BE-249 Office Hours: M,W,F 2-3 PM or by appointment Phone: (831) 459-1073 E-mail: jkubby@soe.ucsc.edu Teaching Assistant Drew Lohn
More information