MATH-3150H-A: Partial Differential Equation 2018WI - Peterborough Campus

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1 MATH-3150H-A: Partial Differential Equation 2018WI - Peterborough Campus Instructor: Instructor: Kenzu Abdella Address: kabdella@trentu.ca Phone Number: x7327 Office: GSC 339 Office Hours: Monday 11:00-11:50 and Thursday 13:00-13:50 Meeting Times: Lectures: Monday 16:00-17:5- CCW A1 Thursday 11:00-11:50 DNA B106 Seminar: Thursday 12:00-12:50 DNA B106 Department: Academic Administrative Assistant: Gina Collins Address: math@trentu.ca Phone Number: 7715 Office: SC327 Description:

2 This course is an introduction to partial differential equations. It explores partial differential equations including the heat, wave and Laplace equations in one, two, and three dimensions, in Cartesian, Polar, and/or Spherical coordinates. It covers method of separation of variables, boundary value problems, Fourier Series, Orthogonal eigenfunction expansion, Bessel functions, the Fourier transform, and Numerical methods if time permits. Learning Outcomes: The course is developed to address several learning outcomes. By the end of the course a successful student should be able to: 1. State the heat, wave, Laplace, and Poisson equations and explain their physical origins 2. Classify partial differential equations and transform into canonical form 3. Solve linear partial differential equations of both first and second order 4. Fundamental concepts of PDEs theory and analytical methods for solving PDEs 5. Identify homogeneous PDEs and evolution equations 6. Define boundary value problem and identify boundary conditions as periodic, Dirichlet, Neumann, or Robin (mixed) 7. Solve the heat, wave, Laplace, and Poisson equations using separation of variables and apply boundary conditions 8. Derive basic properties of the Fourier transform of a function, such as its relationship to the Fourier transform of the derivative 9. Use the Fourier transform to solve the heat and wave equations on unbounded domains and more Texts: Required Texts: Applied Differential Equations with Fourier Series and Boundary Value Problems, Richard Haberman, Pearson, Fifth Edition Recommended Texts (References available at the library) :

3 Linear Partial Differential Equations and Fourier Theory, by M. Pivato, Cambridge University Press Assessments, Assignments and Tests: Course Evaluation: Note: At least 25% of the course marks will be obtained by the final date to withdraw from Winter-term courses (March 9, 2018). 1) Homework Assignments (18%) Due: TBA Three Assignments based on topics covered in the class. Students are given two weeks to complete and submit each assignment. 2) Project (7%) Due: TBA A self-study project emphasizing on a selected topic not covered in the class. Details will be provided during the term. 3) Quizzes (15%) Due: TBA Based upon a list of recommended problems which will be drawn from the exercises in the text. 4) Midterm (20%) Due: March 3rd A close-book exam covering the topics completed between week 1 and week 6. 5) Final Examination (40%) Due: During exam period in April A written comprehensive closed-book exam covering the entire course. Schedule: Week-by-Week Schedule: The schedule of topics is listed below: Although specific dates are not listed, I will follow the order of topics as given and will regularly communicate in class and on the LearningSystem/Blackboard about the pacing of the lectures. For this reason, it

4 Week 1 is important for you to attend class and log on to the LearningSystem/Blackboard regularly. Introduction and classification Week 2-3 Heat and Laplace Equations Week 4-5 Fourier Series Week 6-7 Wave Equation Week 8-9 Eigenfunctions expansion Week 9-10 Higher Dimensional PDEs Week 11 Fourier Transform Week 12 Numerical Solutions (if time permits) Course Guidelines: Course Policies: No late submissions of assignments.

5 Department Policies: Final date to appeal marks for assignments, quizzes or projects for Winter halfcourses is June 28 th, University Policies: Academic Integrity Academic dishonesty, which includes plagiarism and cheating, is an extremely serious academic offence and carries penalties varying from failure on an assignment to expulsion from the University. Definitions, penalties, and procedures for dealing with plagiarism and cheating are set out in Trent University s Academic Integrity Policy. You have a responsibility to educate yourself unfamiliarity with the policy is not an excuse. You are strongly encouraged to visit Trent s Academic Integrity website to learn more: Access to Instruction It is Trent University's intent to create an inclusive learning environment. If a student has a disability and documentation from a regulated health care practitioner and feels that they may need accommodations to succeed in a course, the student should contact the Student Accessibility Services Office (SAS) at the respective campus as soon as possible. Print

Department of Physics & Astronomy Trent University

Department of Physics & Astronomy Trent University PHYS 2610H : INTRODUCTORY QUANTUM PHYSICS 2017FA PETERBOROUGH Instructor: Balaji Subramanian Campus: Peterborough balajisubramanian@trentu.ca SC 322 15063375166