Ordinary and Partial Differential Equations (4:4:0). First- and second-order equations; series solutions; Laplace transform solutions; higher order equations; Fourier series; second-order partial differential equations.
Prerequisite: Math 141, or equivalent courses.
Textbook: Elementary Differential Equations and Boundary Value
Problems, 8th edition, W. E. Boyce and R.C. Diprima, John Wiley and Sons,
Inc.
Instructor: Melchior
Grützmann
e-mail: grutzman.antispam@math.psu.edu
(please remove the .antispam).
office phone: +1-814-86-39036
office: 402 McAllister
mail address: 109 McAllister Bld
University Park, PA 16802
Course home page:
www.math.psu.edu/grutzman/course/, which is also linked under Angel.
Office hours: Mon 4:35-7:00pm, Fri 1:30-3:20pm, or by appointment in
402 McAllister (please see the course home page for changes, additional
annoucements).
Examinations: Two 75-minute midterm examinations, given on October 2
and November 4, and a comprehensive final examination given during the
final examination period. The final examination period will begin on Monday,
December 15 and end on Friday, December 19. Students should not make plans
to leave University Park before Saturday, December 20, 2008.
Please bring your ID to the exams.
Conflict and Makeup Exams: Only students with a verifiable valid reason,
such as illness or class during the regular exam time, are allowed to makeup
exams.
Students must sign up for conflict or
makeup exam at least 3 days in advance of the exam date.
Calculators: A calculator or computer algebra system may be useful for some homework problems involving graphing. However, the use of calculators is not permitted on exams.
Grading Policy: Grades will be assigned on the basis of 450 points distributed as follows:Final grades will be assigned as follows:
A 405-450 pts; A− 390-404 pts; B+ 375-389 pts; B 360-374 pts
B− 345-359 pts; C+ 330-344 pts; C 315-329 pts; D 270-314 pts
F 0-269 pts
Homework and Quizzes: HW will be assigned every Monday on the course home page, and is due next Monday, collected in class. Quizzes will be occasionally at the beginning of class (which I'll announce in advance). Please be present in class to the quizzes. Due to the limited time of the grader late homework should be an exception.
Questions, Problems, or Comments: If you have questions or concerns about the course (quizzes, homework, exams, points, grades, …), please consult your instructor first. If further guidance is needed, you may contact the course coordinator.
Course Coordinator: The department coordinator for Math 251 during the fall 2008 semester is Zachary Tseng. You can reach him by sending an email to tseng.antispam@math.psu.edu (please remove the .antispam).
Tutors: If you need extra help, a (paid) tutors' list is maintained in the Math Department Undergraduate Office in room 104 McAllister building. It is available online at www.math.psu.edu/ug/PrivateTutorList.htm.
All Penn State
policies regarding ethics and honorable behavior apply to this course.
For more information see: http://www.science.psu.edu/
1. INTRODUCTION
1.1 Direction Fields (.5)
1.2 Solution of Some Differential Equations (1)
1.3 Classification of Differential Equations (with defn of partial derivative; 0.5)
2. FIRST ORDER DIFFERENTIAL EQUATIONS
2.1 Linear Equations with Variable Coefficients (2)
2.2 Separable Equations (1)
2.3 Modeling with First Order Equations (mixing problems, plus
either motion with air resistance, compound interest, or Newton’s
law of cooling; 4)
2.4 Differences Between Linear and Nonlinear Equations (1)
2.5 Autonomous Equations and Population Dynamics (stability of
equilibrium solutions; 1)
2.6 Exact Equations (omit integrating factors; 1)
3. SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS
3.1 Homogeneous Equations with Constant Coefficients (1)
3.2 Fundamental Solutions of Linear Homogeneous Equations (1)
3.3 Linear Independence, Wronskian, and Abel's theorem (1.5)
3.4 Complex Roots of the Characteristic Equations (1)
3.5 Repeated Roots (via std solution; 1)
3.6 Nonhomogeneous Equations; Method of Undetermined Coefficients (3)
3.8 Mechanical and Electrical Vibrations (1.5)
3.9 Forced Vibrations (w/o damping) (1)
4. HIGHER ORDER LINEAR EQUATIONS
4.2 Homogeneous Equations with Constant Coefficients (1)
6. THE LAPLACE TRANSFORM
6.1 Definition of the Laplace transform (1)
6.2 Solution of Initial Value Problems (2)
6.3 Step Functions (1)
6.4 Differential Equations with Discontinuous Forcing Functions
(2)
6.5 Impulse Functions (1)
7. SYSTEMS OF TWO LINEAR DIFFERENTIAL EQUATIONS
7.1 Intoduction to Systems of Differential Equations (1)
7.2-7.3 Introduction to 2 x 2 Matrices(1)
7.5, 7.6, 7.8 2 x 2 Linear Systems of Differential Equations (3)
9. NONLINEAR DIFFERENTIAL EQUATIONS AND STABILITY
9.1 Phase Portraits of 2 x 2 Linear Systems (1)
9.2 Autonomous Systems and Stability (.5)
9.3 Almost Linear Systems (.5)
9.5 Predator-Prey Equations(1)
10. PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES
10.1 Two-Point Boundary Value Problems (2)
10.2 Fourier Series (2)
10.3 The Fourier Convergence Theorem (1)
10.4 Even and Odd Functions (1)
10.5 Separation of Variables; Solutions of Heat Conduction Problems
(2)
10.6 Other Heat Conduction Problems (1.5)
10.7 The Wave Equation: Vibrations of the Elastic String (2)
10.8 Laplace's Equation (2)
(Numbers in parenthesis give the approximate number of lectures covering the topic. This schedule might be subject to change.)
This page is maintained by Melchior Grützmann.