Differential
Equations
Fall 2021
Course
Web Site: http://faculty.tcu.edu/gfriedman/ode
Instructor: Dr. Greg Friedman
e-mail: g.friedman@tcu.edu
Office: 358B Tucker Technology
Center
Phone: 817-257-6343
Office
Hours: Office hour Zoom meetings can be
arranged at any time by e-mailing or calling me. Once I receive such a request
I will do my best to meet with you as soon as possible, almost always within 24
hours and most of the time much sooner. I’m also happy to answer questions by
e-mail.
Final
Exam: Thursday, December 16,
8:00-10:30 PM
Class
Schedule: TR 8:30-9:50 PM
Location: TUC 244
Required
Text: Differential
Equations by P. Blanchard, R. Devaney, and G. Hall, 4th edition
Prerequisites: Students are expected to be expert in the material of Calculus I and II.
Asking questions: Ask questions in class! It helps me know what needs to be explained better, and it makes classmates grateful that someone had the courage to ask. You are also encouraged to ask questions before class, after class, in my office hours, by e-mail, over telegraph, and every other possible way. Don't be shy!
Calculators: Most of the assignments will not require you to use a calculator. Occasionally a graphing calculator might be helpful. If you choose to use a calculator during the course, the department suggests Texas Instruments calculators. However, you may not use TI 89 calculators or other calculators with symbolic capabilities during examinations.
Health and Safety
By TCU policy, you must wear a mask at all
times in the classroom. No eating or drinking in class will be permitted. Masks
must be worn properly, covering nose and mouth.
If you are exhibiting new symptoms that may be related to COVID-19 (fever or chills, dry cough, shortness of breath, etc.) or are concerned that you may have been exposed to COVID-19, you must self-quarantine and consult with the Brown Lupton Health Center at 817-257-7949 for further guidance. In addition, you must notify the Campus Life Office immediately at 817-257-7926. Campus Life will inform your professors that you are unable to attend class, and provide any assistance and support needed. Click here for detailed information concerning COVID-19 symptoms: https://www.cdc.gov/coronavirus.
If you are
unwell, but are not exhibiting potential COVID-19-related symptoms, please notify
me via email as soon as possible that you are ill and will not be attending
class
Course Policies and
Procedures
Class Meeting and Attendance: Class meetings will be TR 8:30-9:50 PM. Attendance is expected. You are responsible for all material and information from all class sessions, for handing in all homework on time, and for taking all exams at the appointed times.
Exams: There
will be three midterm exams; see the calendar below (dates subject to change).
The final exam will be on Thursday, December 16, 8:00-10:30 PM.
Problem assignments: Homework problems will
be assigned via the course website at http://faculty.tcu.edu/gfriedman/ode/ode-hw.html. Problems will be listed by textbook section
and typically due at the beginning of the second class session following completion of the textbook
section in class (due dates will be listed with the problems). Occasionally,
writing assignments may be assigned that should be turned in separately – these
will also be indicated on the web site. Unexcused late problem sets
will not be graded and will count as a 0 toward your overall homework grade. You may discuss homework problems with others and
are encouraged to come to me for help at any time. You may collaborate with
other students in class to work on solving homework problems, BUT solutions must be written up individually. In other
words, you may work in groups in attempting to figure out how to solve
problems, but you must write up solutions on your own and demonstrate your own
mastery of the solution. Copying from classmates is not permitted, and handing
in identical written solutions will be considered plagiarism and collusion. It
is imperative that you learn the material for yourself; there will be no
collaboration on exams. Looking up problem solutions online is absolutely
forbidden and will be considered plagiarism.
Plagiarism:
In addition to copying homework solutions from others in the class, looking up
answers on the internet, or anywhere else, and using those answers to write
your homework solutions is plagiarism and will not be tolerated. At
minimum, plagiarism will result in a 0 on the assignment and reporting to the
dean’s office. Other penalties might include a 0 for your overall homework
grade, removal from the course with an automatic grade of F (not replaceable),
or suspension from the university.
Grading: Your final average will be determined approximately as follows: 30% for the final exam, 20% for each midterm, and 10% for homework. In-class quizzes, should any be given, will count as part of the homework grade. A cumulative average of 90% or above guarantees at least an A-, a cumulative average of 80% or above guarantees at least a B-, a cumulative average of 70% or above guarantees at least a C-, and a cumulative average of 60% or above guarantees at least a D-. Actual grade lines will be determined by the instructor; lower numerical averages might earn higher letter grades.
On Concepts: On exams and
homework you will be tested not just on your ability to perform calculations
but also on your understanding of concepts discussed in class and in the book.
Therefore, it is important for you to read the material in the text (which you
will be responsible for) and to study notes from class.
Make-ups and accommodations: In the event that you will be unable to take an exam on time, an official written excuse is required. I expect to be notified at least one week in advance except in the case of serious emergency, and in all cases I expect to be notified as soon as reasonably possible. Excuses may also be given by me to hand in homework late, again provided that a reasonable request is made in advance or proof of emergency situation is presented. Failure to abide by this policy may result in loss of course credit. For any special accommodations or rescheduling you may need, it is your responsibility to contact me at least one week in advance. For final exams, all rescheduling must be initiated by you at least one month in advance.
Students who miss classes for acceptable reasons, including illness, quarantine, or other authorized absences will be provided access to video recordings from a previous semester of the material covered during the missed classes.
Extra help: In addition to help from me, students may seek extra help from the math clinic or through tutoring. Please contact me for more information.
Calendar:
The course will meet at all scheduled course times. Class meetings will be TR
8:00-9:50 PM.
Each week we will cover
the topics contained in the following sections of the text. Homework
assignments will be posted via TCU Online with due dates clearly marked; in
general, homework will be due at the start of the second
class period after the day it is assigned. Sections marked with an
asterisk (*) will be included only if well ahead of schedule (and so are likely
to be skipped). This calendar should be taken as a rough guideline, subject to
much possible change. In particular, midterm exam dates may be pushed back depending
on pace of progress.
Week |
Start Date |
Topics |
Special |
1 |
Aug. 23 |
Section 1.1-1.2 |
|
2 |
Aug. 30 |
Sections 1.3-1.4 |
|
3 |
Sept. 6 |
Sections 1.5-1.6 |
Sep. 6 Labor Day |
4 |
Sept. 13 |
Sections 1.8, 1.9 |
|
5 |
Sept. 20 |
Section 2.1 |
Exam 1 – Sept. 23 |
6 |
Sept. 27 |
Section 2.2, 2.4 |
|
7 |
Oct. 4 |
Sections 3.1-3.2 |
|
8 |
Oct. 11 |
Sections 3.3 |
Oct. 14-15 Fall Break |
9 |
Oct. 18 |
Sections 3.4 |
Exam 2 – Oct. 21 |
10 |
Oct. 25 |
Sections 2.3, 3.6 |
|
11 |
Nov. 1 |
Sections 4.1, 4.2 |
|
12 |
Nov. 8 |
Section 4.3, 6.1 |
Nov. 8 - Last Day to Drop; |
13 |
Nov. 15 |
Sections 6.2 |
Exam 3 – Nov. 18 |
14 |
Nov. 22 |
Thanksgiving week |
|
15 |
Nov. 29 |
Section 6.3, 6.4 |
|
16 |
Dec. 6 |
Review* |
Dec. 7
- Last Day of Class |
17 |
Dec. 13 |
|
Final
Exam - Thursday, December 16, 8:00-10:30 PM |
1.
Model
real-life problems with differential equations
2.
Solve
first-order differential equations quantitatively and qualitatively
3.
Solve
first-order systems of differential equations quantitatively and qualitatively
4.
Solve
second order differential equations, including harmonic oscillator problems,
forcing, and resonance
5.
Solve
differential equations using Laplace transforms
6.
Basic
techniques of linear algebra
Mapping of Course
Outcomes to Course Activities and Assignments
Course
Outcome(s) |
Course
Activities |
1 |
Lectures on textbook material and
associated homework assignments (one per lecture); especially Sections 1.1
and 2.1 but also throughout the course |
2 |
Lectures on Chapter 1 of the text
and associated homework assignments (one per lecture) |
3 |
Lectures on Chapters 2-3 of the
text and associated homework assignments (one per lecture) |
4 |
Lectures on Chapter 4 of the text
and associated homework assignments (one per lecture) |
5 |
Lectures on Chapter 6 of the text
and associated homework assignments (one per lecture) |
6 |
Lectures on Chapter 3 of the text
and auxiliary material and associated homework assignments (one per lecture) |
1, 2, 3, 4, 5, 6 |
Midterm exams |
1, 2, 3, 4, 5, 6 |
Final exam |
|
|
Grading Rubrics
Exams: The number of points available for an exam problem will be displayed on the exam. Exam problems will be graded according to the following approximate rubric. The categorization of your performance for a given problem on the chart below, as well as the precise grade within the category are at the discretion of the instructor. This rubric is intended to give you an idea of what I’m looking for when grading, but ultimately I will assign points according to my own judgment.
Some problems may require multiple steps with the student expected to know what those steps are; in particular, the steps and their corresponding point subtotals may not be provided. In this case each step will be graded according to the rubric below with the weight for a particular step or problem part determined by the instructor. Such weightings will be consistent for all students in the class.
Problems will be scored via a deduction method as follows:
Deduction |
Possible
reasons for deduction |
0% deduction (full credit) |
Answer is completely correct. All
required steps have been performed. All computations are correct. All
requested information has been given clearly and in the expected format (e.g.
full non-technical English sentences if required). |
0%-25% deduction |
Problem is substantially correct
but contains minor errors, such as: a minor copy error, a minor part of a
computation or formula is incorrect, or required conclusions are not stated
clearly or as required. |
25%-50% deduction |
Answer has multiple minor errors
(as above) or a more significant error, such as: overall technique is
generally correct but there are serious computational errors, incorrect
formula or technique has been applied, or conclusion has flaws in correctness
or presentation. |
50-75% deduction |
Answer has several errors,
possibly multiple small or mid-level errors, or a major error, such as:
serious flaws in methodology, critical computational errors, incorrect
results, major flaws in stating conclusions. |
75-100% deduction |
Answer is substantially
incorrect, for example: the correct methods have not been applied, only
rudimentary work has been provided, required mathematical conditions to
proceed with a computation have not been met, conclusions absent. |
100% deduction (no credit) |
Answer has not been submitted. |
Homework will be graded by a student homework grader using an analogous rubric.
University Disclosures
Syllabus Disclosures
(Updated 6/30/2021)
The health and safety of students, faculty, and staff is Texas Christian
University’s highest priority. Safety protocols may change during the semester
and may result in modifications or changes to the teaching format, delivery
method, or the course schedule (e.g., altering meeting times or frequency; changing
beginning or ending dates for a term; or partially or completely moving from a
face-to-face classroom teaching to an online teaching or remote learning
format). Any changes in teaching format, delivery method, or course schedule
will not impact the credit hours for the course.
(Updated
6/30/2021)
If you are exhibiting symptoms that may be related to COVID-19 (fever or
chills, dry cough, shortness of breath, etc.) or are concerned that you may
have been exposed to COVID-19, you must self-quarantine and consult with the
Brown Lupton Health Center at 817-257-7949 for further guidance.
In addition, you must notify the Campus Life Office immediately at 817-257-7926 or use the TCU COVID-19 Self-Report Hotline, 817-257-2684 (817-257-COVI). Campus Life will inform your professors that you are unable to attend class and provide any assistance and support needed. Click here for detailed information concerning COVID-19 symptoms: https://www.cdc.gov/coronavirus.
If you are unwell but are not exhibiting potential
COVID-19-related symptoms, please notify your instructor as soon as possible
that you are ill and will not be attending class.
TCU Policy
for Religious Observations & Holidays
(New 11/1/2020)
“Students who are unable to participate in a class, in any related assignment or in a university required activity because of the religious observance of a holy day shall be provided with a reasonable opportunity to make up the examination or assignment, without penalty, provided that it does not create an unreasonable burden on the University.” For more information, please visit the TCU Policy for Religious Observations & Holidays webpage.
Texas Christian University affords students with disabilities reasonable accommodations in accordance with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act. To be eligible for disability-related academic accommodations, students are required to register with the TCU Office of Student Access and Accommodation and have their requested accommodations evaluated. If approved for accommodations, students are required to discuss their official TCU Notification of Accommodation with their instructors. Accommodations are not retroactive and require advance notice to implement. The Office of Student Access and Accommodation is located in The Harrison, Suite 1200. More information on how to apply for accommodations can be found at https://www.tcu.edu/access-accommodation/ or by calling Student Access and Accommodation at (817) 257-6567.
(Updated 6/30/2021)
Audio recordings of class lectures may be permitted by the instructor or as an approved disability accommodation through Student Access and Accommodation. Recordings are not to be shared with other students, posted to any online forum, or otherwise disseminated.
Only the official TCU student email address will be used for all course notification. It is your responsibility to check your TCU email on a regular basis.
TCU students are prohibited from sharing any portion of course materials (including videos, PowerPoint slides, assignments, or notes) with others, including on social media, without written permission by the course instructor. Accessing, copying, transporting (to another person or location), modifying, or destroying programs, records, or data belonging to TCU or another user without authorization, whether such data is in transit or storage, is prohibited. The full policy can be found at: https://security.tcu.edu/polproc/usage-policy/.
Violating this policy is considered a violation of Section 3.2.15 of the Student Code of Conduct (this policy may be found in the Student Handbook at https://tcu.codes/code/index/), and may also constitute Academic Misconduct or Disruptive Classroom Behavior (these policies may be found in the undergraduate catalog at https://tcu.smartcatalogiq.com/current/Undergraduate-Catalog/Student-Policies/Academic-Conduct-Policy-Details). TCU encourages student debate and discourse; accordingly, TCU generally interprets and applies its policies, including the policies referenced above, consistent with the values of free expression and First Amendment principles.
(FULL SECTION UPDATE 6/30/2021)
Statement on TCU’s Non-Discrimination
Policy
TCU is committed to providing a positive learning, living, and working environment free from unlawful discrimination, harassment, sexual misconduct, and retaliation. In support of this commitment, in its policy on Prohibited Discrimination, harassment, sexual misconduct and retaliation, TCU has a range of prohibited behaviors, including unlawful discrimination and harassment and related sexual and other misconduct based on age, race, color, religion, sex, sexual orientation, gender, gender identity, gender expression, national origin, ethnic origin, disability, predisposing genetic information, covered veteran status, and any other basis protected by law. The Office of Institutional Equity (OIE) is responsible for responding to all reports of discrimination, harassment, sexual misconduct and retaliation.
Please use the following links to review TCU Policy 1.008 Prohibited Discrimination, Harassment, Sexual Misconduct and Retaliation or to review TCU Policy 1.009 Responding to Reports of Prohibited Discrimination, Harassment, Sexual Misconduct, and Retaliation.
To make a report, you may call OIE at 817-257-8228, email oie@tcu.edu, visit us at The Harrison, Suite 1800 or click here: Make a Report.
To
learn about the Campus Community Response Team (CCRT) and Report a Bias
Incident click here: https://inclusion.tcu.edu/campus-community-response-team/
Title IX
TCU’s Title IX Coordinator works within OIE. Andrea Vircks-McDew serves as TCU’s Title IX Coordinator. You may call 817-257-8228 to make a report, email oie@tcu.edu or a.vircks@tcu.edu, or make a report here. Additional Title IX resources and information are available at https://www.tcu.edu/institutional-equity/title-ix/index.php.
Mandatory Reporters
ALL TCU employees, except confidential resources, are considered Mandatory Reporters. Mandatory reporters are required to immediately report to OIE any conduct that raises Discrimination, Harassment, Sexual Misconduct (Title IX or Violence Against Women (VAWA)) or Retaliation. Mandatory reporters cannot promise to refrain from forwarding the information to OIE.
Confidential
On-Campus Resources
Campus Advocacy, Resources & Education
817-257-5225
Counseling & Mental Health Center
817-257-7863
Religious & Spiritual Life
817-257-7830
On Campus Resources
TCU Police
817-257-8400 Non-emergency
817-257-7777 Emergency
Please review TCU’s L.E.S.S. is More public
safety video to learn about Lockdown, Evacuate, and Seek Shelter
procedures. (https://publicsafety.tcu.edu/less-is-more/)
TCU’s Public Safety website provides maps that show our building’s rally point for evacuation and the seek shelter location. (https://publicsafety.tcu.edu/)
In the event of an emergency, call the TCU Police Department at 817-257-7777.
Download the Frogshield Campus Safety App on your phone. (https://police.tcu.edu/frogshield/)
Academic Misconduct (Sec. 3.4 from the TCU Code of Student Conduct): Any act that violates the academic integrity of the institution is considered academic misconduct. The procedures used to resolve suspected acts of academic misconduct are available in the offices of Academic Deans and the Office of Campus Life and are also listed in detail in the Undergraduate Catalog and the Graduate Catalog Specific examples include, but are not limited to:
·
Cheating: Copying from another student’s test
paper, laboratory report, other report, or computer files and listings; using,
during any academic exercise, material and/or devices not authorized by the
person in charge of the test; collaborating with or seeking aid from another
student during a test or laboratory without permission; knowingly using,
buying, selling, stealing, transporting, or soliciting in its entirety or in
part, the contents of a test or other assignment unauthorized for release;
substituting for another student or permitting another student to substitute
for oneself.
·
Plagiarism: The appropriation, theft, purchase or
obtaining by any means another’s work, and the unacknowledged submission or
incorporation of that work as one’s own offered for credit. Appropriation
includes the quoting or paraphrasing of another’s work without giving credit
therefore.
·
Collusion: The unauthorized collaboration with
another in preparing work offered for credit.
·
Abuse
of resource materials:
Mutilating, destroying, concealing, or stealing such material.
·
Computer
misuse:
Unauthorized or illegal use of computer software or hardware through the TCU
Computer Center or through any programs, terminals, or freestanding computers
owned, leased or operated by TCU or any of its academic units for the purpose
of affecting the academic standing of a student.
·
Fabrication
and falsification:
Unauthorized alteration or invention of any information or citation in an
academic exercise. Falsification involves altering information for use in any
academic exercise. Fabrication involves inventing or counterfeiting information
for use in any academic exercise.
·
Multiple
submission: The
submission by the same individual of substantial portions of the same academic
work (including oral reports) for credit more than once in the same or another
class without authorization.
·
Complicity
in academic misconduct:
Helping another to commit an act of academic misconduct.
·
Bearing
false witness:
Knowingly and falsely accusing another student of academic misconduct.