Final Exam Details: 18-DECEMBER-2009
The final examination for APM 346 is scheduled for Friday, 18 December, 9-12 p.m. (Office Hours: Wednesday 16 December, 4-6 p.m.) Room assignments and other details are avaiable on the U.T. exam time table ( http://www.artsci.utoronto.ca/current/undergraduate/exams/dec09 ) . Course material includes chapters 1-5 in the textbook and all material covered in the lecture notes. Students are strongly encouraged to review Homeworks: 1 – 8, Midterm Test 1 and Midterm Test 2 during the final exam preparation. Structure of the final exam: quiz part (52 %) = 10 questions and problem solving part (48 %): 4 problems = 12 *4. Quiz part combines some not all questions: from quiz parts of the two midterm tests plus Fourier transform, max.-min. principle questions, energy method questions, Laplace equation. For the problem solving part it would be usefull to practice a lot with separation of variables and Fourier series method for different intervals, for rectangular domains and for different boundary conditions. Good luck !
Second Midterm Test Details:
The first midterm test will be written during regularly scheduled lecture time on Monday, November 2, lasting about 1.5 hours The test will be written in room GB 404 (A – L) and GB 405 (M – Z) between 8:30am and 10:00am, NOT in the usual lecture room! GB is Galbraith Building.
The test may cover
Lecture notes: 11 – 20, Sections from the textbook: 2.8; 3.1 – 3.6; 4.7 – 4.10; 5.3; repeat 4.1, 4.3 Homeworks: 4-6.
Some of the topics that may be covered by the test include:
- General Fourier Series Questions: sin, cos, full Fourier Series, diferent types of convergence
- Separation of variables: solutions of eigenvalues problems, symmetric boundary conditions, general solution of BVP.
- Solving homogeneous initial value problems on closed intervals by separation of variables.
- Solving nonhomogeneous initial value problems by general Fourier method on closed intervals.
- Fourier Integral as a limiting case of Fourier Series.
- Solving initial value problems by Fourier Integral.
- Comparison of D’Alembert solutions and Fourier Series solutions.
Midterm Test II solutions and marking scheme.
First Midterm Test Details:
The first midterm test will be written during regularly scheduled lecture time on Monday, October 5, lasting about 1.5 hours The test will be written in room GB 404 (A – L) and GB 405 (M – Z) between 8:30am and 10:00am, NOT in the usual lecture room! GB is Galbraith Building.
The test may cover
Lecture notes: 1 – 10, Sections from the textbook: 1.1 – 1.4; 2.1 – 2.3; 2.6; 4.1 – 4.3 (partially), Homeworks: 1-3.
Some of the topics that may be covered by the test include:
- General PDE classifications: order of an equation, linear, nonlinear, homogeneous, inhomogeneous
- Types of the second order PDE: elliptic, parabolic, hyperbolic.
- General solutions of the first-order linear PDE with constant and non-constant coefficients.
- Initial value problems for the first-order linear and quasi-linear PDEs
- Domain of the well-posedness for the initial value problem. Uniqueness and non-uniqueness of the solution.
- General solution of the wave equation with constant coefficients. Initial value problem for the wave equation.
- Change of variables and transformation to the canonical form.
Midterm Test I marking scheme.
GENERAL INFORMATION:
The midterm tests will last approximately 1.5 hours and will be held during regularly scheduled lecture time.
The midterm tests and final exam will be closed book (i.e., NO aids allowed), and the midterm should be written in pen (remarking requests for tests written in pencil will not be accepted) – the test paper will have lots of room for rough work. Colour pencils should be used for pictures.