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MATH 204 Differential Equations Mon, Tues, Wed, and Thurs 1:00 to 2:35 AM Room D108 (MW) B107 (TTh) 5 UNITS Instructor: Larry Green Phone Number Office: 541-4660 Extension 341 Internet e-mail:...greenl@ltcc.edu Home Page: http://www.ltcc.edu/depts/math/ Required Text Elementary Differential Equations seventh edition by William Boyce and Richard DiPrima Course description This is a beginning course in ordinary differential equations, including traditional topics, series solutions, applications and LaplaceYour Grades transforms. Prerequisite A grade of C or better in Math 107 or equivalent. Grading Policy Your letter grade will be based on your percentage of possible points. A 90 -- 100% C 70 -- 79% B 80 -- 89% D 60 -- 69% Homework: ............................................….75 points Poster Session: May 11..............................100 points Midterm 1: April 22....................…...…......150 points Midterm 2: May 19.................................…150 points Midterm 3: June 17.....................…………150 points Final Exam: June 21............................…....375 points Exam Policy Students are to bring calculators, pencils or pens, and paper to each exam. Grading will based on the progress towards the final answer, and the demonstration of understanding of the concept that is being tested, therefore, work must be shown in detail. Any student who cannot make it to an exam may elect to take the exam up to two days before the exam is scheduled. If all homework is completed and no more than three homework assignments are counted late, then the midterm with the lowest score will be dropped. Homework Policy Homework will be turned in at the end of class on the date due or by 5:00 PM at the instructor's office. Homework that is turned in within one week of the due date will be counted as half credit. Homework may be turned later than one week after the due date, but points will not be awarded. Extra Credit Any student who has turned in every homework assignment may elect to work on an extra credit assignment or project that will count as additional points towards either a midterm or the final. Poster Project The project involves investigating an application of differential equations and physics. Exceptions will be made for students without a physics background. The display must be approximately 1 meter by 1.3 meters. You may write any equation by hand. You are encouraged to have Math View, Maple, Origin assist you in the project. Ideally you should work on the project with one partner, but an exception can be made under special circumstances. Your abstract is to be a one-paragraph description of your project. It will be due on May 4. Included in your abstract should be a set of references that you intend to use. From 12:00 to 1:00 on May 11 you will be expected to stand by your project and answer questions from the judges and observers. The projected will be graded on both content and presentation. Course Objectives The successful student will
Registration 1. You must register for this class in order to attend. 2. You may drop the class with no penalty or mark on your record on or before Friday, April 30. 3. After April 30, you may drop the class and receive a grade of W until Friday, June 4. 4. After June 4, if you are enrolled, you will receive one of the following grades: A,B,C,D,F or I (Incomplete, must be negotiated with the instructor and is only allowed in special cases). In this class, it is your responsibility to drop the class in order to avoid an unwanted grade. OFFICE HOURS: Monday ............................ 12:30 to 1:30 PM A210 Tuesday and Thursday...... 10:00 to 11:00 AM GMC Wednesday .................... 11:00 to 12:00 AM A210 Friday........................ 11:00 to 12:00 A210 CALCULATORS: A graphing calculator is required for this class. There are a variety of such calculators on the market. The instructor will be using a Texas Instruments-85. Instructions on the TI 89 Calculator LEARNING DISABILITIES: If you have a learning disability, be sure to discuss your special needs with Larry. Learning disabilities will be accommodated. HOMEWORK ASSIGNMENTS Lecture will always be geared towards an explanation of the topics that will be covered on the upcoming homework assignment. Date Section Topic Exercises 4-5 Introductions 4-6 1.1
Direction Fields
4, 15, 18, 24 4-7 1.3 Classification
2, 6, 11, 17, 20, 23, 27 4-8 2.1 Linear Equations 6, 13, 16, 19, 27, 30, 33
4-12 2.2 Separable Equations 1, 8, 18, 26, 31, 34, 37 4-13 2.3 Modeling 1, 5, 10, 20, 26, 33 4-14 2.4 Linear vs. Nonlinear 3, 10, 16, 23, 27, 30, 33 4-15 2.5 Population Dynamics 2, 12, 16, 18, 21, 23, 24
4-19 2.6 Exact Equations 8, 17, 22, 24, 27, 30 4-20 2.8 Existence & Uniqueness 2, 13, 14, 15, 16, 17, 18 4-21 2.9 Difference Equations 1, 4, 7, 10, 14, 16 4-22 Midterm I
4-26 Return Midterm I 4-27 3.1 Constant Coefficients 2, 10, 17, 21, 30, 37, 41 4-28 3.2 Fundamental Solutions 4, 11, 15, 18, 25, 30, 32, 35 4-29 3.3 The Wronskian 1, 4, 10, 13, 17, 21, 25, 27
5-3 3.4 Complex Roots 3, 7, 14, 20, 27, 37, 42 5-4 3.5 Repeated Roots 8, 14, 18, 19, 23 ,29, 32, 35 5-5 3.6 UC Functions 3, 8, 14, 17, 32, 35 5-6 3.7 Variation of Parameters 1, 10, 16, 20, 22, 23, 30
5-10 3.8 Vibrations 4, 7, 11, 15, 21, 27, 30 5-11 Poster Project An example of forced vibrations gone bad 5-12 3.9 Forced Vibrations 4, 6, 10, 15, 16, 20 5-13 4.1
nth Order Equations
1, 8, 14, 23
5-17 4.3 UC Functions 1, 4, 9, 11, 16, 20, 21 5-18 4.4 Variation of Parameters 1, 6, 8, 11, 13, 14, 16 5-19 Midterm II 5-20 Return Midterm II
5-24 5.1 Power Series 5, 13, 18, 20, 21, 23, 25, 28 5-25 5.2 Series Solutions I 3, 10, 14, 17, 21, 24, 27 5-26 5.3 Series Solutions II 2, 7, 10, 14, 19, 26 5-27 5.4 Regular Singular Points 4, 9, 14, 19, 25
5-31 Memorial Day 6-1 5.5 Euler Equations 4, 15, 19, 23, 27, 31 6-2 6.1 Laplace Transform 5, 10, 14, 18, 25, 26, 27 6-3 6.2 Initial Value 4, 8, 14, 19, 25, 27, 37
6-7 6.3 Step Functions 3, 9, 16, 22, 26, 31 6-8 6.4 Discontinuous Forcing 2, 8, 13, 20 6-9 7.2
Matrix
Review
22, 25 6-10 7.4 System of Diff Eqs. 2, 3, 4, 5, 6, 8, 9
6-14 7.5 Homogeneous Systems 4, 8, 12, 16, 20, 24, 29 6-15 7.6 Complex Eigenvalues 4, 10, 12, 17, 22, 25, 28 6-16 Review 6-17 Midterm III
6-21 Comprehensive Final Exam 2:00 PM - 3:50 PM
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