MATH 3200-002: Elementary Differential Equations, CU-Denver, Fall 04
Fall 2004, University of Colorado at Denver

(Q1+2)/5*0.4/6 + Q2/5*0.4/6 + Q3/5*0.4/6 + max(Q41,Q42)/5*0.4/6 + (Q5+1)/4*0.4/6 + (Q6+1)/4*0.4/6 +
(MT+1)/10*0.3 + F/10*0.3 + P/10*.2 +Ex*0.01

PREREQUISITE:
MATH 2411 (Analytical Geometry and Calculus II)

COREQUISITE:
MATH 3191 (Applied Linear Algebra)

HOURS: Tue,Th 5:30-6:45 pm, Science Building 327.

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo Bldg) 644. Phone: (303) 556-8102.
Office hours: Thursday 2-3:30 pm, or by appointment.
WWW: http://www-math.cudenver.edu/~aknyazev

TEXTBOOK: W. Kohler & L. Johnson, Elementary Differential Equations, Addison Wesley, 2003, plus MyMathLab Student Starter Package.
It is recommended that you use the Student Solution Manual, which contains detailed solutions to odd-numbered exercises.
The whole book is available for download from MyMathLab. Use Course ID: knyazev42644 to register.

HELP:
Addison-Wesley's Math Tutor Center is staffed by professional math tutors who can help you with what you're learning. Visit the Tutor Center's registration page to sign up. Use your MyMathLab course ID knyazev42644 or student access code as your registration number.
Free tutoring is also available from the CU-Denver Center for Learning Assistance/Tutoring at NC 2006, (303) 556-2802.

SUBJECT:
Differential equations are extensively used as a tool for modeling diverse phenomena ranging from population growth to elementary particles. The purpose of this course is three-fold: firstly, to familiarize yourself with various types of differential equations and master the basic solution techniques; secondly, to see how you can use differential equations in studying real-world systems; thirdly, to get an idea of what to do when you cannot solve the equation. We'll cover most of the contents of Chapters 1 - 6.

CONTENTS:
The class will follow the outline below, touching on each major topic in a depth that will be determined by the pace of the class. The dates are tentative and are not guaranteed.

1. Aug 20 - Sep 2. Introduction to Differential Equations.

• Examples of Differential Equations.
• Direction Fields.

2. Sep 2 - 16. First Order Linear Differential Equations.

• Existence and Uniqueness.
• First Order Linear Homogeneous Differential Equations.
• First Order Linear Nonhomogeneous Differential Equations.
• Introduction to Mathematical Models. (Optional, for independent reading.)
• Mixing Problems and Cooling Problems. (Optional, for independent reading.)

3. Sep 17 - Oct 7. First Order Nonlinear Differential Equations.

• Existence and Uniqueness.
• Separable First Order Equations.
• Exact Differential Equations.
• Bernoulli Equations.
• The Logistic Population Model. (Optional, for independent reading.)
• One-Dimensional Motion with Air Resistance. (Optional, for independent reading.)
• One-Dimensional Dynamics with Distance as the Independent Variable. (Optional, for independent reading.)
• Euler's Method.

4. Oct 12 - Nov 2. Second Order Linear Differential Equations.

• Existence and Uniqueness.
• The General Solution of Homogeneous Equations.
• Fundamental Sets and Linear Independence.
• Constant Coefficient Homogeneous Equations.
• Real Repeated Roots; Reduction of Order.
• Complex Roots.
• Unforced Mechanical Vibrations.
• The General Solution of the Linear Nonhomogeneous Equation.
• The Method of Undetermined Coefficients.
• The Method of Variation of Parameters.
• Forced Mechanical Vibrations, Electrical Networks, and Resonance.

5. Nov 4 -11. Higher Order Linear Differential Equations.

• Existence and Uniqueness.
• The General Solution of nth Order Linear Homogeneous Equation.
• Fundamental Sets and Linear Independence.
• Constant Coefficient Homogeneous Equations.
• Nonhomogeneous Linear Equations.

6. First Order Linear Systems.

• The Calculus of Matrix Functions.
• Existence and Uniqueness.
• Homogeneous Linear Systems.
• Fundamental Sets and Linear Independence.
• Constant Coefficient Homogeneous Systems.
• Complex Eigenvalues.
• Repeated Eigenvalues.
• Nonhomogeneous Linear Systems.
• Euler's Method for Systems of Differential Equations.
• Diagonalization.
• Propagator Matrices, Functions of a Matrix and the Exponential Matrix.

GRADING:
In class Midterm Test (on Ch. 1-3) - 30%,
In class Final test (on Ch. 4-6) - 30%.
Computer Project - 20% extra credit,
In class Quizzes - 40%.
The following distribution of grades is used:
A+ 95-100%, A 90-95%, A- 85-90%
B+ 80-85%, B 75-80%, B- 70-75%
C+ 65-70%, C 60-65%, C- 55-60%
D+ 50-55%, D 45-50%, D- 40-45%

COMPUTING:
Individual projects will be accepted in Matlab only. MATLAB can link executable files, it has graphics already built in and it is an interpretive language originally developed to handle mathematical problems. The students are invited to use the MERC lab where computers with MATLAB are available. Students may also consider getting their own individual student version of MATLAB at MATLAB & Simulink Student Version Release 14 Web page, but it is not required for the class.

Traditional Grading Policy for Undergaduate Classes:

No quizz make-ups accepted. Exams make-ups only with a very strong justification. All quizzes and exams are in class. The only materials students are allowed to bring to the exam are writing instruments and erasers with the exeption of specially announced cases. All exams and quizzes are in a multiple choice form.

ATTENDANCE AND HOMEWORK:
Punctual attendance and homework fulfilment are expected of all students. Students are expected to solve most of the odd numbered problems from the text. Homework problems will not be collected unless by students request.

LINKS:

• MATLAB student tutorial from MathWorks

IMPORTANT INFOMATION FOR STUDENTS:

CLAS students must always have an accurate mailing and e-mail
address:  http:/www.cudenver.edu/registrar.

Students are responsible for completing financial arrangements
with financial aid, family, scholarships


INCOMPLETE GRADES (IW/IF):   Incomplete grades (IW or IF) are
not granted for low academic performance.  To be eligible for
an Incomplete grade, students must (1) successfully complete
75 percent of the course, (2) have special circumstances
(verification may be required) that preclude the student from
attending class and completing graded assignments, and (3)
make arrangements to complete missing assignments with the
original instructor.  A CLAS Course Completion agreement is
strongly suggested.


16 August: (5:00 pm)   Payment plan deadline for students
          registering by 23 July 2004
18 August: Students not on financial aid are disenrolled for
          non-payment.  
26 August:  Last day to select the wait-list for a closed
         course.  Students should check wait-list status daily.
30 August - 8 September:   Students are responsible for
         verifying an accurate Fall 2004 registration 
         via SMART.
2 September (midnight):  Last day to add courses via the web
         SMART system.
6 September:  Labor day, no classes. 
8 September (5:00 pm)  Last day to add 16-week structured
              courses.  Treated as an absolute deadline.
             The 8 Sept. add deadline does not apply to 
             independent study, internships, and late-starting 
             modular courses.
8 September (5:00 pm):   Last day to drop a course for full
             refund.  Last day to select P/F grade option
1 November   Last day to drop a Fall 2004 course without
             associate dean approval.
12 November    Last day to drop a Fall 2004 course for CLAS
               students.  Treated as an absolute deadline.
21-27 November   Full week of Fall break, no classes.
11-17 December   Final Exam week.