MATH 3200-002: Elementary Differential Equations, UC Denver, Spring 06

Tutoring is available, see the schedule and the flyers.

PREREQUISITE:
MATH 2411 (Analytical Geometry and Calculus II)
COREQUISITE:
MATH 3191 (Applied Linear Algebra)

HOURS: Tue,Th 4-5:15 pm
LOCATION: NC 1539

INSTRUCTOR:
Prof. Andrew Knyazev
Office: UC Denver Bldg., 6th Floor, room 644
(1250 14th St.) Across Speer Blvd. from Science Building
Phones: 303- 556-8102 (office), 303-556-8442 (math dept main line)
Office hours: Tuesday, Thursday 2:30-3:45 pm, or by appointment.
WWW: http://math.ucdenver.edu/~aknyazev/
EMAIL: andrew_dot_knyazev_at_ucdenver_dot_edu

REQUIRED 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: (to be announced)  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 (to be announced) or student access code as your registration number.

Free tutoring is also available from the UC Denver Center for Learning Assistance/Tutoring at NC 2006, (303) 556-2802.
Space is limited, please get registered as soon as possible!

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.

Jan. 17-19. 1. Introduction to Differential Equations.

• Examples of Differential Equations.
• Direction Fields.

Jan. 19-26. 2. 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.)

Jan. 27 - Feb 28. 3. 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. 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. (Optional, for independent reading.)
• The General Solution of the Linear Nonhomogeneous Equation.
• The Method of Undetermined Coefficients.
• The Method of Variation of Parameters. (Optional, for independent reading.)
• Forced Mechanical Vibrations, Electrical Networks, and Resonance. (Optional, for independent reading.)

5. 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. (Optional, for independent reading.)

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

GRADING:
In class Midterm Test (on Ch. 1-3) - 30%,
In class Final test (on Ch. 4-6) - 30%.
Computer Project - 10% extra credit,
In class 3 Quizzes(best 2 out of 3)- 40%.

No quizz make-ups accepted. Exams make-ups only with a very strong justification. All quizzes and exams are in class, open book/notes, no electronic devices of any kind (including, but not limited to mobil phones, calculators, CD-players, computers). Exams and quizzes may be in a multiple choice form.

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.

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.

• MATLAB student tutorial from MathWorks

The Center for Learning Assistance
* The Center for Learning Assistance is where students go to get help or insight with class assignments, course-loads, and study skills. The Center also helps with arranging tutoring sessions, which take place in the days or evenings.
			North Classroom Building (NC) Room 2006
			(303) 556-2802
			Monday - Thursday 8am-7pm 
			Friday 8am-5pm

Program Access for Persons with Disabilities
* The University of Colorado Denver is committed to providing reasonable accommodations and access to programs and services to persons with disabilities.  Students should contact the Disabilities Services Offices. 
			Arts building 177; 303-556-3450, TTY 303-556-8484.  

Academic Advising Center
* This office serves as the first point of contact for students who are pre-business, pre-engineering, or who have not declared a major in CLAS or CAM.  In addition, the center provides general information and resource referral to all students.
			North Classroom Building (NC) Room 1 
				     Phone # 303-352-3520

Career Center
* The Career Center offers a full array of services that prepare students for career success, such as resume help, internship and career counseling and they have a large career library.
			Tivoli Student Union Room 260