MAT 2384 C: Ordinary Differential Equations, Laplace Transforms and Numerical Methods
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MAT 2384 C: Ordinary Differential Equations, Laplace Transforms and Numerical Methods
Instructor: Dr. Xinhou Hua
E-mail :hxinhou@uottawa.ca (Your email subject: MAT2384C)
Office Hours: Tuesdays, 4pm-5pm, Wednesdays 5:30pm-6:30pm, STM 666; or by email.
Course web: Brightspace. Announcements and course related material including solutions to exams will be posted there. Your grades will also appear there.
(Note: the website is very important to the course, all material and announcements posted there.)
Lectures (Jan 8 - Apr 10):
|
Days & Times |
Locations |
|
Mo 19:00 - 20:20 |
MHN 257 |
|
Mo 20:30 - 21:20 |
MHN 257 |
|
We 16:00 - 17:20 |
MHN 257 |
Calculator: During midterms and final exam, basic scientific calculators are allowed, such as the following Faculty of Science approved calculators: Texas instruments TI-30, TI-34; Casio fx- 260, fx-300. Graphing/or programmer calculators are NOT allowed.
Evaluation:
|
Midterm Test 1: Wednesday, Feb 14, in class,16:00— |
25% |
|
Midterm Test 2: Wednesday, March 20, in class, 16:00— |
25% |
|
Final Exam |
50% |
Note:
1. If you miss a test without a valid reason, then their score is 0.
2. If you submit a valid justification within a week before or from the date of the test, then the percentage will be added to your final exam. No make-up midterms.
3. If your final exam < 40%, then grade is F.
Course description:
General concepts. First order equations. Linear differential equations of higher order. Differential operators. Laplace transforms. Systems of differential equations. Series solutions about ordinary points. Numerical methods including error analysis; numerical differentiation, integration and solutions of differential equations.
Prerequisite: MAT 1341, (MAT 1322orMAT 1325orMAT 1332). The coursesMAT 2384,MAT 2324cannot be combined for units.
References: 1. Advanced Engineering Mathematics, by E. Kreyszig, Wiley
(This is just a reference textbook. All efforts will be made to make detailed notes available in Brightspace.)
2. Ordinary Differential Equations, Laplace Transforms and Numerical methods for Engineers, S. J. DESJARDINS and R. VAILLANCOURT, 2012
Checking the Test/Assignment/Exam Grades:
o It is your responsibility to make sure that your marks recorded correctly by visiting Brightspace.
o Deadline to make any corrections is within one week when you receive marks.
Midterm and Final Exam procedures: You should bring your student card to exams. Students may not enter after or leave before 20 minutes have passed from the beginning of an exam.
Final exam during the exam period (April 2024) will be scheduled by the university.
Changes to the syllabus: Any changes will be announced via Brightspace. It's the responsibility of the students to keep informed in such cases.
COPYRIGHT The materials you receive for this course are protected by copyright and to be used for this course only. You do not have permission to upload the course materials, including any lecture recordings you may have, to any website. If you require clarification, please consult your professor.
Important dates and deadlines
https://www.uottawa.ca/important-academic-dates-and-deadlines/
Reading week: Feb 18-24
April 10: Saturday’s schedule
The following is a list of topics that we will discuss. Please note that some of the topics maybe discussed in a slightly different order and some items maybe mentioned only briefly.
Course Content for the ODEs part:
Chapter 1 - First order ODEs:
Section 1: Introduction, terminology and basic examples - Theorem of Existence and Uniqueness.
Section 2: Separable ODEs and ODEs with homogeneous coe_cients.
Section 3: Exact ODEs and Integrating Factors.
Section 4: Linear first order ODEs, Bernouilli Equations.
Chapter 2 - Homogeneous linear ODEs.
Section 1: Generalities.
Section 2: Second-order linear ODEs with constant coefficients.
Section 3: Second-order Euler-Cauchy Equations.
Section 4: Higher-order linear ODEs with constant coefficients.
Section 5: Higher-order Euler-Cauchy Equations.
Chapter 3 - Non-homogeneous linear ODEs.
Section 1: Generalities.
Section 2: The method of Undetermined Coefficients.
Section 3: The method of Variation of Parameters.
Chapter 4 - Systems of first order ODEs
Section 1: Generalities.
Section 2: Homogeneous systems of first order ODEs with constant coe_cients.
Section 3: Non-homogeneous systems of first order ODEs with con- stant coefficients.
Chapter 5 - Laplace Transforms.
Section 1: Review of Improper Integrals.
Section 2: Definitions, terminology and first properties of Laplace Transforms.
Section 3: Laplace Transforms of basic functions.
Section 4: The Heaviside function, the Dirac-delta function and their Laplace Transforms.
Section 5: The two Shifting Theorems.
Section 6: Solving IVPs using Laplace Transforms.
Section 7: More properties of Laplace Transforms.
Course Content for the Numerical Methods part:
Chapter 1 - Iterative methods for solving equations of the form f(x) = 0.
Section 1: Introduction, Review of the Intermediate Value Theorem.
Section 2: The fixed-point Iteration Method.
Section 3: The Newton's Method, the Secant Method.
Chapter 2 - Interpolation
Section 1: Lagrange Interpolation.
Section 2: Newton's divided-difference Interpolation.
Section 3: Gregory-Newton Interpolation.
Chapter 3 - Numerical Integration.
Section 1: The Midpoint Rule.
Section 2: The Trapezoidal Rule.
Section 3: Simpson's Rule.
Section 4: Gaussian Quadrature
Chapter 4 - Numerical Methods to solve first order IVPs.
Section 1: Euler's Method.
Section 2: The Improved Euler Method (Heun's Method).
Section 3: The Runge-Kutta Method of order 4.
2024-01-12