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Math 319 -  Techniques in Ordinary Differential Equations

Credits: 3.00

Course Designations and Attributes:

Breadth - Natural Science

Level - Advanced

L&S Credit - Counts as Liberal Arts and Science credit in L&S

Meeting Time and Location:  TuTh 1:00 - 2:15pm,

Instructional Mode: In-person

Specify how Credit Hours are met by the Course: The five credit hours are met by two 75-minute meetings and two 50-minute meetings and an expected six hours of out of class student work per week for 14 weeks.

INSTRUCTORS AND TEACHING ASSISTANTS

Instructor Title and Name: Dr. Nathan Fisher, Van Vleck Visiting Assistant Professor

Office: Van Vleck 407

Instructor Email/Preferred Contact: [email protected] 

Teaching Assistants:

 Mingfeng Chen

[email protected]

Lauren Neudorf

[email protected]

OFFICE HOURS

Instructor:

● Wednesdays 11:00 am - 1:00 pm in Van Vleck 407

● Or by appointment

TA Office/Office Hours: You are welcome to attend office hours for either of our two TAs.

Tuesdays

● 10:00 - 11:00 am with Mingfeng in MLC, Van Vleck B224

Thursdays

● 3:00 - 4:00 with Lauren, https://uwmadison.zoom.us/j/96113884339

Fridays

● 10:00 - 11:00 am with Mingfeng in MLC, Van Vleck B224

OFFICIAL COURSE DESCRIPTION

Course Description

Review of linear differential equations; series solution of linear differential equations; boundary value problems; Laplace transforms; possibly numerical methods and two dimensional autonomous systems.

Requisites

MATH 222, 276 or graduate/professional standing

LEARNING OUTCOMES

Course Learning Outcomes

The course is not proof based; it is about techniques and methods. However, many proofs in the subject are elementary and can be presented in the lectures. We expect after taking the course the student can:

● First order equations

○ Solve first order linear, separable and exact equations.

○ Draw direction fields.

○ State and explain the existence and uniqueness theorem.

○ Find the existence interval for a solution.

○ Draw the phase line for an autonomous equation and determine stability of equilibria.

○ Use Euler’s method.

● Second order linear equations

○ Find the general solution of a second order homogeneous equation with constant coefficients.

○ State and explain basic properties of linear differential equations: superposition principle, linear independence, Wronskian.

○ Use the method of variation of parameters to solve nonhomogeneous equations.

● Laplace transform

○ State the definition of Laplace transform and explain its main properties.

○ Find Laplace transform and inverse Laplace transform using the table of Laplace transforms.

○ Solve nonhomogeneous differential equation with constant coefficients using Laplace transform.

○ Understand the idea of the delta function and be able to use it with differential equation,

● First order systems

○ Rewrite a higher order differential equation as a first order system.

○ Find the inverse of a function and solve a system of linear algebraic equations.

○ Find eigenvalues and eigenvectors of a matrix.

○ Solve a linear homogeneous system with constant coefficients in 2 and 3 dimensions in case of simple and repeated eigenvalues.

○ Find the fundamental matrix and use it to write a solution of a nonhomogeneous system.

● Two dimensional systems and the phase plane.

○ Classify the phase portraits of a linear system in 2 dimensions.

○ Explain the notion of stability of an equilibrium.
Determine stability for a quasilinear system.

○ Be able to explain the phase portrait of the pendulum and of a population model.

○ Boundary value problems (time permitting)

GRADING

Midterm 1 - 20%

Midterm 2 - 20%

Final exam - 25%

Discussion quizzes - 15% (1 drop)

Online homework - 20%

LETTER GRADES: your total scores will fit on the following curve:

A ≥ 92%

AB ≥ 87%

B ≥ 82%

BC ≥ 77%

C ≥ 70%

D ≥ 60%

F < 60%

REQUIRED TEXTBOOK, SOFTWARE & OTHER COURSE MATERIALS

● Elementary Differential Equations and Boundary Value Problems, 9th Edition, by Dennis G. Zill (digital copy included in WebAssign)

● By being registered in this course, you are automatically charged for your WebAssign materials, so you DO NOT need to purchase anything

○  If you purchased Cengage Unlimited, you should opt-out of being charged.  https://kb.wisc.edu/academictechnologypilots/page.php?id=77524

To access your course materials login through your Canvas course.

Student directions:  https://startstrong.cengage.com/webassign-canvas-ia-yes/

If you have questions or issues about WebAssign, the following are a couple of options for you.  Please don’t contact your professor with WebAssign issues.

● To verify the system is up, please go to https://techcheck.cengage.com/  (Links to an external site.)

● If you have specific technical issues, please contact technical support 24/7

○ 1-800-354-9706

○ Online chat and self-help www.cengage.com/support

○ Make sure to allow pop-ups: https://www.cengage.com/lms_docs/system_check/popupsfailed/popupsfailed_chrome.htm 

If you do create a tech ticket and have not heard back in 24-48 hours, please email [email protected].

EXAMS, QUIZZES, PAPERS & OTHER MAJOR GRADED WORK

There will be two midterms and a final for this course. By nature of the course, Midterm 2 and the Final Exam, while emphasizing new material, will be cumulative. The dates for these exams are

● Midterm 1: Tuesday, October 10, 5:45 - 7:00 pm, room TBA

● Midterm 2: Tuesday, November 14, 5:45-7:00 pm, room TBA

● Final exam: Saturday, December 16, 5:05-7:05 pm, room TBA

Please note that the midterm exams are in the evenings on days we have class. On exam days, class will be optional, and I will use those lecture periods as a review and to answer student questions.

All exams are closed book, closed notes and no calculators or electronic devices of any kind are allowed. Exams are proctored in-person.

HOMEWORK & OTHER ASSIGNMENTS

● Quizzes

There will be approximately 6 short quizzes during discussion throughout the semester. Quizzes will always be announced in advance. The lowest quiz grade will be dropped. You are encouraged to save these drops for personal emergency situations. Makeup quizzes will not be given.

● Homework

There will be weekly online homework assignments to be completed on WebAssign. There will be links to each assignment on Canvas.

Requesting extensions: Since it is quite possible that in the course of the semester you will either experience a technical difficulty (e.g., missed the deadline, your computer shut down as you were submitting it, internet outage, etc) or a personal emergency (being sick, attending a funeral, etc), for each assignment you can request an extension through WebAssign (you do not need to inform your instructor or TA). If you request an extension, any problems you have not yet completed by the deadline will be accessible until 72 hours after the original deadline. A 30% penalty will be applied to any problems which were not completed by the original due date. Extensions cannot be requested any later than 72 hours after the original due date.

COURSE WEBSITE, LEARNING MANAGEMENT SYSTEM and INSTRUCTIONAL TOOLS

● Our Learning Management System is Canvas. The site for our course is: https://canvas.wisc.edu/courses/363865

● The learning software WebAssign will be used for homework sets. You will also be able to access the e-textbook through Cengage / WebAssign.

● We will use Piazza, which you can access through Canvas. This page is a forum for you to discuss the material of this class with other students and your TAs and/or instructor. Posts to this page should be confined to questions regarding the material and logistical questions about the class (e.g., exam dates and locations). Any posts containing unrelated or inappropriate comments will be deleted. Unprofessional conduct may result in disciplinary action. Please do not use email to ask math questions.

● We will use Gradescope for grading exams.

● Some TA and/or instructor office hours may be held remotely. Zoom or MSTeams may be used for this purpose.

RULES, RIGHTS & RESPONSIBILITIES

● See the Guide’s Rules, Rights and Responsibilities

COLLABORATION

We encourage you to discuss topics from the course with other students. In particular, you may collaborate on the homework. Collaboration is NOT allowed during discussion quizzes or exams.

ACADEMIC INTEGRITY

By enrolling in this course, each student assumes the responsibilities of an active participant in UW-Madison’s community of scholars in which everyone’s academic work and behavior are held to the highest academic integrity standards. Academic misconduct compromises the integrity of the university. Cheating, fabrication, plagiarism, unauthorized collaboration, and helping others commit these acts are examples of academic misconduct, which can result in disciplinary action. This includes but is not limited to failure on the assignment/course, disciplinary probation, or suspension. Substantial or repeated cases of misconduct will be forwarded to the Office of Student Conduct & Community Standards for additional review. For more information, refer to studentconduct.wiscweb.wisc.edu/academic-integrity/.

ACCOMMODATIONS FOR STUDENTS WITH DISABILITIES

McBurney Disability Resource Center syllabus statement: “The University of Wisconsin-Madison supports the right of all enrolled students to a full and equal educational opportunity. The Americans with Disabilities Act (ADA), Wisconsin State Statute (36.12), and UW-Madison policy (Faculty Document 1071) require that students with disabilities be reasonably accommodated in instruction and campus life. Reasonable accommodations for students with disabilities is a shared faculty and student responsibility. Students are expected to inform faculty [me] of their need for instructional accommodations by the end of the third week of the semester, or as soon as possible after a disability has been incurred or recognized. Faculty [I], will work either directly with the student [you] or in coordination with the McBurney Center to identify and provide reasonable instructional accommodations. Disability information, including instructional accommodations as part of a student's educational record, is confidential and protected under FERPA.” http://mcburney.wisc.edu/facstaffother/faculty/syllabus.php

DIVERSITY & INCLUSION

Institutional statement on diversity: “Diversity is a source of strength, creativity, and innovation for UW-Madison. We value the contributions of each person and respect the profound ways their identity, culture, background, experience, status, abilities, and opinion enrich the university community. We commit ourselves to the pursuit of excellence in teaching, research, outreach, and diversity as inextricably linked goals.

The University of Wisconsin-Madison fulfills its public mission by creating a welcoming and inclusive community for people from every background – people who as students, faculty, and staff serve Wisconsin and the world.” https://diversity.wisc.edu/ 

Digital Course Evaluation (AEFIS)

UW-Madison now uses an online course evaluation survey tool, AEFIS. In most instances, you will receive an official email two weeks prior to the end of the semester when your course evaluation is available. You will receive a link to log into the course evaluation with your NetID where you can complete the evaluation and submit it, anonymously. Your participation is an integral component of this course, and your feedback is important to me. I strongly encourage you to participate in the course evaluation.

Teaching & Learning Data Transparency Statement

The privacy and security of faculty, staff and students’ personal information is a top priority for UW-Madison. The university carefully evaluates and vets all campus-supported digital tools used to support teaching and learning, to help support success through learning analytics, and to enable proctoring capabilities. View the university’s full teaching and learning data transparency statement.

Privacy of Student Records & the Use of Audio Recorded Lectures Statement

View more information about FERPA.

Lecture materials and recordings for this course are protected intellectual property at UW-Madison. Students in this course may use the materials and recordings for their personal use related to participation in this class. Students may also take notes solely for their personal use. If a lecture is not already recorded, you are not authorized to record my lectures without my permission unless you are considered by the university to be a qualified student with a disability requiring accommodation. [Regent Policy Document 4-1] Students may not copy or have lecture materials and recordings outside of class, including posting on internet sites or selling to commercial entities. Students are also prohibited from providing or selling their personal notes to anyone else or being paid for taking notes by any person or commercial firm without the instructor’s express written permission. Unauthorized use of these copyrighted lecture materials and recordings constitutes copyright infringement and may be addressed under the university’s policies, UWS Chapters 14 and 17, governing student academic and non-academic misconduct.

Academic Calendar & Religious Observances

Pursuant to university policy UW-880 (see the link below), students are required to inform their instructors during the first two weeks of class about religious conflicts with quizzes and exams taking place during the semester.  Students who will miss quizzes and/or exams during the semester because of religious holidays/observances must email their instructor to inform them of possible conflicts.  The instructor will work with the individual student to find suitable alternatives that adhere to university and departmental guidelines. Note that if a conflict is not raised during the initial 2 week period then we cannot guarantee that suitable accommodations will be provided. Because of this, it is vital that students with religious conflicts contact their instructor in a timely manner during the first two weeks of class.

The university policy UW-880 can be found here: https://policy.wisc.edu/library/UW-880