Math-305, Numerical Methods & Matrices
Dr. Kevin G. TeBeest
Fall 2014

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• You should check this page daily and begin working the assignments immediately after they are posted.
• You are expected to do all assigned problems. You may need to do additional problems for practice.
• You are expected to read the textbook as we cover the material.
• The day the assignment was posted is shown.

 Assignments will be posted below AS we cover the material. Do all the examples in the first Maple tutorial entitled Basics. October 6 Do not use the shortcut menu buttons in the left panel of Maple. Rather, manually type the commands as they appear in the Maple examples. You should work all assigned Maple examples immediately to help you prepare for the programming assignments. There may be Maple related questions on exams (see the course policy). Kettering has made Maple amply available on many PCs throughout the AB. Read Sections 0.1, 0.4, and 0.6. October 6 (Because you should always read sections as we cover the material, normally I do not post reading assignments.) Repeat the example I worked in class but pretend you are a 3-digit rounding computer. October 9 Do this problem on truncation error. (requires Acrobat Reader) October 9 Section 0.7 – Polynomial Nested Form / Truncation Error. October 9 Since the use of Maple is required in this course, you should be finished with Assignment 1 by now. Read Sections 1.1 and 1.2. Also play with Maple.  October 10 Do all the examples in the second Maple tutorial entitled Solutions of Equations. October 10 You should complete Assignment 1 before doing this one. Remember that these assignments will acquaint (or reacquaint) you with Maple and prepare you for the programming assignments. Section 1.1 – Bisection Method. October 13 Write the Maple code for the Bisection Method. October 15 NOTE: Do this immediately, and play with the code by changing the starting interval, the tolerance, even the function. You will use this code as the template for writing the codes for other methods and for our first programming assignment. Do all the examples in the 8th Maple tutorial entitled Formatted Printing and Plot Options. October 15 Then change your Maple code for the bisection method so that it uses formatted printing. From now on we will use the printf command for printing. Section 1.2(a) – False Position. October 15 Section 1.3 – Newton's Method. October 16 Section 1.5 – Fixed Point Method. October 17 Section 1.5(b) – Fixed Point Method with Aitken Acceleration. October 22 ``` ``` THE FINAL EXAM CONTENT BEGINS HERE. . . Section 3.2 – Newton-Gregory Interpolating Polynomials. October 27 Do this example that shows how to use Maple to generate an interpolating polynomial through points. October 31 Sections 5.2 & 5.3 – Proper Integrals: Trapezoidal Rule and Simpson's Rules. November 5 Note:   This is a running assignment — do the problems on this sheet as we cover the material. Write the Maple code for the trapezoidal rule. November 7 NOTE: Do this immediately, and play with the code by changing the number of subintervals, the limits of integration, even the integrand f(x). You will use this code as the template (model) for writing the codes for other methods and for the second programming assignment. Section 5.3:   Simpson's – 1/3 Rule. November 7 Section 5.3:   Simpson's – 3/8 Rule. November 7 Program Assignment 2.   Due Wednesday, Nov. 19 (Week 7).   Posted Nov. 8 You should have the trapezoidal rule code (see Assignment 17) running properly before you attempt this program assignment. You will use it as a template (model) for this project. Read this document before beginning this assignment. Recall that Assignment 16 is a running assignment. Do all the examples in the third Maple Tutorial entitled Derivatives and Integrals. November 10 Section 5.6 – Gauss Quadrature. November 12 Section 5.1 – Numerical Differentiation. November 14 Chapter 6 (a) – Implicit Euler Method. November 19 Chapter 6 – Numerical Solutions of ODEs. November 19    This is a running assignment. Write this Maple code for Euler's Method. November 19 NOTE: Do this immediately, and play with the code by changing the nodal stepsize, the interval endpoints, the IC, even the ODE. Use it to check your work on some of the homework problems. You will use this code as the template (model) for writing the codes for other methods and for the third project. BEWARE:    The math faculty have observed that during the final 3 to 4 weeks of a term, especially around and after Thanksgiving, many students have a tendency to: 1) skip class more, and 2) let their studies in math courses slide as they complete term projects or term papers in other courses. Be careful not to do that! I often see students leave entire pages blank on the final exam (indicating that they probably did not do the assigned homework), and they end up seriously hurt their course grade. Remember that the final exam is worth 30% of the course grade, so make sure you continue to study and do all the assigned homework. Also, realize that one purpose of a final exam is so you can show that you have mastered a concept that you might have scored poorly on in one of the exams. So view the final exam as an opportunity to raise rather than lower your course grade. Review the Maple tutorial entitled Formatted Printing and Plot Options. November 20 Don't forget that Assignment 25 is a running assignment. Program Assignment 3. Due Thursday, December 11 (Week 10) at 1:20. Posted November 30. Also read this document Programming Requirements. Here are the formulas for the Runge-Kutta-Fehlberg method. See some of the results for the sample problem in Part I. Section 6.3: Runge-Kutta-Fehlberg and Runge-Kutta-Verner Methods. December 1 Additional Programs for Solving IVPs. December 1 Section 2.1 – Matrix Introduction. December 3 Section 2.2 – Gauss Elimination. December 4 On Friday I will finish the example I started on Thursday. (You could actually finish it yourself as there is little left to do.) Section 2.2(b) – LU Decomposition. December 5 Read and do these Maple examples for solving a system of linear equations. December 8 Determinants and Existence–Uniqueness of Solutions. December 10 Section 2.2(d) – Homogeneous Systems. December 10 Have you read the information about our final exam under the Announcements at the top of this web page? Nineteen (19) of 62 students (31%) worked Opportunity 3 correctly. I will return them tomorrow (Friday). If you worked it correctly, then I will have you return it to me immediately (to avoid having some of you forget to bring it with you to the final exam). Section 2.3 – Matrix Inversion. December 12 Section 2.3(b) – Determinants and Singular Matrices. December 13 Section 2.4 – Vector & Matrix Norms. December 16 Section 2.4(c) – Residuals, Condition Number, and Ill-Conditioned Matrices. December 16 ``` ``` Facie (noun)   \'fā • cē,    'fay • see\    pl. facies   \'fā • cēz,    'fay • seez\ : an image of one's face taken by oneself or by another person using a digital camera or phone, especially for posting on social networking sites or smartphones for personal identification. a photo ID showing only the face. First Known Use of FACIE – 16:34 UTC, October 12, 2014 by Kevin G. TeBeest, Michigan USA Formerly:   "profile photo" (archaic) Usage:  Professor TeBeest sent a photo of himself playing his drums to his brother who wanted a photo ID for his smartphone. The brother whined saying, "Send me a photo of your ugly face you stupid. . .!" So Professor TeBeest sent his brother a facie. Etymology:  French façade ("a false, superficial, or artificial appearance or effect," Merriam–Webster); Italian facciata, a derivative of faccia ("front"), from Latin facies ("face"); Geographical Use:  worldwide Not to be confused with selfie, which is a photo taken by oneself of one's own body or part of the body, usually due to vanity. The photo on your state driving license is an example of a facie. Inform your friends and family! Let's make it go viral. Start using it in conversations and online and explain it when they ask you what it means. It's fun! ` `

Remember that:

1. You are responsible for successfully completing all assigned problems in all your courses.
2. The exams may include problems similar to these assignments and lecture examples and may include questions about Maple.
3. We must maintain a steady pace to cover the material that constitutes Math-305. If you have difficulty with a section, be sure to see me for help immediately.
4. No matter how simple a topic appears when you see my examples or read the text, you will almost certainly have difficulty completing an exam if you do not practice the examples and do the assignments beforehand.