APM 541, Fall 2004

Math Analysis for Engineers I


Faculty: M. Shillor

Office: 554 SEB

Phone: 370-3439

email: shillor@oakland.edu

Class Time: MW 5:30-7:17 pm

Room: 365 SFH 

Section: 42064


Important Dates:

September 14 - Last day for no-grade drop

November 2 - Last day for official withdrawal (W)

December 6 - Last day of classes

Wednesday, December 8 - Final Examination -- 7:00 - 10:00 PM


Advice about doing well in the course, given by previous students.

Common errors and mistakes.


Discussion board and chat room

Click on APM541, I will check it once a day or so.


Prerequisites:

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

Text:

Advanced Engineering Math., E. Kreyszig, 8th ed. We shall cover parts of Chapters 5, 8-10, and some additional material from Ch. 6 and 7 (see detailed syllabus below).

Office Hours:

Monday and Wednesday 3:30--5:00 PM in  my office. Students who are unable to make the announced hours may make individual appointments.

Exams:

The grade in this course will be based on two 120-point one-hour exams, on Wednesday September 29,

and on Monday, November 1, and one 160-point final exam, 400 points in total.

The exams are closed book exams.You may bring to each of the exams a one two-sided page freely written, and a photocopy of the tables of transforms.

The Final Exam will be given on Wednesday, December 8, 7:00-10:00 PM.

It will be comprehensive and will cover the entire material of the course.It will take place in the same classroom. The Final Exams is a closed book exam. You may bring a two sided page freely written, and a photocopy of the tables of the Laplace and the Fourier transforms.

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.

In case the university is officially closed on a scheduled exam date, the exam will be held on the next class date that the university is officially open.

Grades:

The grading scale in this course is:

95%----4.0

65%----2.0

80%----3.0

50%----1.0

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 hour of lecture in class. 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, walkmans, pagers, beepers, 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, which can be found online at: http://www2.oakland.edu/deanofstudents/handbook/acr.cfm

CALCULATOR POLICY:

For this course, a graphing calculator is strongly recommended. You may use a calculator (but not a computer) on all tests and homework assignments. 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.

EMERGENCY CLOSING:

If the University is closed at the time of a scheduled test, quiz, or examination (for example, because of snow), it will be given during the next class period when the University reopens. The Oakland University emergency closing number is 370-2000.

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 "cribsheet."

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.


INTENDED SYLLABUS:

We will follow the schedule below.

Week of --- Sections


August 30 --- 5.1 - 5.3
HW-- 5.1(p 257): 1, 3, 5, 6, 9-12, 18, 20, 22, 25*, 29, 30
HW-- 5.2(p 264): 1, 2, 4, 6, 9
HW-- 5.3(pp 273-4): 2, 5, 7, 11, 12, 18, 20-22, 28-30, 32, 34, 38


September 6 --- 5.3, 5.4
HW-- 5.4(p 278): 1, 5, 7, 10, 14

September 13 --- Review of the Laplace Transform, 5.5, 5.7 6.1, 6.2
Make sure that you are very familiar with the Tables of Laplace transforms.
All the info is there! (but you will need a bit of partial fractions)
HW--5.5(p 283-4): 1, 3, 4, 8, 10, 16, 21-24, 28, 30
HW--5.7(pp 294-5): 1-4, 8
HW--6.1(p 309): 1, 6, 7, 15, 16

HW--6.2(pp 319-20): 1, 7, 8, 12-16

September 20 --- 6.3-6.5, 6.7
HW--6.3(pp 329-30): 4-6, 9, 16, try any one, or all of 17-19, and 20*, 21*, 22*
Gauss elimination is an integral part of many commercial packages
in which linear systems arise, such as FEMs or Boundary Element Methods.
HW--6.4(pp 336-7): 1-8, 10, 11, 13, 18-25
This is the theoretical basis for Gauss elimination and the rest of linear algebra.
Make sure that you understand the concepts of `linear independence' and
`vector space.'
HW--6.7(p357): 1 - 4, 10*, 11, 12*, 13*, 14*

September 26 --- Review on Monday, Test #1 on Wednesday
The material for the test includes sections 5.1-5.5, 6.1-6.5, 6.7
The test has 10 questions, you have to answer 7 questions.
Answer 5 out of questions 1-8. You have to answer questions 9 and 10.
Each of questions 1-8 is worth 20 points
and questions 9 and 10 are worth 10 points each (for total of 120 points).
Mark clearly the question you do not want to be graded.
Bring a photocopy of the Laplace Transforms (only) pp. 296-9, and one page
freely written on two sides. Please attach the tables and the page to the exam.

The solutions, in PDF format, of Exam-1A and  Exam-1B

Exam #1: Median=96 (80% -- 49 students) 

  Grade distribution for the exam:

95% - 100% (OU grd 4.0)

85% - 94% (grd 3.5-3.9)

75% - 84% (grd 3.0-3.4)

65% - 74% (grd 2.5-2.9)

50% - 64% (grd 1.5-2.4)

0% - 49% (OU grd 0.0)

9

13

15

5

7

 

  Highest mark for the exam: 120 (5 students)



October 4 --- 7.1,7.2, 8.1- 8.3
HW--7.1(p375): 1 - 8 
HW--7.2 (pp379-80): 2, 3, 5, 7
HW--8.1(p 407 ): Do as many as you need from 1-33 to feel comfortable
with the material.
HW--8.2(pp 413-4): 7, 9, 10, 16, 17, 23-26, 36*, 37*
HW--8.3(pp 421-2): 7-10, 20, 21, 22, 24, 27  

October 11 --- 8.4 - 8.9
HW--8.4(pp 427-8): 4, 6-9, 12, 14, 15, 17, 20, 25-30
HW--8.5(pp 433-4 ): 2-4, 6, 9, 10, 12, 14, 18, 20, 21-26, 31*
HW--8.6(pp 439-40): 1, 3, 5, 7, 13*, 14*, 15*, 16*
HW--8.9(pp 452-3 ): 1-6, 7-9, 13*, 14, 16, 18, 20, 21, 23, 25, 32-35


October 18 ---  8.10 , 8.11, 9.1, 9.2
HW--8.10(pp 456-7 ): 1-8, 10-12, 13*(a)-(d), 14, 16, 18, 20
HW--8.11(p 459): 2-7, 9, 11, 13, 14*
The concepts: gradient, divergence and curl are very important in many
engineering applications. They are at the heart of models using partial
differential equations, and therefore in many commercial solvers for PDEs.

HW--9.1(p 470 ): 1-10
This is where parametric representation of curves is used extensively.
HW--9.2(p 477-8 ): 2-9, 11, 13, 15, 17, 19


October 25 --- 9.3  9.4, Review on Wednesday
Sections 9.3 and 9.5 deal with material from Calc III. Double integrals
and surfaces. If you feel rusty
please review and make sure it is sitting where it should.

HW--9.4(pp 490-1 ): 1-10, 14, 15, 19*


The material for the second test includes the sections: 8.1 - 8.11, 9.1 - 9.4.
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 10 questions, you have to answer 7, and only 7, questions.
Answer 5 out of questions 1-8. You have to answer questions 9 and 10.
Each one of questions 1-8 is worth 20 points and questions 9 and 10 are
worth 10 points each (for total of 120 points).
Mark clearly the question you do NOT want to be graded.
Bring one page freely written on both sides. Please attach it to the exam.

November 1 --- Exam #2 on Monday, Solution of the exam.

The solution of exam 2A: click here

Exam #2: Median=95 (80% -- 48 students)

·  Grade distribution for the exam:

95% - 100% (OU grade 4.0)

85% - 94% (grd 3.5 - 3.9)

75% - 84% (grd 3.0 - 3.4)

65% - 74% (grd 2.5 - 2.9)

50% - 64% (grd 1.5 - 2.4)

0% - 49% (grd 0.0)

7

13

14

8

6

 

·  Highest mark for Exam 2: 120 (four students)



November 8 --- 9.5, 9.6, 9.7, 9.8
HW--9.6(pp 503-4 ): 1-9(odd), 10, 13, 15
HW--9.7(pp 509-10 ): 2-7, 10, 11, 13-19
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--9.8(pp 514-5 ): 2-8, 11*

November 15 --- 10.1-10.3
HW--10.2(pp 536-7 ): 1-4, just write as f(x)=..., and 5-15(all odd ones)

HW--10.3(p 540 ): 1, 3, 4, 5, 9, 18*

November 22 --- Review of Chapters 8 and 9, Special lecture on Wednesday on the VeCHSS,
a spring with negative spring constant, thermistors etc.

Have a Good Thanksgiving Break!

December 1 ---  10.4, 10.10,
HW--10.4(p 546-7): 1-8, 11, 14, 15, 17, 18
HW--10.10(p 575): 1-3, 8, 9

December 6 --- Last class! - Review


The final is comprehensive.

The material for the Final Exam includes the following sections:
5.1-5.5, 5.7;
8.5, 8.6, 8.9, 8.10, 8.11
9.1, 9.2, 9.4, 9.6, 9.7 9.8;
10.1, 10.2, 10.3, 10.4, 10.10
You may use a photocopy of the Tables of Laplace and FourierTransforms,
and two sheets of paper written freely on both sides.

 

The main topics of the course:


Lapalce 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 Transform.


The format of the final exam is:
There are 15 questions on the exam for the total of 160 points.
You need to answer 12 questions.
Choose 10 questions out of questions 1-13 (14 points each);
Questions 14 and 15 are mandatory (10 points each).


Wednesday, December 8 --- Final Exam -- 7:00 - 10:00 pm
Room 365 SFH (the classroom)

ADVICE: Sleep well the night before the exam!
You cannot do well if you are sleepy and unable to concentrate!

GOOD LUCK AND BE WELL!

Final Grades: Median=3.4 (49 students)

·  Grade distribution:

  4.0

  3.5 - 3.8

3.0 -   3.4 

2.5 - 2.8 

2.0 - 2.4

 0.0    

6

15

19

5

2

2