Differential Equations

MATH 30613-040

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.

By TCU policy, if you will need to be absent at any point due to a religious holiday or observance not recognized by the official TCU calendar, you should contact me about this within the first two weeks of the semester.

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.

 

Class Schedule

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

 

 

Course Learning Outcomes

 

Learning Outcomes

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

 

 

Campus Life and the Student Experience

(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.

 


Health and Wellness

(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.





Student Access and Accommodation

 

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.

 

Audio Recording Notification:

(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.

 


Technology Policies

Email

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.

 

Course Materials

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.

 


Anti-Discrimination and Title IX Information

(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

www.care.tcu.edu

817-257-5225

 

Counseling & Mental Health Center

www.counseling.tcu.edu

817-257-7863

 

Religious & Spiritual Life

www.faith.tcu.edu

817-257-7830

 

On Campus Resources

TCU Police

www.police.tcu.edu

817-257-8400 Non-emergency

817-257-7777 Emergency

 

 

Emergency Response Information

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

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.