Math 01-236 – Mathematics for Engineering Analysis II
Spring 2007

Professor: Dr. Paul J. Laumakis

Office: Robinson Hall Room 229G

Phone: x 3872

E-mail: laumakis@rowan.edu

Office Hours: TTh 1:35 p.m.– 3:05 p.m. and by appointment

Course Description: This course involves the study of various analytical and numerical solution techniques for both ordinary and partial differential equations. Topical coverage includes second order and higher ordinary differential equations, the Laplace transform method, systems of first order ordinary differential equations, Fourier analysis, partial differential equations, and numerical analysis. The Mathematica computer algebra system is required for this course.

Course Objectives: This course is intended to provide the student with the working mathematical knowledge that is required to support continued study in the engineering disciplines. The development of critical thinking and mathematical problem solving skills will be accomplished primarily through a student-centered learning process. Through this process, students will develop the crucial ability to learn on their own. In-class group work, in addition to small team efforts on application-oriented projects derived from a variety of disciplines, will serve to improve the student’s ability to work with others while strengthening communication skills. Additionally, these application problems will allow the student to acquire expertise in the mathematical modeling process and engage the student in the prudent use of available technology.

Attendance: In order to effectively accomplish the course objectives, students are expected to attend every class and be on time. If you are absent from class for any reason, it is your responsibility to find out what you missed, including any announcements. You may find out what you missed from your classmates or by contacting me directly. Excessive absence or lateness may result in a lower final grade for the course.

Textbook: Fundamentals of Differential Equations, 6th edition, Nagle, Saff, & Snider, Addison-
Wesley, 2004.

Academic Honesty: All forms of academic dishonesty will not be tolerated. First-time offenders will be issued an immediate grade of F for the course and a permanent record of the cheating offense will be included in your academic transcript.
Miscellaneous: In order to avoid disruption during class, all cell phones, beepers, and the like are to be turned off before entering the classroom.

Grading Policy: Final grades will be determined as follows:

Quizzes 400 pts.
Group Projects 450 pts.
Project Quizzes 150 pts.
Participation 100 pts.
Total 1100 pts.

Notes: (1) All students must be present for all graded events. No make-ups will be given
and a grade of zero will be assigned for any missed graded events.
(2) The lowest Quiz grade for each student will be dropped at the end of the semester.
(3) The final letter grade assigned to each student will be determined based on
performance in the above listed categories relative to the other students in
the course.

Class Day/Date Section Topic/Activity
1 T/16 Jan Course Overview
2 Th/18 Jan 4.2 Homogeneous Equations with Constant Coefficients
3 M/22 Jan 4.3 Auxiliary Equations with Complex Roots
4 T/23 Jan 4.4 Quiz 1; Undetermined Coefficients
5 Th/25 Jan 4.5 Principle of Superposition
6 M/29 Jan 4.6 Variation of Parameters
7 T/30 Jan 4.8 Quiz 2; Modeling Free Mechanical Vibrations
8 Th/1 Feb 4.9 Modeling Forced Mechanical Vibrations
9 M/5 Feb 5.6 Electrical Systems
10 T/6 Feb 6.1-6.2 Quiz 3; Higher Order Constant Coefficients
11 Th/8 Feb 6.3 Higher Order Undetermined Coefficients
12 M/12 Feb 6.4 Higher Order Variation of Parameters
13 T/13 Feb CLASS DROP FOR PROJECT 1
14 Th/15 Feb PROJECT 1 DUE; PROJECT 1 QUIZ
15 M/19 Feb 9.1, 9.4 Introduction to Systems of Differential Equations
16 T/20 Feb 9.5 Homogeneous Systems with Constant Coefficients
17 Th/22 Feb 9.6 Homogeneous Systems with Complex Eigenvalues
18 M/26 Feb 9.7 (pp. 551-552) Nonhomogeneous Linear Systems
19 T/27 Feb 7.2 Quiz 4; Laplace Transforms
20 Th/1 Mar 7.3 (pp. 360-363) Properties of the Laplace Transform
21 M/5 Mar 7.4 Inverse Laplace Transforms
22 T/6 Mar 7.5 Quiz 5; Solving Initial Value Problems
23 Th/8 Mar No Class – Enjoy Spring Break
24 M/19 Mar 7.6 (pp. 384-390) Transforms of Discontinuous Functions
25 T/20 Mar 7.8 Impulses and the Dirac Delta Function
26 Th/22 Mar CLASS DROP FOR PROJECT 2
27 M/26 Mar PROJECT 2 DUE; PROJECT 2 QUIZ
28 T/27 Mar 10.1-10.2 (to p. 583) Heat Flow and Separation of Variables
29 Th/29 Mar 10.3 (pp. 589-597) Fourier Series
30 M/2 Apr 10.4 Fourier Cosine and Sine Series
31 T/3 Apr 10.3 (pp. 599-603) Convergence of Fourier Series
32 Th/5 Apr 10.5 (pp. 612-615) Quiz 6; The Heat Equation
33 M/9 Apr 10.5 (pp. 616-617) The Heat Equation
34 T/10 Apr 10.2 (pp. 583-587) The Wave Equation
35 Th/12 Apr 10.6 (pp. 625-627) Quiz 7; The Wave Equation
36 M/16 Apr 10.7 (pp. 638-641) Laplace’s Equation
37 T/17 Apr Handout Quiz 8; Numerical Solution of the 2-D Heat Eqn.
38 Th/19 Apr Handout Numerical Solution of the 2-D Heat Equation
39 M/23 Apr Handout Numerical Solution of the 1-D Heat Equation
40 T/24 Apr Handout Quiz 9; Numerical Solution of the 1-D Wave Eqn.
41 Th/26 Apr CLASS DROP FOR PROJECT 3
42 M/30 Apr PROJECT 3 DUE; PROJECT 3 QUIZ