MAT 303 (Calculus IV with Applications)

Introduction to Differential Equations

Spring 2010

Most of the fundamental laws and principles of nature are expressed mathematically as differential equations. This course discusses the the basic methods for solving ordinary differential equations, with applications to the physical, biological and social sciences. Particular emphasis is given to linear differential equations and systems of equations.

The prerequisite is completion of one of the standard calculus sequences (either MAT 125-127 or MAT 131-132 or MAT 141-142) with a grade of C or higher in MAT 127, 132 or 142 or AMS 161. The course will rely heavily on material you've learned in Calculus I-II. Familiarity with complex numbers and the basic concepts of linear algebra will be important, so the 200-level classes MAT 203/205 (Calculus III) or AMS 261/MAT 211 (Linear Algebra) are strongly recommended.

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Announcements:

• Review Sessions: Review sessions for the Final Exam are:
  Steve Taylor, Friday, May 7, 11:45am - , in Physics P123.
  Ben Balsam, Monday, May 10, 10:00am - , in Math P131.
  Steve Taylor, Monday, May 10, 7:00pm - , in Math P131.
  
  
• Final Exam: The Final Exam is on Thursday, May 13, 5:15-7:45pm, in the usual lecture room, Library W4525. The exam will be cumulative, covering the full semester of material from Chapters 1 - 5, but with some emphasis on Ch.5. The character of the exam is similar to the Midterms. There will be 9-10 problems, mostly computational, but with a couple of conceptual/theoretical problems testing basic understanding of the theory. A practice exam will be up on this site this weekend (May 8), as well as suggested problems for Ch.5.6 (variation of parameters).
  
  Here is a Practice Final and the Solutions from a previous year. Ignore the instructions (which are not valid here) and consider only the problems 2-5, 8 and 12-19. These problems represent however only a portion of the material that may be on the exam itself. It would be better to prepare by going over earlier HW problems and solutions and testing yourself on other problems from the text. The problems on the final will be very similar (maybe identical) to problems at the end of the sections in the text. For Section 5.6, consider for example problems 23 or 25. (Problem 17 was done in class). The problems on the exam will not be computationally very complicated, but test your ability to carry out the methods you've learned.
  
  
• Midterm II: the 2nd Midterm is on Thursday, April 8, 12:50-2:10pm, in class.
  Here is a Practice Midterm II from a few years ago. Note: both the problems and the solutions are together here, so you may want to ``cover-up'' the solutions and try the problems yourself before looking at the solutions. Ignore Problem 5. You can also look at Midterm II exams from previous semesters by looking at this link
  The exam will cover the material in Chapter 2.4 and everything we did in Chapter 3, so up to and including 3.6.
  
  
• Midterm I: the 1st Midterm is on Thursday, Feb 25, 12:50-2:10pm, in class.
  Here is a Practice Midterm I from a few years ago. A few inaccuracies: the Midterm will last 80 minutes and will have 5-7 problems. Also, ignore Problems 8, 12 and 13 on the practice exam; otherwise, the problems accurately reflect the character of the actual Midterm.
  
  

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• Instructor: Michael Anderson

• Office Location: 4-110 Math Tower

• Email: anderson at math.sunysb.edu

• Web site: http://www.math.sunysb.edu/~anderson

• Office hours: MWF 1-2pm in 4-110 Math Tower

  MAT 303

  Lectures and Recitations Note: May not be taken for credit in addition to MAT 305 or AMS 361.

  Final Exam: Thursday May 13, 5:15-7:45pm, Place: TBA

  LEC 1	41259	Tu,Th	12:50pm- 2:10pm	Library	W4525	Michael Anderson
  R01	41005	F	11:45am-12:40pm	Physics	P123	Stephen Taylor
  R02	49316	W	11:45am-12:40pm	Physics	P123	Benjamin Balsam
  R03	58873	M	10:40am-11:35am	Soc Behav Sci.	N436	Benjamin Balsam

• R01: Stephen Taylor

• Email: taylor at math dot sunysb dot edu

• Office: 3-101 Math Tower

• Office hours: Tu: 11:30-12:30 in 3-101, Th: 11:30-12:30 in MLC

• R 02,03: Benjamin Balsam

• Email: balsam at math dot sunysb dot edu

• Office: 3-104 Math Tower

• Office hours: Tues: 10-11 in 3-104, Wed: 2-3 in MLC

Course Text:

• Differential Equations and Boundary Value Problems, by C. H. Edwards, Jr. and D. E. Penney (Prentice-Hall, Inc.), Fourth Edition.(Note, that problem sets in different editions do not coincide)

Computer resources:

• DiffEqWeb a graphical ordinary differential equation solver written by Simo Kivelä and Mika Spåra of the Helsinki University of Technology.

• Programs for Euler's method and slope field generation for graphing calculators (Texas Instruments TI-82, TI-85 and Sharp EL-9300, EL 9200).

• MAPLE reference pages. Elementary numerical and graphical examples (these pages were prepared by Stewart Mandell for use in our course MAT 126 several years ago). If you need help getting used to MAPLE, these are a good place to start.

• Some additional reference pages which describe how to use MAPLE to investigate properties of differential equations :

  • a beginning tutorial (introduces you to the syntax of MAPLE)

  • direction fields

  • symbolic solutions of differential equations

  • numeric solutions of differential equations

Homework and Quizzes:

There will be both Homework assignments and quizzes, alternating weekly; one week HW, the next week quiz, etc. There will be HW problems given every week - see the assignments below - and each quiz will contain problems taken from the HW assignments. HW will be collected during the recitations, as determined by your TA; they should always be turned in at the beginning of class. Please, remember that your solutions of the homework problems and quizzes are important documents. You should keep them to the end of the semester.

Although only a random selection of problems on each homework will be graded by your TA, it is important that you do all the HW problems (or at least as many as possible). You should not expect to do well on the exams without the work and experience that goes into solving the HW and quiz problems.

Late homeworks will not be accepted except under very exceptional circumstances. Likewise, no late quizzes will be given. All policies regarding HW, quizzes and your grades for this part of the course are fully decided by your TA.

Grading Policy:

Grades will be computed according to the following percentages:

No make-up exams will be given. If a midterm exam is missed because of a serious (documented) illness or emergency, your semester grade will be determined on the basis of other work done in the course. Exams missed for other reasons will be counted as failures.

Resources: If you have questions regarding the course material at any time during the semester, you are encouraged to visit your instructor or TA during office hours, or make a separate appointment if necessary. Your instructors will also reply to email, within reason. Another excellent source of help is the Mathematics Learning Center (S240A in the Math Building - basement level), which is staffed by advanced math majors and graduate students daily. For a schedule of their hours, check their website.

Students with Disabilities: If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, you are strongly urged to contact the staff in the Disabled Student Services (DSS) office: Room 133 in the Humanities Building; 632-6748/TDD. DSS will review your concerns and determine, with you, what accommodations are necessary and appropriate. All information and documentation of disability is confidential. Arrangements should be made early in the semester so that your needs can be accommodated.

Schedule of Topics

but do not hand in for grading. Instead, a quiz will be given that week, based on the assigned HW problems.

Week of	Topics	Problems Due	Recitation Due Dates
Jan. 25	1.1: Mathematical Models 1.2: General and Particular Solutions	-----------
Feb. 1	1.3: Direction Fields 1.4: Separable Equations	1.1: 3,5,13,19,27 1.2: 4,8,15,42 1.3: 2,8,21	HW #1: FMW, Feb 5 - Feb 10
Feb. 8	1.5:Linear First Order Equations 1.6: Subsitution/Exact Equations	1.4: 1,2,3,4,6,47,48 1.5: 1,2,3,12,15	HW #2: FMW, Feb 12 - Feb 17
Feb. 15	2.1:Population Models 2.2: Equilibrium Solutions	1.6: 3,8,17,34,57 2.1: 2,4,10,11	HW #3: FMW, Feb 19 - Feb 24
Feb. 22	2.4:Numerical Methods Midterm I Exam	No HW or Quiz this week, due to Midterm	No HW due
Mar 1	3.1:Second order linear equations 3.2: General solutions of linear equations	2.2: 9, 21 2.4: 4,8 3.1: 4,10,14,34,40,46	HW #5: FMW, Mar 5 - Mar 10
Mar 8	3.2:General solutions of linear equations 3.3: Homogeneous constant coeff. equations	3.1: 17,20,21,29 3.2: 1,8,18,31 3.3: 4,13,14,34	HW #6: FMW, Mar 12 - Mar 17
Mar 15	3.4:Mechanical Vibrations 3.5: Non-Homogeneous equations	3.3: 18,23 3.4: 1,3,14,15,16 3.5: 1,2,3,9	HW #7: FMW, Mar 19 - Mar 24
Mar 22	3.6:Forced Oscillations and Resonance 3.7: Electrical Circuits	3.5: 6,11,35,38 3.6: 1,8,11,19	HW #8: (Quiz) FMW, Mar 26,Apr 5/7
Apr 5	4.1:First order systems Midterm II
Apr 12	5.1:Matrices and Linear Systems 5.2: Eigenvalue Method; Homogeneous systems.	4.1: 1,6,11,13,21,22,23	HW #9: FMW, Apr 16 - Apr 21
Apr 19	5.4:Multiple Eigenvalues (briefly) 5.5: Matrix Exponentials	5.1: 14,22,26,35 5.2: 9,12,19,41 5.4: 2,3,11	HW #10: FMW, Apr 23 - Apr 28
Apr 26	5.5:Matrix Exponentials 5.6:Nonhomogenous Systems	5.5: 2,4,10,16,26 5.6: 2,5,14	HW #11: FMW, Apr 30 - May 5