CRN 13026

Syllabus

The simplicity of nature is not to be measured by that of our conceptions.
Infinitely varied in its effects, nature is simple only in its causes,
and its economy consists in producing a great number of phenomena,
often very complicated, by means of a small number of general laws.
Pierre-Simon Laplace (1749-1827)

• Time and Place. MWF 9:30-10:20 in LART 308

• Instructor. Helmut Knaust, Bell Hall 219, hknaust@utep.edu, 747-7002

• Office Hours. MWF 10:30-11:20, or by appointment.

• Other Sources of Help.
  • Consult the differential equations section of S.O.S. Mathematics online.
  • Visit the (new!) MaRCS Tutoring Center on the second floor of the Library.

• 
  Textbook. Paul Blanchard, Robert L. Devaney, Glen R. Hall. Differential Equations. Brooks/Cole, 3rd edition. The textbook is required at all class meetings, and the parts covered in class are intended to be read in full.

• Prerequisites. I will assume that you have a thorough knowledge of the material covered in your Precalculus and your first two Calculus courses. In particular, it is essential that you are comfortable with techniques of integration and the method of partial fractions.

• Course Contents. The course will cover the following material:
  • Chapter 1.1-1.9 (4 weeks)
  • Chapter 2.1-2.4 (2.5 weeks)
  • Chapter 3.1-3.7 (4 weeks)
  • Chapter 5.1-5.2 (1.5 weeks)
  • Chapter 6.1-6.4 incl. selected topics from Chapter 4 (2.5 weeks)

• Course Objectives. During the course you should expect (and I will expect) that you make considerable progress in the following areas:

1. Apply standard techniques to analyze and solve ordinary differential equations: using analytical, numerical and qualitative methods; using the method of the Laplace transform.
2. Be able to model with differential equations and interpret the results of their mathematical analysis.
3. Understand the fundamental difference between linear and non-linear differential equations.
4. Improve your ability to communicate Mathematics effectively in written form.

• Homework. I will regularly assign homework. Although the homework will not be collected or graded, it is essential for your success in this class that you diligently work all the homework problems. Homework will include reading assignments.

• Tests. Exams will be given on the following dates: September 24 (changed!), October 15 and November 10. Each exam counts 20% of your grade.

• Quizzes. I will give regular, but unannounced quizzes. Quiz problems will be identical to prior homework assignments and/or designed to check on your understanding of the assigned reading material. Your worst two quizzes will be dropped, the others will make up your quiz score, which accounts for 15% of your grade.

• Make-up Exams. Make-up tests will only be given under extraordinary circumstances, and only if you notify the instructor prior to the exam date. There will be no make-up quizzes.

• Final exam. The final on Wednesday, December 10 at 10:00-12:45, is mandatory and comprehensive. It counts 25% of your grade.

• Calculators. You must not use a calculator during quizzes, tests and the final.

• Time Requirement. I expect that you spend an absolute minimum of six hours a week outside of class on reading the textbook, preparing for the next class, reviewing your class notes, and completing homework assignments. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.

• Attendance. You are strongly encouraged to attend class every day. I expect you to arrive for class on time and to remain seated until the class is dismissed. Students with excessive absences (excused or unexcused) will be dropped from the course with a grade of "F".

• Drop Policy. The class schedule lists Friday, October 31, as the last day to drop with an automatic "W". After the deadline, I can only drop you from the course with a grade of "F". Beginning with the fall 2007 semester, all freshmen enrolled for the first time at any Texas public college or university will be limited to six course withdrawals (drops) during their academic career. Drops include those initiated by students or faculty and withdrawals from courses at other institutions! This policy does not apply to courses dropped prior to census day or to complete withdrawals from the university.

• Students with Disabilities. If you have a disability and need special accommodation, please contact the Disabled Student Services Office (DSSO) in Union East 106, 747-5148, dss@utep.edu.

• Academic Integrity. All students must abide by UTEP's academic integrity policies, see http://academics.utep.edu/Default.aspx?tabid=23785 for details.

Homework

• 12/1/08: R 6.2. P 6.2: 1,2,4,5,10
• 11/26/08: None.
• 11/24/08: R 6.1,6.2. P 6.1: 1-3,5,8-10,14
• 11/21/08: R 5.2,6.1-6.2. P 5.2: 1,2,4,7,8
• 11/19/08: R 5.2,6.1.
• 11/17/08: Turn in Worksheet 2 on Friday!
• 11/14/08: R 5.1,5.2. P 5.1: 2-5,9-10
• 11/12/08: R 5.1,5.2.
• 11/10/08: Test 3.
• 11/7/08: None.
• 11/5/08: None.
• 11/3/08: R 3.6,3.7,5.1. P 3.6: 1,2,10,11,14,32; 3.7: 9,10
• 10/31/08: R 3.6,3.7.
• 10/29/08: R 3.5,3.6. P 3.5: 17,18
• 10/27/08: R 3.5,3.6. P 3.5: 1,4,11
• 10/24/08: R 3.4,3.5. P 3.4: 1,4,5,15-17,20
• 10/22/08: R 3.4.
• 10/20/08: R 3.3,3.4. P 3.3: 9,10,14,19
• 10/17/08: R 3.2-3.4. P 3.2: 1-4,11,12
• 10/15/08: Test 2.
• 10/13/08: None.
• 10/10/08: None.
• 10/8/08: R 3.1,3.2. P 3.1: 5,6,8,10,13,14,16
• 10/6/08: R 2.3,2.4,3.1. P 2.3: 15; 2.4:1,4,7-9
• 10/3/08: R 2.3-2.4. P 2.3: 6,7,10
• 10/1/08: R 2.2-2.4. Turn in Worksheet 1 next time!
• 9/29/08: R 2.1-2.3. P 2.1: 20ab; 2.2: 2,5,7,10
• 9/26/08: R 2.1,2.2. P 2.1: 1,2,4,6,8
• 9/24/09: Test 1.
• 9/22/08: None.
• 9/19/08: R 1.9, 2.1. P 1.9: 5,6,9,10,20,24
• 9/17/08: R 1.8 (pp.112-114),1.9. P 1.7: 12,16
• 9/15/08: R 1.7. P 1.7: 4,9
• 9/12/08: R 1.6, 1.7. P 1.6: 8,12,20,30,33,39,40
• 9/10/08: R 1.5-1.7. P 1.5: 1,2,4,10,14,15
• 9/8/08: R 1.5, 1.6.
• 9/5/08: R 1.4, 1.5. P 1.4: 2,3,7,8,11
• 9/3/08: R 1.4, 1.5. P 1.3: 11,15,16
• 8/29/08: R 1.3, 1.4. P 1.3: 2,3,7,10
• 8/27/08: R 1.2, 1.3. P 1.2: 7,12,15,30,35,38
• 8/25/08: R 1.2. P 1.2:1,2

Software

• Slope Field Calculator, by Marek Rychlik.
• ODE 2D Calculator, by Marek Rychlik.
• Interactive Differential Equations, by Beverly West, Steven Strogatz, Jean Marie McDill, John Cantwell, and Hubert Hohn.
• ODE Toolkit, by Harvey Mudd College.
• Spreadsheet for Euler's Method
• Mathematica notebook Video: An Introduction to Mathematica

Other Stuff

A 3D-plot of a solution to a system of 2 autonomous differential equations

• Laplace Formula Sheet Quiz 6 Worksheet 2 Test 3 Quiz 5 Quiz 4 Test 2 Quiz 3 Worksheet 1 Test 1 Quiz 2 Quiz 1 (partial solution) Quiz 1
• Oliver Heaviside
• Animation of a Damped Spring
• Animation of a Damped Pendulum
• Trace Determinant Plane (18MB). An animation of the vector fields of some systems of linear differential equations \(Y'(t)=A\cdot Y(t)\) for which \((\mathop{\rm tr}A)^2+(\det A)^2\) is constant. Here is a similar example for systems of the form \(Y'(t)=\begin{pmatrix}a&b\\1&1\end{pmatrix}\cdot Y(t)\).
• The Lorenz equation is a non-linear system of three differential equations\[x'=\sigma (y-x), \quad y'=\rho x -y -x z, \quad z'=-\beta z + x y\]. The constants are chosen as follows\[ \sigma=10,\ \rho=28,\ \beta=8/3\]. This animation illustrates the sensitivity to initial conditions exhibited by solutions to the Lorenz equation: Three solutions (in red, blue, and green, respectively) with nearly identical initial conditions are tracked over time.
• Frederick W. Lanchester
• Animation of logistic growth with harvesting. The family of differential equations has the form \(y'=y(1-\frac{y}{5})-h\).
• Rabbits in Australia