APM 5441-F20-Syllabus PDF

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Department of Mathematics and Statistics Math Analysis for Engineers I APM 5441, Fall 2020 Section 40220 Class Time: MW 5:30-7:17 PM Class Room: FULLY ONLINE! Credits: 4 Faculty: Meir Shillor Office: 553 MSC (Not in use currently) Phone: 248-370-3439 (Not in use currently) email: [email protected] Office Hours: Monday 1:30-3:00 PM, Thursday 5:00-6:30 PM, or by appointment. These will be held on the web, and the details will be provided when available.

Important Dates: Sept. 3 - First class Sept. 17 - last day 100% tuition refund and last day "no-grade" drop Nov. 9 - Last day for official withdrawal (W grade) Nov. 25- Thanksgiving Dec. 7 - Last class Dec. 14 - Final Exam

Discussion board and chat room Please post course related questions in Moodle, and answer questions of your colleagues if you can. I will check it often.

Prerequisites: Passing grade in MTH 254 (Multivariable Calc), MTH 256 (Linear Algebra), and MTH 257 (Int. Differential Equations).

Text: Advanced Engineering Math., E. Kreyszig, 10th Ed. If you have the 8th or the 9th eds please check the homework problems, as these are usually shifted a bit. We shall cover parts of Chapters 6, 9-11, and some additional material from Chpts. 7 and 8 (see detailed syllabus below).

Exams: The grade in this course will be based on two 90 min web exams, each worth 150-pts and a Final Exam worth 200 pts, to total of 500 pts. The exams schedule (during class time 5:30-9:00): Monday Oct. 12, Monday, Nov. 16, Final Exam Dec. 14 (comprehensive), 7-10 PM The exams are closed book exams. You may use in each of the midterm exams a one ONE-sided freely written page. In the Final you may use one sheet freely written on both sides. The technical details are not known yet. There will be no make-up exams. In case a legitimate, documented reason for missing an exam is promptly given to the instructor, a grade for that exam will be determined by that portion of the final exam corresponding to the missed material, or by another way agreed with the student. The details of how the exams will be conducted will be posted when available!

GRADES: The grading scale in this course is: 94-100%----A 87-93%----A79-85%---- B+ 73-78%----B 65-72%----B60%----C 50%----D

HOMEWORK: Homework will be assigned on a regular basis, but will not be collected. In order to do well on the tests, you must do the homework assignments on a regular basis. At least two hours should be spent on homework for each. The homework assignments represent the minimum amount of mental exercise necessary to learn the material; students having difficulties with any particular topic should do more than just the assigned problems. In addition to doing the homework, you should keep on top of the subject by regularly reviewing earlier material, asking questions in class, and making use of office hours.

CONDUCT: Success in this course requires an atmosphere conducive to learning. As a courtesy to your fellow students and instructor, please come to class on time and refrain from extraneous conversation during class. All electronic communication devices such as portable stereos, phones, etc. must be turned off prior to entering classroom. If circumstances make it necessary for you to leave early, please notify the instructor in advance and sit near the door. Otherwise, come prepared to stay for the entire class. For proper and improper academic behavior please consult the Oakland University Academic Conduct Regulations.

CALCULATOR POLICY: For this course, a graphing calculator or a computer with symbolic manipulator (such as Maple or Mathematica) are strongly recommended. You may use a calculator (but not a computer) on all tests. Tests will be constructed assuming only that you have a calculator with logarithmic, exponential, and trigonometric functions as well as memory storage. No matter what kind of calculator you have, it is important to learn to use it effectively. In particular, know how to do long calculations without writing down intermediate answers, and be aware of how many digits of accuracy you can expect an answer to have. To receive full credit on tests, be sure to show all the mathematical work necessary for setting up a calculation before using the calculator. Try to use your calculator imaginatively, too; for example, calculators often provide you with ways to verify an answer (e.g. by graphing with a graphing calculator, or plugging in particular values of variables). Using a calculator to store formulas you need

for a test is not permitted.

COMPUTER USAGE: Computer Laboratories are not a formal part of this course. However, there are some excellent "computer algebra" packages such as Mathematica and Maple available on desktop and remote computers; this software is capable of performing many of the calculations that one does in a course such as this (e.g., solving algebraic equations, simplifying complicated algebraic expressions, differentiating, integrating, and drawing graphs). Interested students should talk to their instructor about obtaining access to such systems and experiment with them. Also, you may use for the homework the website WolframAlpha

ACADEMIC HONESTY: Cheating is a serious academic crime. Oakland University policy requires that all suspected instances of cheating be reported to the Academic Conduct Committee for adjudication. Anyone found guilty of cheating in this course will receive a course grade of 0.0, in addition to any penalty assigned by the Academic Conduct Committee. Working with others on a homework assignment does not constitute cheating; handing in an assignment that has essentially been copied from someone else does. Receiving help from someone else or from unauthorized written material during a quiz, test, or final exam is cheating, as is using a calculator as an electronic "crib-sheet."

STUDY HABITS: Cultivating good work and study habits is necessary for doing well in mathematical sciences courses. You should keep on top of the subject by doing large amounts of homework (frequently working on problems not assigned), regularly reviewing earlier material, asking questions in class, and making good use of your instructor's office hours. Regular reviewing of older material in the course will put you in good stead when it comes to final exam time. This will help you to avoid the usual non-retention problems students encounter at the end of the course. You should expect that doing all of these things will take at least two hours outside of class for each hour in class. Many students find it helpful to spend some of this time working with others, in study groups, and you are encouraged to work in a group.

LEARNING OUTCOMES: A student who succewssfully completes the course will unerstand and will be able to apply the ideas and methods related to: Solving differential equations using the Laplace Transform; multivariable Differential and Integral Calculus in engineering and scientific settings; Fourier Transform and the frequencies present is a signal.

INTENDED TENTATIVE COURSE DETAILS: We will follow the schedule below, and update it as we go along. Week of --- Sections --- HW September 7 (Wednesday) --- 6.1, 6.2 HW-- 6.1 (pp. 210-1): 1, 3, 5, 6, 11, 13, 15, 19, 26, 31, 33, 43 HW-- 6.2 (pp. 216-7): 1, 3, 5, 7, 10, 11, 13, 19, 21, 27, 29 September 14 --- 6.3 - 6.5. HW-- 6.3 (pp. 223-5): 3, 5, 7, 13, 15, 23-5, 29, 35, 39 HW-- 6.4 (p. 231): 4-7, 10 HW-- 6.5 (p 237): 1, 3, 8-14, 17, 21 September 21 --- 6.6, 6.7, Model for Covid-19, control HW—6.6 (pp. 241-2): 3, 4, 15 HW—6.7 (pp. 246-7): 3,4,16

September 28--- 7.3, 7.4, 8.1, 8.2, HW--7.3 (p. 280): 3, 5, 7, 9 Gauss elimination is an integral part of many commercial packages in which linear systems arise, such as FEMs or Boundary Element Methods. HW--7.4 (p. 287): 3, 5, 7, 8 This is the theoretical basis for Gauss elimination and the rest of linear algebra. Make sure that you understand the concepts of `linear independence.' HW--8.1(p. 329): 2-10, 13, 14 HW--8.2 (p. 333-4): 2-5, 16*, 18* October 5--- 9.1, 9.2, Review (Wednesday) HW--9.1 (p. 360): Do as many as you need from 1-37. HW--9.2 (p. 367): 1, 3, 5, 12, 18-20, 26, 29, 31*, 32*, 33*, 35* October 12 --- Exam 1 (Monday), 9.3, 9.7 HW--9.3 (p. 375): 4, 11, 13, 15, 17, 19, 25, 27, 28*, 29 HW--9.7 (p. 402): 1-3, 6, 11-15, 18-21 (no need to sketch, although it is useful), 28, 29*

The material for the test includes sections 6.1-6.7, 7.3, 7.4, 8.1, 8.2, 9.1, 9.2 Make sure that you are very familiar with the Tables of Laplace transforms. All the info is there! (however, you will need a bit of partial fractions) The Linear Algebra part 7.3, 7.4, 8.1, 8.2, should be straightforward. The vector calculus is basic material. The test has 12 questions, you have to answer 10 questions. Answer 8 out of questions 1-10. You have to answer questions 11 and 12. Each question from 1-10 is worth 16 pts and questions 111 and 12 are worth 10 points each (for total of 150 points). Mark clearly the two questions you do not want to be graded. You may bring a one page freely written on ONE side, and attach it to the exam. Exam #1: Median= (%) (students)

Grade distribution for the exam: 95%-100% 87% - 94% AA

77% - 83% B+

67% - 73% B-

57% - 63% C

Highest mark for the exam: ( students) The solutions will be posted on Moodle October 19 --- 9.4, 9.5, 9.8, 9.9, We skip the torsion and curvature parts in 9.5. HW--9.4 (p. 380-1): 1, 3, 5, and use software for 15, 17, 19, 20 HW--9.5 (pp. 390-1-9): 1-6, 11-15, 24-28 (skip finding the normal and the sketching) 37, 43, 44, and have fun using any computer program to graph 23!HW--9.8 (pp. 405-6): 1-7, 11, 12, 13, 15-17, use any computer program to graph 10! The divergence of a vector field is a fundamental concept in many branches of engineering!

October 26 --- 10.1, 10.2, 10.3, 10.4 HW--10.1 (pp. 418-9): 2-11, 15-20 HW--10.2 (p. 4325-6): 4-7, 13-19 HW--10.3 (p. 432): try some of the questions 2-11 HW--10.4 (p. 438): 1-8, 13-17, 18* November 2 --- 10.3, 10.4, 10.6, 10.7 Sections 10.3 and 10.5 deal with material from Calc III. Double integrals and surfaces. If you feel rusty, please review and make sure it is placed where it should be. HW--10.5 (pp. 442-3): 1, 3-5, 7, 13, 14-17, (you may want to use software!) HW--10.6 (p. 450): 1-10 HW--10.7 (p. 457-8): 1-8, 13, 16-18

November 9 --- 10.8, Review on Wednesday The Divergence Theorem is a basic result used extensively with partial differential equations- in modeling, analysis and in numerical methods. It is used often in FEM. HW--10.8 (p. 463): 6, 8,9, 10*, 11* November 16 --- Exam 2, (Monday) 11.1 HW--11.1 (pp. 482): 1-3, 6-8, 14, 15 (use software for the integration), 16-21, 22 [in 16-21 just write down the function f ]

The material for the second test includes the sections: 9.3, 9.4, 9.5, 9.8, 9.9, 10.1-10.4, 10.7 and 10.8 The material deals with: functions of many variables, partial derivatives, curves in space and tangents, directional derivatives, gradient, the meaning of the gradient of a function, divergence, the meaning of the divergence of a vector field, the continuity equation, the curl of a vector function, the meaning of the curl of a vector function, line integrals, work, path independence- meaning and ways to check it, Green's Theorem The test has 12 questions, you have to answer 10 questions. Answer 8 out of questions 1-10. You have to answer questions 11 and 12. Each question from 1-10 is worth 16 pts and questions 111 and 12 are worth 10 points each (for total of 150 points). Mark clearly the two questions you do not want to be graded. You may bring a one page freely written on ONE side, and attach it to the exam. Exam #2: Median= xxx (xx%) (xx students) Grade distribution for the exam:

95%-100% 87% - 94% A A-

77% - 83% B+

67% - 73% B-

57% - 63% C

Highest mark for the exam: ( students) The solutions will be posted on Moodle

November 23 --- 11.2, 11.3, Wednesday special lecture-topic to be announced HW--11.2 (p. 490-1): 1-3, 5*, 8, 9, 11, 13 HW--11.3 (p. 494): 6-8, 13*, 14*

November 28-Thanksgiving! November 30 --- 11.7--11.8, Review (Wednesday) HW-- 11.7 (p. 517): 1, 3, 5, 7*, 11 HW-- 11.8 (p. 522):1, 3, 5, 9, 13 HW-- 11.9 (p. 533): 3, 5, 7, 9, 19

December 7 --- Last class! Final Review December 14 --- Final Exam 7-10 PM The exam is comprehensive and includes all of the course material. It lasts 3 hrs. The test has 15 questions, you have to answer 12 questions. Answer 10 out of questions 1-13. You have to answer questions 14 and 15. Each question from 1-13 is worth 17 pts and questions 14 and 15 are worth 15 points each (for total of 2000 points). Mark clearly the three questions you do not want to be graded. You may bring a one page freely written on both sides, and attach it to the exam.

The main topics of the course: Laplace Transform: Existence, linearity, derivatives, integrals, differential equations, unit step function, shifting in 't' and in 's', differentiation and integration of transforms, convolution, integral equations Differential Calculus: dot product, curves, parametric representation, tangents, velocity, acceleration, gradient of a scalar function, directional derivative, curl of a vector field. Integral Calculus: line integrals, path independence, Green's theorem in the plane, Gauss divergence theorem and its applications Fourier Series: periodic functions, odd, even, Fourier series, Euler equations Fourier integral. The frequency distribution in a signal, and FFT

GOOD LUCK AND BE WELL!...