MATH 251 Sections 4/5/6 Spring Semester 2011 INSTRUCTOR: Zachary Tseng OFFICE: 410 McAllister Building OFFICE HOURS: Monday 4:40 to 5:30 PM; Wednesday 12:20 to 1:10 PM OFFICE PHONE: 865-1401 E-MAIL: [email protected] MAILBOX: Located in 109 McAllister Building URL: http://www.math.psu.edu/tseng/class/sp2011.html COURSE DESCRIPTION: Ordinary and Partial Differential Equations (4:4:0). First- and second-order equations; Laplace transform solutions; higher order equations; second-order linear partial differential equations; Fourier series. PREREQUISITE: Math 141, or equivalent courses. TEXTBOOK: Elementary Differential Equations and Boundary Value Problems, 9th (or 7 / 8th) edition, W. E. Boyce and R.C. Diprima, John Wiley and Sons, Inc. EXAMINATIONS: Two 75-minute midterm examinations (6:30 to 7:45pm), and a comprehensive final examination. ATTENDANCE POLICY: Regular classroom attendance is expected and required. Attendance will be taken on random days through out the semester. Any recorded absence beyond the third instance, and without an accompanying official university excuse, WILL negatively impact your semester grade (approx. −1% of your final course score per absence). Since different sections might have attendance taken on different days, be sure to attend the section in which you are registered under. Unless you have my permission in advance, you must be present in your registered section for your attendance to count. GRADING POLICY: Grades will be assigned on the basis of 450 points distributed as follows 100 points midterm examination I (2-17-2011) 100 points midterm examination II (4-4-2011) 100 points quizzes/homework 150 points final examination TOPICS: INTRODUCTION 1.1 Direction Fields 1.2 Solution of Some Differential Equations 1.3 Classification of Differential Equations FIRST ORDER DIFFERENTIAL EQUATIONS 2.1 Linear Equations with Variable Coefficients2.2 Separable Equations 2.3 Modeling with First Order Equations 2.4 Differences Between Linear and Nonlinear Equations 2.5 Autonomous Equations and Population Dynamics 2.6 Exact Equations (omit Integrating Factors) SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS 3.1 Homogeneous Equations with Constant Coefficients 3.2 Fundamental Solutions of Linear Homogeneous Equations 3.3 Complex Roots of the Characteristic Equations 3.4 Repeated Roots; Reduction of Order 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients 3.7 Mechanical Vibrations 3.8 Forced Vibrations (w/o damping) HIGHER ORDER LINEAR EQUATIONS 4.2 Homogeneous Equations with Constant Coefficients THE LAPLACE TRANSFORM 6.1 Definition of the Laplace transform 6.2 Solution of Initial Value Problems 6.3 Step Functions 6.4 Differential Equations with Discontinuous Forcing Functions 6.5 Impulse Functions SYSTEMS OF TWO LINEAR DIFFERENTIAL EQUATIONS 7.1 Intoduction to Systems of Differential Equations 7.2-7.3 Introduction to 2 x 2 Matrices 7.5, 7.6, 7.8 2 x 2 Linear Systems of Differential Equations NONLINEAR DIFFERENTIAL EQUATIONS AND STABILITY 9.1 Phase Portraits of 2 x 2 Linear Systems 9.2 Autonomous Systems and Stability 9.3 Almost Linear Systems 9.5 Predator-Prey Equations PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES 10.1 Two-Point Boundary Value Problems 10.2 Fourier Series 10.3 The Fourier Convergence Theorem 10.4 Even and Odd Functions 10.5 Separation of Variables; Solutions of Heat Conduction Problems 10.6 Other Heat Conduction Problems 10.7 The Wave Equation: Vibrations of an Elastic String 10.8 Laplace's Equation (This schedule is subject to change.) ACADEMIC INTEGRITY STATEMENT: All Penn State Policies regarding ethics and honorable behavior apply to this
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