MATH 321-03, 06 Differential Equations Section 03: MWF 1:00pm-1:50pm McLaury 306 Section 06: MWF 3:00pm-3:50pm EEP 208 Instructor: Brent Deschamp Email: brent.eschamp@ssmt.eu Office: McLaury 316B Phone: 605-394-2476 Website: http://webpages.ssmt.eu/ bescham Office Hours: Monay 10-11am Tuesay 9-10am, 3-4pm Wenesay 2-3pm Thursay Friay 10-11am An by appointment Text: A First Course in Differential Equations by Dennis G. Zill, Tenth Eition. Course Description: Selecte topics from orinary ifferential equations incluing evelopment an applications of first orer, higher orer linear, an systems of linear equations, general solutions an solutions to initial-value problems using matrices. Aitional topics may inclue Laplace transforms an power series solutions. MATH 225 an MATH 321 may be taken concurrently or in either orer. In aition to analytical methos this course will also provie an introuction to numerical solution techniques. Prerequisites: MATH 125 with a minimum grae of C. 3 creits. Course Outcomes: A stuent who successfully completes this course shoul be able to: 1. Ientify an appropriate metho an use it to solve first orer orinary ifferential equation. 2. Solve homogeneous an non-homogeneous higher-orer orinary ifferential equations. 3. Implement the use of Laplace Transforms to solve an orinary ifferential equation. 4. Analyze an solve applications involving orinary ifferential equations. Some examples of applications inclue: circuits, vibrating systems, chemical mixing, an population moeling. 5. Apply the techniques for solving linear systems of orinary ifferential equations. 6. Implement the use of a software package to ai in solving ifferential equations numerically an analytically. Graing: Graing will be ifferent between the two sections. Be sure to rea the correct column in the following table. 1
Section 03 Section 06 Homework 17% 0% Quizzes 15% 15% Exam 1 17% 21% Exam 2 17% 21% Exam 3 17% 21% Exam 4 17% 22% Exams will be hel uring the common exam hour 7-8am on Thursays, ates to be etermine. The final exam is scheule for Wenesay, May 6, from 3-4:50pm. For the purposes of this class no grae of D will be given. Help: I am here to make sure you learn an unerstan the material. It is your job to let me know when you are having ifficulties. I will be gla to work aroun your scheule to help you. Stuents with special nees or requiring special accommoation shoul contact the instructor an the campus ADA coorinator at 394-1924 at the earliest opportunity. Technology: Maple 13 will be require. While computers are not banne from the classroom, the only reason you shoul have your computer out is to take notes. If you are taking notes, your computer screen shoul be own. This is a consequence of past problems, an this ecision has been mae in orer to improve stuent performance. Homework: Homework will be hanle ifferently between the two sections. Be careful to rea the correct section. Section 03: Homework will be assigne an collecte via WebAssign. You will nee to log in to the WebAssign website an enroll in this course. Homework will be ue one week after the material for that section is complete in class. Section 06: Homework will be assigne regularly, but will not be collecte. Assignments will be short, but will cover the material presente. Homework is a learning tool. If quiz an exam scores are low it is an inication that more homework shoul be one beyon what is assigne. Quizzes: Quizzes will be given regularly. They will mirror homework problems, an may be given one week after homework for that section has been assigne. The extra time provies an opportunity for questions. No warning of quizzes will be given. Quizzes are there to give you an inication of how well you unerstan the material. If quiz scores are low it is an inication that more homework shoul be one beyon what is assigne. Makeup quizzes will only be given for those who give avance notice of a legitimate absence. 2
Freeom in Learning: Uner Boar of Regents an University policy stuent acaemic performance may be evaluate solely on an acaemic basis, not on opinions or conuct in matters unrelate to acaemic stanars. Stuents shoul be free to take reasone exception to the ata or views offere in any course of stuy an to reserve jugment about matters of opinion, but they are responsible for learning the content of any course of stuy for which they are enrolle. Stuents who believe that an acaemic evaluation reflects prejuice or capricious consieration of stuent opinions or conuct unrelate to acaemic stanars shoul contact the ean of the college which offers the class to initiate a review of the evaluation. All of this is subject to change. 3
The Dealy Sins of Mathematics (Aapte from Dr. Kowalski) If any of the following mistakes are mae on a quiz or exam problem, zero points will be assigne as a grae for that problem. 1. False Distribution Thou shalt no istribute (or factor) anything across a sum (or ifference), except multiplication. a b+c a b + a c a+b c = a c + b c (a + b) c a c + b c Ex1: (x + 2) 2 x 2 + 2 2 (x + 2) 2 = x 2 + 4x + 4 Ex2: t + 5 t + 5 sin (a + b) sin a + sin b e a+b e a + e b log (a + b) log a + log b log (ab) = log a + log b 2. False Cancellation Thou shalt not cancel any expression from a fraction, except common factors foun after thou hast factore first. ax+b a sin a sin b a b ln a ln b a b x + b 3. False Proucts Thou shalt not ifferentiate any prouct (or quotient, or composition) factor-by-factor. f (f(x)g(x)) ( f(x) g(x) g ) ( f(x) ) g(x) (f g)(x) f(x)g(x) (f g)(x) = f(g(x)) f ((f g)(x)) g 4
4. Trignorance Thou shalt not plea ignorance of trigonometric (or inverse trigonometric) functions at stanar values. Thou shalt also know the stanar trigonometric an inverse trigonometric erivatives an integrals. cos (2x) 2 cos (4x) tan 1 (x) cot x (tan x) 1 = cot x (sec (2x)) sec tan (2x) (sec (2x)) = 2 sec (2x) tan (2x) 5. Other common sins ln 0 0 ln 1 = 0 e a ln b ab e a ln b = e ln ba = b a 9 3 9 = 3i ln (x) 1 x 5
MATH 321 Differential Equations Homework Assignments (Zill, Tenth Eition) Section Page Problems 1.1 Definitions 10 1 8, 13, 14 2.2 Separable Equations 51 1 7, 23 2.3 Linear Equations 61 1 10 3.1 Linear Moels 90 3, 5, 9, 17 2.5 Bernoulli ODE 74 15 22 - Reucing Secon Orer Equations see below Exam 1 4.3 Homogeneous Equations 137 1 19 (o) 4.2 Reuction of Orer 131 1 4, 9 11 4.4 Metho of Unetermine Coefficients 147 2 11, 21 24 4.6 Variation of Parameters 161 2, 3, 5, 6, 10, 12 5.1 Linear Moels 205 21, 25, 29 Exam 2 7.1 Laplace Transform 280 11 18, 25, 28, 30 32 (use table) 7.2 Inverse Transforms 288 [1 9 (o), 11 13, 16, 17, 20, 23 29 (o), 30] [31, 32, 35, 37, 39] 7.3 Operational Properties I 297 [27 30], [37 39, 41 43, 45, 47, 49 54, 63 68] 7.5 Dirac Delta Function 315 4, 5, 8, 10, 11 Exam 3 8.1 Linear Systems 332 1, 7, 11 8.2 Homogeneous Linear Systems 346 [1 3, 11], [33 35, 41], [22 25] 8.3 Nonhomogeneous Linear Systems 354 12, 15, 21 24 2.6 Euler s Metho 79 1 4 9.2 Runge-Kutta Methos 371 3 6 9.4 Higher-Orer Methos 379 1 4 Exam 4 Aitional problems for 2.5. Solve the following ODE s by reucing the ODE to first orer. 1. t 2 y + 2ty 1 = 0, t > 0 2. ty + y = 1, t > 0 3. y + t(y ) 2 = 0 4. y 2y = 2e 2t 5. y + y = e t 6. t 2 y = (y ) 2, t > 0 6