|
|
JOHN CABOT UNIVERSITY
COURSE CODE: "MA 495"
COURSE NAME: "Differential Equations"
SEMESTER & YEAR:
Spring 2022
|
SYLLABUS
INSTRUCTOR:
Sara Munday
EMAIL: [email protected]
HOURS:
MW 1:30 PM 2:45 PM
TOTAL NO. OF CONTACT HOURS:
45
CREDITS:
3
PREREQUISITES:
Prerequisites: MA 298 and MA 350 or permission of the instructor
OFFICE HOURS:
MW 14:15-15:00 or by appointment
|
|
COURSE DESCRIPTION:
This course provides an introduction to ordinary differential equations. These equations contain a function of one independent variable and its derivatives. The term "ordinary" is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. Ordinary differential equations and applications, with integrated use of computing, student projects; first-order equations; higher order linear equations; systems of linear equations, Laplace transforms; introduction to nonlinear equations and systems, phase plane, stability.
|
SUMMARY OF COURSE CONTENT:
This course provides an introduction to ordinary differential equations. where "ordinary" means that we consider only functions of one variable. One half of the course will be an introduction to various classes of differential equations that can be solved exactly, and the other half will instead consist of numerical methods for finding approximate solutions where an exact solution is not possible. We start from Euler's method, and study progressively more modern and more accurate methods, finishing with a class of algorithms that were first introduced in the 1980s, and are still the topic of active research.
|
LEARNING OUTCOMES:
At the end of the course, the student will be familiar with linear equations, various techniques for solving simple first order equations, and will have some experience of modelling with differential equations. The student will also learn some basic techniques for finding approximate numerical solutions, starting with Euler's method. At the end of the course we will look into some more modern techniques and models.
|
TEXTBOOK:
| Book Title | Author | Publisher | ISBN number | Library Call Number | Comments | Format | Local Bookstore | Online Purchase |
| Elementary Differential Equations and Boundary Value Problems | W. Boyce, R. DiPrima | Wiley | 978-1-119-32063-0 | | | | | |
|
REQUIRED RESERVED READING:
RECOMMENDED RESERVED READING:
|
GRADING POLICY
-ASSESSMENT METHODS:
| Assignment | Guidelines | Weight |
| midterm exam | | 30% |
| projects | There will be two projects given out, one group and one individual, which will be graded on a handed-in written copy and a presentation in class (for the group presentation, you wil take turns presenting bits of the work). Each project will be worth 15% of your grade. | 30% |
| Final exam | The final will be comprehensive, but with slightly more weight put on the topics from after the midterm. | 40% |
-ASSESSMENT CRITERIA:
AWork of this quality directly addresses the question or problem raised and provides a coherent argument displaying an extensive knowledge of relevant information or content. The student demonstrates complete, accurate, and critical knowledge of all the topics, and is able to solve problems autonomously.
BThis is highly competent level of performance and directly addresses the question or problem raised.There is a demonstration of some ability to critically evaluate theory and concepts and relate them to practice. The work does not suffer from any major errors or omissions and provides evidence that the student uses clear logic in his/her arguments.
CThis is an acceptable level of performance and provides answers that are clear but limited, reflecting the information offered in the lectures. Mathematical statements are properly written most of the time.
DThis level of performances demonstrates that the student lacks a coherent grasp of the material. Important information is omitted and irrelevant points included. Many mistakes are made in solving the problem raised. In effect, the student has barely done enough to persuade the instructor that they should not fail.
FThis work fails to show any knowledge or understanding of the subject-matter. Most of the material in the answer is irrelevant
-ATTENDANCE REQUIREMENTS:
Students are required to provide documentation if they must miss a class.
|
|
|
ACADEMIC HONESTY
As stated in the university catalog, any student who commits an act of academic
dishonesty will receive a failing grade on the work in which the dishonesty occurred.
In addition, acts of academic dishonesty, irrespective of the weight of the assignment,
may result in the student receiving a failing grade in the course. Instances of
academic dishonesty will be reported to the Dean of Academic Affairs. A student
who is reported twice for academic dishonesty is subject to summary dismissal from
the University. In such a case, the Academic Council will then make a recommendation
to the President, who will make the final decision.
|
STUDENTS WITH LEARNING OR OTHER DISABILITIES
John Cabot University does not discriminate on the basis of disability or handicap.
Students with approved accommodations must inform their professors at the beginning
of the term. Please see the website for the complete policy.
|
|
|
SCHEDULE
|
|
|
Week 1 - Introduction
Week 2 - Direction fields
Week 3 - Linear first order ODEs
Week 4 - Euler's method
Weeks 5 and 6 - Solving first order ODEs - modelling population dynamics, separable equations, exact equations
Week 7 - More advanced numerical methods
Week 8 - revision class and midterm
Weeks 9 to 12 - Further methods for finding closed form solutions: second-order ODEs, series methods, Laplace transforms, stability
Week 13 - The parareal algorithm (predicting the near and far future simultaneously)
Week 14 - Exercise classes
|
|
|