SOLVING SECOND ORDER DIFFERENTIAL EQUATION NON-LINEAR

calculate imaginary quadratic roots in C code using one square root, Holt Pre-Algebra pre-algebra exercises, simplifying expressions worksheet AND combining like terms, using symbolic equations to solve real world problems Thank you for visiting our site! You landed on this page because you entered a search term similar to this: __solving second order differential equation non-linear__, here's the result:

An introduction to elementary techniques, concepts, theory and applications. SHORTCUT TO THE ASSIGNMENTS: - Assignment: | |
ANNOUNCEMENTS: - The final exam is now posted. I selected a due date after the break. If you want to wait to take it, I will have office hours devoted to ODEs when you get back, to ask any last-minute questions.
- My office hours generally will be Thursday, 4:00-5:30 and Friday, 4:00-5:30. In addition, I will schedule evening hours once or twice each week.
- Unless otherwise indicated, homework will be dueFridays at 5:30 PM inthe "In Box" outside my office, Olin Center 261. Graded homework papers will be available in a box outside my office in the Olin Center.
0. Information - Outline -- The course outline is available here.
Reading -- Read the note on written homework found here. Problem -- If you have not filled one out for me before, please complete the information sheet found here and bring it to class on Tuesday, January 31. Final Examination Due Thursday, March 30.You can download the final examination when you are ready totake it. Budget three hours. You may download the instructions for thefinal at any time.The exam is thorough, and substantially based on problems verysimilar to homework exercises and quizzes. You can best prepare byreviewing the topics that were covered by the quizzes, by reading thetextbook examples in the sections that we covered, and by reviewingyour homework notebooks. There are 12 problems on the exam. The first8 are largely mechanical and cover all of the basic methods forsolving first and second order equations that we have learned. Thelast four problems are application problems that involve analyzing agiven model, or setting up a simple ODE from a description and thenanalyzing that. I would say that of the problems, two of them aresomewhat challenging, seven of them are eight of them arestraightforward, and the other two somewhere in between. You may takethe exam at any time. If you want to finish it before break, turn itin at my office. If you want to finish it over break, you may fax itto me at 781-292-2505. Here are some good practice problems for the exam, from the text:2.1.10, 2.1.11, 2.2.8, 2.2.20, 2.3.4, 2.5.17, 2.5.23, 3.1.10, 3.4.18,3.4.12, 3.6.6, 3.6.9, 3.6.13, 3.7.2, 3.7.3, 3.8.27, 3.9.11. 6. Due Wednesday, March 15 : Applications of second-order equations to mechanical systems; higher order constant coefficient equations; linear systems of differential equations. - Read these sections in the text: 3.9; 4.2; 7.5
Write-up the following graded exercises. Be sure to read the guidelines for writing homework assignments. (3.9) 9, 12, 13, 17 (4.2) 39 (7.5) 1, 5 (We will cover this topic in class on Tuesday.) You can download Quiz 3 when you are ready to take it. The quiz will take 40 minutes. You will be asked on the quiz to use your computer to produce graphs of solution formulas that you detemine. Before starting the quiz, please review how to produce graphs of functions in Matlab or Maple. You might review how to draw a graph of a function that is piecewise defined (e.g. y = f(t) for 0 5. Due Wednesday, March 8 : Applications of second-order equations to mechanical systems; higher order constant coefficient equations. - Read these sections in the text: 3.8, 3.9, 4.1, 4.2
Write-up the following graded exercises. Be sure to read the guidelines for writing homework assignments. (3.8) 6, 9, 27, 29 (4.2) 12, 17, 29, 34 (you may use a computer or calculator to find zeros of the characteristic polynomial) You can download Quiz 2 when you are ready to take it. The quiz will take 40 minutes. 4. Due Thursday, March 2 : Second order linear equations; initial value problems; fundamental sets of solutions; constant coefficient, homogeneous equations; non-homogeneous equations; method of undetermined coefficients; method of variation of parameters; applications to mechanical systems; resonance; beats. - Read these sections in the text: 3.6, 3.7, 3.8, 3.8
Work on the following practice exercises, that you should keep a record of in a notebook, but do not have to write-up and turn in: (3.6) 1, 2, 6, 11 (3.7) 1, 3 (3.8) 1, 7, 15 Write-up the following graded exercises. Be sure to read the guidelines for writing homework assignments. (3.4) 14, 22, 33 (3.6) 8, 11, 13, 29 (3.7) 2, 5, 21 (3.8) 11, 13, 21 - Read these sections in the text: 3.1, 3.2, 3.3, 3.4, 3.5
Work on the following practice exercises, that you should keep a record of in a notebook, but do not have to write-up and turn in: (p.132) 34a (3.1) 1, 3, 5, 13 (3.4) 2, 4, 6, 8 (3.5) 1, 5, 7, 9, 17 Write-up the following graded exercises. Be sure to read the guidelines for writing homework assignments. (p. 132) 33, 35 (3.1) 8, 15, 21 (3.4) 10, 14, 19, 24, 33 (tricky!) (3.5) 10, 14, 18, 19 You can download Quiz 1 when you are ready to take it. 2. Due Friday, February 10: Linear and non-linear equations; separation of variables; integral curves; initial value problems; physical applications; non-dimensionalization and change of variable; autonomous equations; population models. - Read these sections in the text: 2.3,2.4; 2.5
Work on the following practice exercises, that you should keep a record of in a notebook, but do not have to write-up and turn in: (2.4) 13, 14, 15, 17, 27 (2.5) 1, 2, 4, 7, 10, 15 Write-up the following graded exercises. Be sure to read the guidelines for writing homework assignments. (2.3) 25 (2.4) 25, 26, 28, 32 (Note: These problems do not depend on the Theorems in (2.4) ) (2.5) 3, 19, 20 In addition do the following problem: For an object moving vertically in a uniform gravitational field with a viscous drag force proportional to velocity: (1) Write the equation of motion for velocity (2) Determine a change of scales to non-dimensionalize the equation (3) Solve the non-dimensional equation (4) From this solution, determine the solution to the problem in the original units. - Read these sections in the text: 1.1, 1.2, 1.3; 2.1, 2.1, 2.3,2.4; 2.5
Work on the following practice exercises, that you should keep a record of in a notebook, but do not have to write-up and turn in: (1.1) 1, 3, 22, 23 (1.2) 9, 17 (2.1) 5, 6, 9, 10, 17, 21, 22 (2.2) 1, 4, 15, 21, 27 (2.3) 1, 20, 21 Write-up the following graded exercises. Be sure to read the guidelines for writing homework assignments. (2.1) 31, 38 (2.2) 16, 21, 30 (2.3) 2, 15, 22 |

1-26-06 |