HelmutKnaust: Created page with "==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,
..."

2012-07-17T22:14:37Z

Created page with "==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, ..."

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==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.'' 
[http://www-history.mcs.st-andrews.ac.uk/Biographies/Laplace.html Pierre-Simon Laplace (1749-1827)]

* '''Time and Place.''' MWF 11:30-12:20 in LART 307

* '''Instructor.''' Helmut Knaust, Bell Hall 219, [mailto:hknaust@utep.edu 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 [http://www.sosmath.com/diffeq/diffeq.html S.O.S. Mathematics] online.
** Visit the (new!) MaRCS Tutoring Center on the second floor of the Library.

* [[image:BDH.JPG|right]]'''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:

# Apply standard techniques to analyze and solve ordinary differential equations: using analytical, numerical and qualitative methods; using the method of the Laplace transform.
# Be able to model with differential equations and interpret the results of their mathematical analysis.
# Understand the fundamental difference between linear and non-linear differential equations.
# 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 13:00-15:45''' 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, [mailto:dss@utep.edu 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 6.3. P 6.3: 3,7,16,27,28
* 11/26/08: R 6.2,6.3. P 6.2: 1,2,4,5,10,17,20a
* 11/24/08: None.
* 11/21/08: R 6.1,6.2. P 6.1: 1-3,5,8-10,14
* 11/19/08: R 5.2,6.1. P 5.2: 1,2,4,7,8
* 11/17/08: Turn in [http://helmut.knaust.info/class/200910_2326/Worksheet02.pdf Worksheet 2] on Friday!
* 11/14/08: R 5.2,6.1.
* 11/12/08: R 5.1,5.2.
* 11/10/08: Test 3.
* 11/7/08: R 5.1,5.2. P 5.1: 2-5,9-10
* 11/5/08: None.
* 11/3/08: R 5.1.
* 10/31/08: R 3.7,5.1. P 3.7: 9,10
* 10/29/08: R 3.7,5.1.
* 10/27/08: R 3.5-3.7. P 3.5: 17,18; 3.6: 1,2,10,11,14,32
* 10/24/08: R 3.5,3.6. P 3.5: 1,4,11
* 10/22/08: R 3.4,3.5.
* 10/20/08: R 3.4,3.5. P 3.4: 1,4,5,15-17,20
* 10/17/08: R 3.3,3.4. P 3.3: 9,10,14,19
* 10/15/08: Test 2.
* 10/13/08: None.
* 10/10/08: R 3.3.
* 10/8/08: R 3.2. P 3.2: 1-4,11,12
* 10/6/08: R 2.4,3.1. P 2.4: 7-9; 3.1: 5,6,8,10,13,14,16
* 10/3/08: R 2.3,2.4,3.1. P 2.3: 6,7,10,15; 2.4:1,4
* 10/1/08: R 2.2-2.4. Turn in [http://helmut.knaust.info/200910_2326/Worksheet01.pdf 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
* 9/24/08: 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
* 9/15/08: R 1.7. P 1.7: 4,9,12,16
* 9/12/08: R 1.6,1.7. P 1.6: 8,12,20,30,33,39,40
* 9/10/08: R 1.6,1.7.
* 9/8/08: R 1.5,1.6. P 1.5: 1,2,4,10,14,15
* 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==
*[http://www.math.rutgers.edu/~sontag/JODE/JOdeApplet.html Slope Field Calculator], by Marek Rychlik.
*[http://www.math.rutgers.edu/~sontag/JODE/JOdeApplet2D.html ODE 2D Calculator], by Marek Rychlik.
*[http://www.aw-bc.com/ide/idefiles/navigation/gettingstarted.htm Interactive Differential Equations], by Beverly West, Steven Strogatz, Jean Marie McDill, John Cantwell, and Hubert Hohn.
*[http://odetoolkit.hmc.edu/ ODE Toolkit], by Harvey Mudd College.
*[http://helmut.knaust.info/class/200910_2326/Euler.xlsx Spreadsheet for Euler's Method]
*[http://helmut.knaust.info/class/200910_2326/DEQ.nb ''Mathematica'' notebook] [http://url.wolfram.com/3.pPa0/ Video: An Introduction to Mathematica]

==Other Stuff==
[[Image:Pic01.gif|frame|A 3D-plot of a solution to a system of 2 autonomous differential equations]]
* [http://helmut.knaust.info/class/200910_2326/Laplace_shell.pdf Laplace Formula Sheet] [http://helmut.knaust.info/class/200910_2326/Quiz06B.pdf Quiz 6] [http://helmut.knaust.info/class/200910_2326/Worksheet02.pdf Worksheet 2] [http://helmut.knaust.info/class/200910_2326/Test3B.pdf Test 3] [http://helmut.knaust.info/class/200910_2326/Quiz05B.pdf Quiz 5] [http://helmut.knaust.info/class/200910_2326/Quiz04B.pdf Quiz 4] [http://helmut.knaust.info/class/200910_2326/Test2B.pdf Test 2] [http://helmut.knaust.info/class/200910_2326/Quiz03B.pdf Quiz 3] [http://helmut.knaust.info/class/200910_2326/Worksheet01.pdf Worksheet 1] [http://helmut.knaust.info/class/200910_2326/Test1B.pdf Test 1] [http://helmut.knaust.info/class/200910_2326/Quiz02B.pdf Quiz 2] [http://helmut.knaust.info/class/200910_2326/Quiz01B.pdf Quiz 1]
* [http://en.wikipedia.org/wiki/Oliver_Heaviside Oliver Heaviside]
* [http://helmut.knaust.info/class/200910_2326/spring.html Animation of a Damped Spring]
* [http://helmut.knaust.info/class/200910_2326/Pendulum.html Animation of a Damped Pendulum]
* [http://helmut.knaust.info/class/200910_2326/TDani.html Trace Determinant Plane (18MB)]. An animation of the vector fields of some systems of linear differential equations <math>Y'(t)=A\cdot Y(t)</math> for which <math>(\mathop{\rm tr}A)^2+(\det A)^2</math> is constant. [http://helmut.knaust.info/class/200910_2326/TDani2.html Here] is a similar example for systems of the form <math>Y'(t)=\begin{pmatrix}a&b\\1&1\end{pmatrix}\cdot Y(t)</math>.
* [http://helmut.knaust.info/class/200910_2326/Lorenzb.html The Lorenz equation] is a non-linear system of three differential equations: <math>x'=\sigma (y-x), \quad y'=\rho x -y -x z, \quad z'=-\beta z + x y</math>. The constants are chosen as follows: <math> \sigma=10,\ \rho=28,\ \beta=8/3</math>. [http://helmut.knaust.info/class/200910_2326/Lorenzp2.html 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.
* [http://en.wikipedia.org/wiki/Frederick_Lanchester Frederick W. Lanchester]
* [http://helmut.knaust.info/class/200910_2326/bifurcation.gif Animation of logistic growth with harvesting]. The family of differential equations has the form <math>y'=y(1-\frac{y}{5})-h</math>.
* [http://en.wikipedia.org/wiki/Rabbits_in_Australia Rabbits in Australia]

CRN 13027 - Revision history

HelmutKnaust: Created page with "==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, ..."

HelmutKnaust: Created page with "==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,
..."