General Information

      Instructor: Dave Rusin ( 
      Office hrs: MWF 2-3:30 and by appointment, in RLM 9.140 .
      (I am usually in my office during ordinary business hours but if you
      want to be sure I'm available, let me know in advance.)

      Text: Applied Mathematics, by J.D. Logan (4th Edition, Wiley, 2013)
      You may also use the all-electronic version of the book.

      This course has Unique ID 54350 and meets MWF at 10am in RLM 7.104

      Registration in this course is closed; I can't put anyone into
      it. If you think you will probably drop the course, please do
      so promptly and allow another student to take your place.

      Your final exam will be held Monday, December 12, 7:00 PM -- 10:00 PM
      There is no provision for taking the final exam earlier or later.
      You can always confirm your own exam schedule at the Registrar's web site.
      The exam may not be held in the regular classroom; I will announce the
      location when I know it.

Course webpage: It is unlikely that I will post any important material to Canvas; for any additional information I want to give you outside of class you should come to this webpage.

OOPS! I messed up the sheep-population model in class today so I prepared a detailed writeup of the model, including some actual data that you can play with if you like. here it is. You'll need this for homework 4.

BONUS! I found some notes I had made regarding the differential equation you addressed in HW 5 (y'' + y = epsilon y (y')^2). Read 'em and weep!

AND I wrote up solutions to HW7 for you to prepare for the exam.

AND at your request I wrote up one solution to HW6 too.

AND now an updated HW 6 sheet.

Course Description

This course is for students interested in mathematical modeling and analysis. The goals are to develop tools for studying differential equation models that arise in applications, and to illustrate how the derivation and analysis of models can be used to gain insight and make predictions about physical systems. Emphasis will be placed on concepts and examples, and a broad range of applications from the engineering and physical sciences will be considered. Topics include: dimensional analysis, scaling, dynamical systems, stability and bifurcation, perturbation methods, and calculus of variations.


Mathematics 427J or 427K, and 341 or 340L, with a grade of at least C- in each; and some basic programming skills.

Class structure

I would like to use our very limited time together to be more productive by getting you to do things rather than sit passively listening to me drone on and on. We will work individually or in groups, and some of you may present work for the rest of the class to see.

Graded material

Homeworks: I intend to assign homework problems approximately weekly. By all means work with your friends but you must write up your own work.

I will drop the two lowest homework grades and average the rest to give you a "Homework Score" of up to 100 points for the semester

Here are the homework assignments I have set so far: HW01 HW02 HW03 HW04 HW05 HW06 (fixed 11/18, sorry) HW07

Homework scores will be converted to letter grades using the following scale:

Exams: There will be 2 mid-term exams, to be held during the usual class period, and a comprehensive final exam.

I will use the scale above to convert your raw score to a letter grade, but because my exams tend to be hard, I will also use the following alternative method if it gives you a higher letter grade. After I compute the mean and the standard deviation of the class grades, I will determine how many standard deviations above or below the mean your grade is. If your score is greater than the mean by less than one standard deviation, you will get a B (or B+ or B-, as appropriate); higher scores get A's, lower scores get C's, D's, and F's. For example, suppose the class average on the exam was 78.3 points and the standard deviation was 14.4 points. Then the conversion from raw scores to letter grades will be based on these brackets (of width 14.4/3 = 4.8 up and down from 78.3) :
In this way I am literally giving grades of "above average" (A's and B's) exactly to students whose scores are above the class average. (Mean is not the same as median; most of the students last semester got A's and B's; only 11% of the letter grades were D's and F's.)

Note that in this example any student whose raw score was 87 or higher would get a higher letter grade based on the traditional 90-80-70-60 scale shown earlier, and thus for those students the more generous scale will be used.

Letter Grades

Your final semester grade is simply a weighted average of the components: homework 30%, midterms 20% each, and the final exam 30%. I do the arithmetic as is done for high-school GPAs: A=4.0, B=3.0, etc; "+" and "-" are one-third of a letter grade up or down. An average of 3.83 rounds down to an A- (4-1/3) while 3.84 rounds up to an A (4.00), etc. Sadly, the university does not permit me to report scores of "A+" but internally I do track those terrific students whose semester average is 4.17 or above!


Classroom activity: Our meeting times together are very short so we must make the most of them. Come to class daily and ask questions; this is greatly facilitated by reading ahead each day and doing the homework problems as they are assigned. Please silence your cell phones. I will always assume that any talking I hear is about the course material so I may ask you to share your conversations with the class.

Make-ups: It is in general not possible to make up missing learning modules or homework assignments after the due date. If you believe you will have to miss a graded event, please notify me in advance; I will try to arrange for you to complete the work early.

Students with disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.

Religious holidays: If you are unable to participate in a required class activity (such as an exam) because it conflicts with your religious traditions, please notify me IN ADVANCE and I will make accommodations for you. Typically I will ask you to complete the required work before the religious observance begins.

Academic Integrity. Please read the message about Academic Integrity from the Dean of Students Office. I very much prefer to treat you as professionals whose honesty is beyond question; but if my trust is violated I will follow the procedures available to me to see that dishonesty is exposed and punished.

Campus safety: Please familiarize yourself with the Emergency Preparedness instructions provided by the university's Campus Safety and Security office. In the event of severe weather or a security threat, we will immediately suspend class and follow the instructions given. You may wish to sign up with the campus alert programs.

Counseling: Students often encounter non-academic difficulties during the semester, including stresses from family, health issues, and lifestyle choices. I am not trained to help you with these but do encourage you to take advantage of the Counselling and Mental Health Center, Student Services Bldg (SSB), 5th Floor, open M-F 8am-5pm. (512 471 3515, or

Calendar: Please note that there will be no class the day before Thanksgiving (Nov. 23) this year. Aug 29 is the last day to drop without approval of the department chair; Sept 9 is the last day to drop the course for a possible refund; Nov 1 is the last day an undergraduate student may, with the dean's approval, withdraw from the University or drop a class except for urgent and substantiated, nonacademic reasons.

Computers: You are welcome to use the department's computer facilities. Our 40-seat undergrad computer lab in RLM 7.122, is open to all students enrolled in Math courses. Students can sign up for an individual account themselves in the computer lab using their UT EID. We have most of the mainstream commercial math software: Mathematica, Maple, Matlab, etc., and an assortment of open source programs. If you come to my office you will see me use some of this software to help illustrate concepts. Please see me if you would like more information.