MAT 311-01 Calendar Fall 2007
See WeBWorK for a list of on-line homework problems.
This is a tentative schedule for MAT 193-01. Please check this page frequently for new homework assignments and updates.
Section numbers (e.g. "8.1") refer to sections in our textbook.
- 1st week. Aug. 29-31
- 1.1 Basic definitions and concepts
- 1.2 Some basic theory
- Homework:
- Obtain a copy of the textbook and read sections 1.0-1.2
- Write down a system of ordinary differential equations to describe this situation: n points (x1,y1), (x2,y2), (x3,y3), ... , (xn,yn) are moving around in the x,y plane. Each point is chasing after the next point: the first point chases after the second, the second chases the third, and so on, and the nth point chases the first. All points are moving at speed 1 (in whatever units you choose, e.g. meters per second). Hint: since the points are moving their coordinates are functions of t=time: x1=x1(t), y1=y1(t), etc. The fact that each point chases the next point and moves at unit speed tells you something about their velocities.
- 2.7 The Direction Field
- Solving ODEs with a computer. Download this file dirfield.m (corrected). To prevent your browser from changing the file when you download it, right-click the link then select "save-as" and save it as a file named dirfield.m If your browser asks you what type of file it is, select "All". The ".m" (that is dot-m) at the end of the file name tells Octave or MATLAB that the file contains an executable program. This "mfile" will run on Octave or MATLAB. I will show you how to use it. If you save dirfield.m in in Octave or MATLAB's working directory you can also get brief instructions for using it by typing help dirfield in Octave or MATLAB.
- Problems in the textbook: 1.2 #2, 7, 15, 20, 33 (Due next Wednesday).
- 2nd week. Sept. 3-7
- 3rd week. Sept. 10-14
- Existence and Uniqueness Theorem I
- Discussion: points chasing each other around the plane
- 2.7 The Direction Field and Euler's method
- Due next Monday: a list of differential equations describing the "points chasing each other around on the plane" problem.
- Due next Monday: WeBWorK problems (see link at the top of this page.)
- Due next Wednesday: Answers to questions on Wednesday's handout.
- 4th week. Sept. 17-21
- More discussion: the "points chasing each other around on the plane" problem.
- 2.2 Separable Equations
- 2.1 Linear Equations (with Variation of Parameters)
- Due next Friday 9/28 (Note: Date changed) more WeBWorK problems. (Check the website at the top of this page).
- Due Monday: set up some reasonable initial conditions for the "points chasing each other around on the plane" problem. Make tables of the positions of the points as functions of time. and plot the result. Your plot should show how all the points move around on the plane together. Do this for at least 3 different sets of initial conditions. Write up a brief report describing your solution to this problem in words, including the differential equations you derived, the initial conditions you tried, the commands you typed into the computer to solve the equations, the output, and the plots. Evaluate your own solutions: do you think they are reasonable? (If not then try to fix them and make sure they are!)
- Solution.
- 5th week. Sept. 24-28
- 6th week. Oct. 1-5
- Monday Oct 1. First midterm exam. Solutions to Exam problems.
- More discussion of the "points chasing each other around the plane" problem and how to solve it numerically with Octave/MATLAB. Example chase.m file
- Phase line, Logistic Equation
- 7.5 The Logistic Equation and the Path to Chaos
- Phase plane, predator prey equation, equilibrium points
- 2.8 Higher-order numerical methods
- Second order equations as systems of first order equations, existence and uniqueness theorem
- 3.1 Introduction to Second-order Linear Equations
<--->
- 7th week. Oct. 8-12
- 3.2 Fundamental Solutions of the Homogeneous Equation
- 3.3 Reduction of Order
<--->
- 3.4 Homogeneous Equations with Constant Coefficients: Real Roots
- 3.5 Homogeneous Equations with Constant Coefficients: Complex Roots
- 8th week. Oct. 15-19
- 3.6 Nonhomogeneous Equations
- 3.7 Solving Nonhomogeneous Equations: Method of Undetermined Coefficients
- 3.8 Solving Nonhomogeneous Equations: Method of Variation of Parameters
- 9th week. Oct. 22-26
- 10th week. Oct. 29-Nov. 2
- Supplementary homework: write up nicely and turn in these exercises from the textbook: 3.11 #9, #10. Solutions.
- 3.9 Mechanical Systems and Simple Harmonic Motion
- 3.10 Unforced Damped Vibrations
- 3.11 Forced Vibrations
- 11th week. Nov. 5-9
- Review
- Wednesday Nov 7 Midterm Exam Solutions
- 12th week. Nov. 12-16
- Monday Nov. 12 Veterans' Day Holiday
- 4.1 Review of Power Series
- 4.2 Power Series Expansions about Ordinary Points: part I
- 4.3 Power Series Expansions about Ordinary Points: part II
- Homework in textbook: 4.2 #16, 18, 4.3 #10 12. Give at least five terms in the solution. Due Wednesday 11/21.
- Make-up homework (Optional, only for those who did not turn in problem 3.11 #9,#10) Do 3.11#9 but change the equation to u''+8u'+48u=36cos(6t). Do #10) but assume the weight stretches the spring 6.4 ft. instead of 1.6 ft.
- 13th week. Nov. 19-23
- Second order equations: theory. Existence and uniqueness, numerical solutions. Notes
- Friday Nov. 23 Thanksgiving Day Holiday Break
- 14th week. Nov. 26-30
- 8.1 Phase Plane Analysis of Autonomous Systems
- 8.2 Equilibrium Points and Stability for Linear Systems
- Supplementary notes: Linear systems: Eigenvalues and Eigenvectors
- 15th week. Dec. 3-7
- Example of graphical analysis of nonlinear system of ODEs: Predator-prey equations. Also Logistic growth.
- Review
- Final Exam Week. Dec. 10-14