Engineering Mathematics I (Math 351 sec. 011) Fall 2001
PRN 238 - Monday, Wednesday & Friday 1115-1205
©2001 L. F. Rossi All rights reserved.

Prof. L. F. Rossi
Office: Ewing 524
Telephone: x1880
Email: rossi@math.udel.edu
WWW: http://math.udel.edu/$\sim$rossi
Computer project number: 2005

Course description: Linear algebra and differential equations are interesting and essential areas of mathematics commonly used for the analysis and solution of problems in engineering, physics, chemistry, biology and finance. In this course, we will explore some of the foundations of these topics and develop the mathematical tools commonly used for manipulating, analyzing and solving linear algebraic systems and linear systems of differential equations. Also, time permitting, we hope to apply knowledge of linear systems to nonlinear, autonomous systems of equations.

Prerequisites:

Your objectives:

In this course, everyone will master the following skills:

• Identify the order of a differential equation.

• Recognize a variety of types of differential equations.

• Solve a first order linear differential equation.

• Solve an exact differential equation.

• Solve a separable differential equation.

• Understand the properties of inner products and norms.

• Solve a linear system with Gaussian elimination and Gauss-Jordan reduction.

• Find the inverse of a matrix.

• Solve certain second order linear systems.

• Model and analyze linear mechanical and electronic oscillators.

• Find the eigenvalues and their corresponding eigenspaces.

• Solve linear systems of differential equations.

• Diagonalize a diagonalizable matrix.

• Analyze autonomous systems in the phase plane.

Your resources: All of the following will help you achieve your objectives:

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Time: The best way to learn mathematics is to spend time with it. It is your responsibility to come to class each day, and it is unlikely that you will pass if you miss more than a day or two, regardless of the reason. Attendance is crucial to success in this course.

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Textbook: Differential Equations & Linear Algebra by Michael D. Greenberg.

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Office hours: Mon 1300-1400, Wed 1300-1400, Thur 1000-1100 or by appointment. This is time that I have set aside especially for you. Office hours are one of the most valuable and least used resources at the University, and I hope you will take advantage of them. I want to help you learn this material, so do not be shy about seeing me outside of class. Your exams will only be distributed during office hours. If you need to see me at a time other than an office hour, feel free to ``drop in'' or make an appointment.

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Computer Algebra Systems: Maple will be used both in and out of class. If used properly, it can function as both an interactive textbook and a powerful tool that you can use to explore different concepts.

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Calculator: I expect everyone to have at least a scientific calculator. You will probably never need to use it on an exam though it might come in handy for some of the homework problems. You will not be allowed to use calculators with symbolic mathematical capabilities on exams.

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Your classmates: Math is not a competitive sport. There are many obvious reasons to work together. Even if you end up helping others most of the time, teaching is one of the best ways to gain a deeper understanding of a subject.

Grading policy: Your grade is determined solely by your understanding of mathematics and your ability to communicate this knowledge to me on exams and other assignments.

Homework and quizzes	10%
Report problems	10%
Exams (20% each)	60%
Final exam	20%

Final letter grades will be assigned strictly based on the following percentages of your total point score:
100 $\leftarrow$ A $\rightarrow$ 93 $\leftarrow$ A- $\rightarrow$ 90 $\leftarrow$ B+ $\rightarrow$ 87 $\leftarrow$ B $\rightarrow$ 83 $\leftarrow$ B- $\rightarrow$ 80 $\leftarrow$ C+ $\rightarrow$ 77 $\leftarrow$ C
C $\rightarrow$ 73 $\leftarrow$ C- $\rightarrow$ 70 $\leftarrow$ D+ $\rightarrow$ 67 $\leftarrow$ D $\rightarrow$ 63 $\leftarrow$ D- $\rightarrow$ 60 $\leftarrow$ F $\rightarrow$ 0



I reserve the right to adjust this scale to improve grades if the course material proves to be unreasonably demanding.

Exams: All exams will occur in class on the days listed on the syllabus. There are no makeup exams without prior notification and a valid, documented reason. Graded exams will be handed back in person in office hours only.

Homework and quizzes: I will drop your lowest three homework or quiz scores during the semester. I do not accept late homework, so do not squander these three assignments. You might be sick sometime and not be able to do your homework on time. Each assignment is worth 10 points, 5 for completeness and 5 for the accuracy of several randomly selected problems.

Student conduct: To provide the best learning environment for all my students, I expect all my students to conduct all their scholarly activities with honesty and integrity. Students should note that in certain situations doing nothing can be dishonest. Though I hope there will never be a need to address academic dishonesty, I will strongly enforce all provisions noted in the Academic Regulations for Undergraduates. See The University of Delaware Undergraduate and Graduate Catalog

http://www.udel.edu/catalog/current/ugacadregs.html#acadhonesty

for further discussion on basic responsibilities.

Tentative schedule:

Week of	Section(s)	Topic(s)
Aug 29	1.2, 2.3	Preliminaries, first order equations.
Sep 5	2.4, 3.2-3.3	Applications, separable equations.
Sep 10	3.4-3.6, 4.2-4.4	Exact equations, integrating factors, vectors.
Sep 17	4.5-4.6	Solving linear systems, Gaussian elimination, spanning sets.
Sep 24	4.7-4.8	Linear dependence, vector spaces, Exam 1.
Oct 1	4.9, 5.2-5.3	Basis, dimension, matrix algebra.
Oct 8	5.4-5.6	Determinant, rank, matrix inverses.
Oct 15	5.7, 6.3-6.4	Linear independence, homogeneous equations.
Oct 22	6.5	Constant coefficients, Exam 2.
Oct 29	6.6-6.7, 7.2	Cauchy-Euler problems, nonhomogeneous problems, harmonic oscillators.
Nov 5	7.3-7.5	Phase plane, forced oscillations.
Nov 12	9.2-9.4	Eigenvalue problems, symmetric matrices, boundary value problems.
Nov 19	10.1-10.2, 10.4	Systems, solutions via eigenvalues.
Nov 26	10.5, 11.2	Diagonalization, Exam 3, the phase plane.
Dec 3	11.3-11.4	Singular point analysis, review.

Important dates:

Sep 11	Last day to drop without record.
Sep 28	Report Problem #1 due. Exam 1.
Oct 24	Report Problem #2 due. Exam 2.
Oct 30	Last day to drop with a ``W''.
Nov 28	Exam 3.
Dec 7 (1300-1500)	Final exam.

Problem sets: The best way to learn and understand mathematics is by trying problems. An excellent way to prepare for an exam is to make sure you can solve these problems without referring to your book or notes. To receive credit, you must show your work. Below are problem assignments from the book. Underlined problems have solutions in the back of the book. If only the problem number is indicated for a multipart problem, you are required to do all non-underlined parts for that problem. Thus, if problem 1 is assigned and parts a,b and f of problem 1 are underlined, you need only hand in parts c-e. However, working the underlined problems may help you understand the material.

Assignment	Problems
1	1.2: 1bf, 2d, 5dh; 2.2: 1f, 2f; 2.3: 1in
2	2.2: 7c; 2.3: 3d, 7b; 2.4: 2, 9, 11, 13; 3.2: 1k, 4c, 5b, 6e; 3.3: 1b
3	2.3: 9; 2.4: 17, 18; 3.3: 5; 3.4: 1fi, 4b, 5f; 3.5: 1b, 3d; 4.2: 3; 4.3: 1h; 4.4: 1fh, 2df
4	3.4: 9b, 13, 14; 4.2: 6, 8d; 4.3: 2, 4d; 4.4: 3b, 7ab; 4.5: 2hj; 4.6: 2d
5	4.4: 8c, 11b; 4.5: 13b; 4.6: 4f; 4.7: 1, 2d; 4.8: 1d, 3
6	4.7: 3i, 6a; 4.8: 5d, 6; 4.9: 1f, 2e; 5.2: 2d, 3, 5bc; 5.3: 1b, 6, 7de
7	4.9: 4f; 5.2: 6, 15, 20; 5.3: 8e; 5.4: 2df, 6d; 5.5: 1dh, 4b; 5.6: 1fm, 7d
8	5.2: 22; 5.3: 9; 5.4: 4df, 7; 5.5: 9, 10; 5.6: 13; 5.7: 1df; 6.3: 1, 2c; 6.4: 1bh
9	6.4: 2df, 9df; 6.5: 2chp, 4bck
10	6.5: 12bd; 6.6: 1chi, 5; 6.7: 2eh; 7.2: 1bef, 7
11	6.6: 8b, 9f; 6.7: 4bh, 7; 7.2: 8; 7.3: 1, 2bde; 7.4: 1, 2, 7bcf; 7.5: 1bcef, 3
12	7.4: 8ab; 9.2: 1fhkn, 3f; 9.3: 3ef, 4; 9.4: 1bd, 2abc
13	9.2: 4d, 8, 11; 9.3: 5bg, 6a; 9.4: 3acd; 10.1: 3; 10.2: 3; 10.4: 1bk, 2bd
14	9.2: 9, 18; 9.4: 4; 10.4: 5, 6d; 10.5: 1eh, 2df; 11.2: 1, 2
15	10.5: 5, 7; 11.2: 9dfh; 11.3: 4bcfkn; 11.4: 9, 11

Report problems: A special component of this course called report problems are designed to augment the textbook's approach. They will focus on problem solving, abstract reasoning and applications. The guidelines for reports are:

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Reports must be handed in by the due date.

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The intended audience of the report is your fellow classmates. You must explain each step you take clearly, neatly and accurately. A report should not exceed five pages.

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A single report may be submitted by teams of up to three people. Each team member must contribute roughly one third to the content of the report.

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Reports either receive full credit or a ``REDO.'' Full credit is awarded for a clear, concise and correct solution. REDO's are awarded otherwise.

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One can resubmit a corrected REDO for full credit for up to two weeks after reports are returned.

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Periodically, you may be asked to submit a progress report to help to make steady progress toward completing your reports. To receive credit for a report problem, you must hand in all the progress reports.

I have excellent examples of report problems available in my office for you to look at if you are unsure of what I expect.