MATH 251 Ordinary and Partial Differential Equations Spring Semester 2011 Syllabus Course Description: 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, 9th edition (7th or 8th ed ok), W. E. Boyce and R.C. Diprima, John Wiley and Sons, Inc. Examinations: Two 75-minute midterm examinations, given on February 17 and April 4, and a comprehensive final examination given during the final examination period. The final examination period will begin on Monday, May 2 and end on Friday, May 6. Students should not make plans to leave University Park before Saturday, May 7, 2011. Calculators: A calculator 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 100 points midterm examination I (6:30 - 7:45 pm, 2-17-2011) 100 points midterm examination II (6:30 - 7:45 pm, 4-4-2011) 100 points quizzes/homework 150 points final examination 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 Note: The above is the common policy across all sections of Math 251. Please check with your instructor for other section-specific policies. Theses include, but are not limited to: office hours, homework and quiz schedule, late homework policy, and attendance requirement. Questions, Problems, or Comments: If you have questions or concerns about the course, please consult your instructor first. If further guidance is needed, you may contact the course coordinator whose address is given below. Course Coordinator: The department coordinator for Math 251 during the spring 2011 semester is Zachary Tseng. You can reach him by sending an email to [email protected] Course Outline: 1. INTRODUCTION 1.1 Direction Fields (.5) 1.2 Solution of Some Differential Equations (1) 1.3 Classification of Differential Equations (.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 (cover mixing problems, plus either motion with air resistance, compound interest, or Newton’s law of cooling) (3) 2.4 Differences Between Linear and Nonlinear Equations (1) 2.5 Autonomous Equations and Population Dynamics (cover stability of equilibrium solutions) (1.5) 2.6 Exact Equations (omit Integrating Factors) (1.5) 3. SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS 3.1 Homogeneous Equations with Constant Coefficients (1) 3.2 Fundamental Solutions of Linear Homogeneous Equations; Wronskian (2) 3.3 Complex Roots of the Characteristic Equations (1) 3.4 Repeated Roots; Reduction of Order (1.5) 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients (3) 3.7 Mechanical and Electrical Vibrations (2) 3.8 Forced Vibrations (w/o damping) (1) 4. HIGHER ORDER LINEAR EQUATIONS 4.1 General Theory of n-th Order Linear Equations (.5) 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 (1.5) 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 an Elastic String (2) 10.8 Laplace's Equation (2) (This schedule is subject to change.) ACADEMIC INTEGRITY STATEMENT: All Penn State policies regarding ethics and honorable behavior apply to this course. For more information see:
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