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JOHN CABOT UNIVERSITY
COURSE CODE: "MA 495"
COURSE NAME: "Differential Equations"
SEMESTER & YEAR:
Spring 2024
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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
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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.
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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.
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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.
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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 | | | | | |
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REQUIRED RESERVED READING:
RECOMMENDED RESERVED READING:
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GRADING POLICY
-ASSESSMENT METHODS:
| Assignment | Guidelines | Weight |
| midterm exams | There will be two midterm exams, the first on Tuesday 7th March, and the second on Thursday 6th April (week 11) | 60% |
| projects | There will be two small projects to be done at home, one over spring break, and the other due in the final week of term. | 10% |
| Final exam | The final will be comprehensive, but with more weight put on any topics which did not appear on either of the midterms. | 30% |
-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.
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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.
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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.
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SCHEDULE
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Week 1 - Introduction
Week 2 - PDEs and Direction fields
Week 3 - Euler's method, and we will start to look at linear first order ODEs
Week 4 - further linear equations and separable equations.
Weeks 5 and 6 - Orthogonal trajectories, Euler homogeneous equations, economics applications + first project
Week 7 - MIDTERM, then existence and uniqueness of solutions
Week 8 - 9 More advanced numerical techniques
Weeks 9 to 12 - Second-order ODEs, series methods (second MIDTERM in Week 11)
Week 13 - The parareal algorithm (predicting the near and far future simultaneously)
Week 14 - Exercise classes
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