MAT 275 MODERN DIFFERENTIAL EQUATIONS FALL 2020 Disclaimer: All items on this syllabus are subject to change. Any in-class announcement, verbal or written, is considered an official addendum to this syllabus. Course materials and information will be accessible through Canvas Learning Management System (link on your “My ASU” page). Instructor: Baer Office: personal Zoom meeting room: https://asu.zoom.us/j/7048540230 Classroom/Class time: via Zoom: Check Canvas for current link/ 12:00-1:15 T, Th Office Hours: T, Th 4:30-5:30, F 3:00-4:00, or by Appointment E-Mail: [email protected] Prerequisites: MAT 266 or MAT 271 with a C or higher. Textbook: Elementary Differential Equations and Boundary Value Problems, 11th Edition, by William E. Boyce and Richard C. DiPrima, John Wiley & Sons, Inc. There is also ASU custom edition of this textbook: MAT 275 – Modern Differential Equations. Course Description: Introduces differential equations, theoretical and practical solution techniques. Applications. Problem solving using MATLAB. Learning outcomes: At the completion of this course, students will be able to, among other things: • Sketch and interpret direction fields for first order Ordinary Differential Equations (ODEs) and sketch integral curves • Find equilibrium (constant) solutions of autonomous ODEs and classify them as stable, unstable or semi-stable. • Verify, by substitution, that a given function is a solution of a given ODE • Given the general solution of a ODE, use initial conditions to find the particular solution. • Classify differential equations by their order and linearity • Derive differential equations that model simple applied problems. • Use the method of integrating factor to integrate linear first order ODEs. • Solve separable equations and determine the interval of validity of the solution. • Given a first order Initial Value Problem (IVP), use the appropriate theorems to determine existence and uniqueness of solutions. • Use Euler’s method to derive recursive approximations for a given IVP. • Use the characteristic equation to solve linear homogeneous ODEs with constant coefficients. • Use the Wronskian to determine linear independence of solutions of high order DEs. • Apply the method of reduction of order for solving linear second order DEs. • Apply the method of undetermined coefficients for finding a particular solution of non-homogeneous DEs. • Derive and interpret solutions of ODES modeling damped and undamped mechanical vibrations with or without forcing term. • Compute Laplace transform using the definition and/or using the table. • Solve ODEs using the Laplace transform. • Write a piecewise function in terms of unit step functions and solve ODEs involving piecewise continuous forcing terms. • Use the Laplace transform to solve ODEs involving the impulse function • Write a linear system of differential equations in vector-matrix form. • Write higher order linear ODEs as a first order system of ODEs. • Use the Wronskian to determine whether solutions of a linear system of a DE are linearly independent. • Use the eigenvalue method to solve homogeneous linear system of ODEs with constant coefficients. • Use MATLAB ODE solvers to solve IVPs.MAT 275 Fall 2020 Syllabus Baer 2/8 SYNC modality: Classes will meet at the time and dates listed in the official ASU Schedule of Classes, and will be held via Zoom. Your attendance is required as it would be in a normal in-person class. Zoom Etiquette: During the Zoom sessions, please log in on time and assure that you have a reasonably secure connection. Please use your full name or first name-last initial. No outside attendees will be allowed, and during the sessions, please keep your microphone's audio muted except when needing to talk to the instructor. The instructor reserves the right to remove anyone from the Zoom sessions for disruptive behavior. This class will be taught 100% remotely using Zoom !! No in-person class sessions for this section of MAT 275. The first class will be August 20th: 12:00-1:15 Course Access This ASU course is accessed in CANVAS using ZOOM. Technology Requirements ASU Sync classes can be live streamed anywhere with the proper technology. We encourage you to use a PC or Apple laptop or desktop equipped with a built-in or standalone webcam. You will need an internet connection that can effectively stream live broadcasts. It is recommended that your internet download speed is at least 5.0 mbps. You can use this tool to test your current connection. We do not recommend the use of iPads or Chromebooks for ASU Sync as these devices do not work for class exams that may be proctored remotely. If you are not able to personally finance the equipment you need to attend class via ASU Sync, ASU has a laptop and WiFi hotspot checkout program available through ASU Library. Who is eligible? • Any currently enrolled ASU student is eligible to checkout a laptop. The current availability of laptops can be found here. • Borrowing and returning laptop rules • Laptops are lent on a first-come, first-serve basis, and cannot be reserved in advance. They can be returned at any time, but will be due at the conclusion of the fall 2020 semester. • Rentals are limited to one laptop per student. • Laptops are available for checkout at the following libraries on all four campuses. (Please check online for current library hours) o Downtown Phoenix campus Library o Polytechnic campus Library o Tempe: Hayden and Noble Libraries o West campus: Fletcher Library • Return laptops to any ASU Library Information Desk (not at the drop box or other location) • Refer to ASU Library Computer Use Policy and ASU Computer, Internet, and Electronic Communications Policy. • Borrowers are responsible for loss, damage, and theft of the laptop while in their possession. Borrowers should verify the condition of the laptop at the time of check-out and upon check-in. Additional Requirements:MAT 275 Fall 2020 Syllabus Baer 3/8 This course requires the following technologies: • Web browsers (Chrome, Mozilla Firefox, or Safari) • Adobe Acrobat Reader (free) • Adobe Flash Player (free) • Webcam, microphone, headset/earbuds, and speaker • Microsoft Office (Microsoft 365 is free for all currently-enrolled ASU students) • MATLAB (available through MyApps for all currently-enrolled ASU