Instructor: Dr. William Nesse
Email: nesse@math.utah.edu
Lecture section 4 when and where: M,W,H,F , location: Canvas (here!).
Laboratory on Canvas, Thursdays: 

Section 5: 8:35-9:25 AM

Section 6: 9:40-10:30 AM

Section 7: 7:30-8:20 AM

Section 8: 8:35-9:25 AM

Nesse's Office hours: Tuesdays 9:45-11:15 AM; Wednesdays 12:30-1:30 PM on Zoom.

First Midterm: Friday, October 2 (Week 6) 
Second Midterm: Friday, November 6 (Week 11) 
Course Final: Wednesday, December 9, 2020. 8:00 – 10:00 am 

Drop Deadline: Friday, September 4 
Labor Day (NO CLASS): Monday, September 7
Withdraw Deadline: Friday, October 16
Thanksgiving Break: Thurs-Sun, November 26-27 (No class) 
Reading Day: Friday, December 4 (no class)

Textbook: Differential Equations and Linear Algebra (ISBN-13: 978-0134497181). An e-text version will be offered within Canvas (see more below).

The work you will complete in Math 2250 comprises weekly homework and quizzes, two midterm exams, and a comprehensive final exam. Homework will be submitted and quizzes will be given every Friday except during exam days and holidays. The three lowest homework scores will be dropped and the two lowest quiz scores will be dropped. Midterm exams will be given on scheduled Fridays (see above). 

Details about the content of each assignment type are as follows:

Homework: Roughly three textbook sections are due every Friday. The homework will typically cover lectures from the preceding week or two. If you click on a homework assignment, you will see listings of problems, about three of which will be randomly selected for grading by the grader. Three of a student's lowest homework scores will be dropped. 
Quizzes: On many Fridays after class, a short 1-2 problem quiz will be given through Canvas, due by Midnight  taking roughly 10-25 minutes to complete. The quizzes can be taken at a self-selected time during the day.  The quiz will cover relevant topics covered in the week's lectures and in the lab section group work. Two of a student's lowest quiz scores will be dropped. 
Midterm exams: Two 65-minute midterm exams will be given on select Fridays. A practice exam will be posted about a week prior to the midterm that will cover the same material. Review of the practice exam will occur both in lecture and in the lab section.
Final exam: A two-hour and fifteen minute comprehensive exam will be given. As with the midterms, a practice final will be posted about a week prior. 
Gradescope:  The exams and homeworks will be scored on gradescope.com. Regrade requests (in gradescope, not email) must be lodged in a timely fashion within a week of grade posting. Final exams will be posted and three days will be allotted to lodge regrade requests before final scores are posted. Regrade requests may involve crafting an argument for why you deserve more points. All regrade requests will be considered but should be based on the facts of the problem, the rubric employed, and the work given on the page of the exam, but not what you intended to write, or thought, or any other rationales. The goal of grading is to fairly apply a grading procedure to every student, so, a regrade request may result in an increase, decrease, or no change in score. 
Lab: Every Thursday a Teaching Assistant- (TA) directed lab section will be held. These lab sections will have smaller class sizes, consisting of working on lab worksheet-reports. The lab worksheet-reports will tend to cover longer, more in-depth problems than that found in homeworks and exams, and will sometimes require use of instructor-supplied Maple or Matlab software to complete. The TA will be there to help guide students through the problems. Completion of worksheet-reports will require work outside of the lab hour. The lab work serves the the goal of learning complete problem solving fluency (see below), where students will develop skills to solve problems involving multiple coordinated skills, including interpretation and identification of relevant variables and unknowns, operationalization of the question into a series of executable methods, and interpretation and communication of results. The lab represents 20% of the class time every week, and worth 15% of your total grade. 
Extra help: The TA will hold office hours and will be available for any questions, especially for helping complete lab assignments. TAs from other Math 2250 sections will also hold their office hours in the tutoring lab. These TAs will be familiar with your lab assignments and homework and should offer a broad time availability for any help you may need.
Letter grades are determined as follows: If X is your percentage grade, then {X ≥ 93% ⇒ A,X ≥ 90% ⇒ A−,X ≥ 87% ⇒ B+,X ≥ 83% ⇒ B ,X ≥ 80% ⇒ B− ,X ≥ 77% ⇒ C+ ,X ≥ 73% ⇒ C,X≥70%⇒C−,X≥67%⇒D+,X≥63%⇒D,X≥60%⇒D−,X<60%⇒E}. Letter grade assignments can be changed uniformly for all students, at the discretion of the instructor. 
E-textbook: through the Inclusive Access program. Students should receive an email to their email account a week prior to class start that gives them the options to OPT OUT if they do not wished to be charged the textbook fee. If students do nothing they will be automatically OPTED IN and charged the fee.

Online Course Considerations: Due to the ongoing epidemic this course is fully conducted in the virtual space through interactive video conferencing (IVC) via the Zoom App. All assignments and exams will be submitted via Gradescope.com.

Students must have a reliable internet connection from which to participate on Zoom and submit via Gradescope.
Lectures will be given via Zoom during the scheduled class time. Attendance, interaction, and questions are highly encouraged. The lecture notes and video will be recorded and posted later each day as a resource.
Thursday laboratory sessions will entail working in small groups of fellow students that will be administered using the Zoom breakout rooms. 
Students must abide by the Student Honor Code. During exams and quizzes, students are not permitted to collaborate with each other, or communicate or seek help from third parties in-person or on the web. All work must be original, solely performed by the student.
Exams are expected to be completed in roughly 55 minutes, but roughly an extra 10 minutes are allowed for students to complete the upload process (65 minutes total). Many assignments will be given prior to the exam in which to practice the upload process.
Students are highly encouraged to collaborate together on homeworks or lab assignments to enhance their knowledge. However, the work a student writes on their submitted assignment must reflect their own knowledge (i.e., no copying others' work).
Course Learning Objectives:

The Basic Topics

Be able to model dynamical systems that arise in science and engineering, by using general principles to derive the governing differential equations or systems of differential equations. These principles include linearization, compartmental analysis, Newton’s laws, conservation of energy and Kirchoff’s law.

Learn solution techniques for first order separable and linear differential equations. Solve initial value problems in these cases, with applications to problems in science and engineering. Understand how to approximate solutions even when exact formulas do not exist. Visualize solution graphs and numerical approximations to initial value problems via slope fields.

Become fluent in matrix algebra techniques, in order to be able to compute the solution space to linear systems and understand its structure; by hand for small problems and with technology for large problems.

Be able to use the basic concepts of linear algebra such as linear combinations, span, indepen- dence, basis and dimension, to understand the solution space to linear equations, linear differential equations, and linear systems of differential equations.

Understand the natural initial value problems for first order systems of differential equations, and how they encompass the natural initial value problems for higher order differential equations and general systems of differential equations.

Learn how to solve constant coefficient linear differential equations via superposition, particular solutions, and homogeneous solutions found via characteristic equation analysis. Apply these techniques to understand the solutions to the basic unforced and forced mechanical and electrical oscillation problems.

Learn how to use Laplace transform techniques to solve linear differential equations, with an em- phasis on the initial value problems of mechanical systems, electrical circuits, and related problems.

Be able to find eigenvalues and eigenvectors for square matrices. Apply these matrix algebra con- cepts to find the general solution space to first and second order constant coefficient homogeneous linear systems of differential equations, especially those arising from compartmental analysis and mechanical systems.

Understand and be able to use linearization as a technique to understand the behavior of nonlinear autonomous dynamical systems near equilibrium solutions. Apply these techniques to non-linear mechanical oscillation problems and other systems of two first order differential equations, including interacting populations. Relate the phase portraits of non-linear systems near equilibria to the linearized data, in particular to understand stability.

Develop your ability to communicate modeling and mathematical explanations and solutions, using technology and software such as Maple, Matlab or internet-based tools as appropriate. 

Problem Solving Fluency

Students will be able to read and understand problem descriptions, then be able to formulate equations modeling the problem usually by applying geometric or physical principles. Solving a problem often requires specific solution methods listed above. Students will be able to select the appropriate operations, execute them accurately, and interpret the results using numerical and graphical computational aids.

Students will also gain experience with problem solving in groups. Students should be able to effectively transform problem objectives into appropriate problem solving methods through collaborative discussion. Students will also learn how to articulate questions effectively with both the instructor and TA, and be able to effectively convey how problem solutions meet the problem objectives.

Students with disabilities

The University of Utah seeks to provide equal access to its programs, services and activities for people with disabilities. If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, 581-5020 (V/TDD). CDS will work with you and the instructor to make arrangements for accommodations. All information in this course can be made available in alternative format with prior notification to the Center for Disability Services. 

Addressing Sexual Misconduct: Title IX makes it clear that violence and harassment based on sex and gender (which includes sexual orientation and gender identity/expression) is a Civil Rights offense subject to the same kinds of accountability and the same kinds of support applied to offenses against other protected categories such as race, national origin, color, religion, age, status as a person with a disability, veteran¹s status or genetic information. If you or someone you know has been harassed or assaulted on the basis of your sex, including sexual orientation or gender identity/expression, you are encouraged to report it to the University’s Title IX Coordinator; Director, Office of Equal Opportunity and Affirmative Action, 135 Park Building, 801-581-8365, or to the Office of the Dean of Students, 270 Union Building, 801-581-7066.  For support and confidential consultation, contact the Center for Student Wellness, 426 SSB, 801-581-7776.  To report to police, contact the Department of Public Safety, 801-585-2677(COPS).

Campus Safety: The University of Utah values the safety of all campus community members. To report suspicious activity or to request a courtesy escort, call campus police at 801-585-COPS (801-585-2677). You will receive important emergency alerts and safety messages regarding campus safety via text message. For more information regarding safety and to view available training resources, including helpful videos, visit safeu.utah.edu (Links to an external site.)

Week by week guide (subject to change)

Week 1: 1.1-4—Differential equations, mathematical models, integral as general and particular solutions, slope fields, separable differential equations

Week 2: 1.4-5, 2.1-2—Separable equations cont., linear differential equations, circuits, mixture models, popula- tion models, equilibrium solutions and stability

Week 3: 2.2-4—Equilibrium solutions and stability cont., acceleration-velocity models, numerical solutions

Week 4:2.5-6, 3.1—Numerical solutions cont., linear systems

Week 5: 3.1-4—Linear systems, matrices, Gaussian elimination, reduced row echelon form, matrix operations Rules

Week 6: 3.5-3.6—Matrix inverses, determinants, review; Midterm exam 1 covering material from weeks 1-5

Week 7: 4.1-4—Vector spaces, linear combinations in Rn, span and independence, subspaces, bases and dimen- sion

Week 8: 5.1-3—Second-order linear DEs, general solutions, superposition, homogeneity and constant coefficients

Week 9: 5.4-6—Mechanical vibrations, pendulum model, particular solutions to non-homogeneous problems, forcing and resonance; Super quiz

Week 10: 10.1-4—Laplace transforms, solving IVPs with transforms, partial fractions and translations

Week 11: 10.4-5—Unit steps, convolutions; Midterm exam 2 covering weeks 6-10 material

Week 12: 6.1-2, 7.1—Eigenvalues and eigenvectors, diagonalization, first-order systems of ODE Parts.

Week 13: 7.2-5—Matrix systems, eigenanalysis, spring systems, forced undamped systems, practical resonance

Week 14: 9.1-2—Equilibria, stability, phase portraits for non-linear systems.

Week 15:  Review