# Ordinary and Partial Differential Equations

CATALOG DESCRIPTION: Ordinary and Partial Differential Equa-
tions (4) First- and second-order equations; special functions; Laplace trans-
form solutions; higher order equations; Fourier series; partial differential
equations.

PREREQUISITE: MATH 141 or MATH 141H

TEXT: Elementary Differential Equations and Boundary Value Problems,
William E. Boyce & Richard C. DiPrima

9th Edition ISBN: 978-0-470-38334-6

or

8th Edition ISBN: 978-0-471-43338-5:

INSTRUCTOR: Vitaliy Gyrya

Office hours: Wednesday & Friday, 11am-noon, 3pm-4pm.

EXAMINATIONS: There will be two midterm exams and one final exam.
Exam I will be held on Thursday 2/26/06.
Exam II will be announced.
Final Exam will be during Final Exam Week as scheduled by the Registrar.
Makeup exams will be given only if a University recognized excuse is pro-
vided.

 Exam I 100 points Grade Cut off Exam II 100 points A 90% Homework & Quizzes 150 points B 80% Final Exam 150 points C 70% Total 500 points D 60%

COURSE DESCRIPTION and NUMBER of LECTURES :

 INTRODUCTION 1.1 Direction fields 1 1.2 Solutions of Some DE's .5 1.3 Classification of DE's .5 FIRST ORDER DE's 2.2 Separable Equations 1 2.1 Linear Equations with Variable Coefficients 2 2.3 Modeling with First Order Equations (do mixture, interest and air resistance) 3 2.4 Differences Between Linear and Nonlinear Equations 1 2.5 Autonomous Equations, Population Dynamics (cover stability and concavity) 1 2.6 Exact Equations (omit integrating factors) 1 SECOND ORDER LINEAR EQUATIONS p.131 The case of the missing y and the case of the missing t 1 3.1 Homogeneous Equations with Constant Coefficients (cover the equations with missing y or missing t, initial value problems with data specified not at 0) 2 3.2 Fundamental Solutions of Linear Homogeneous Equations 2 3.3 Complex Roots of the Characteristic Equations 2 3.4 Repeated Roots ; Reduction of Order 1 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficient 3 3.7 Mechanical Vibrations (omit electrical vibrations) 2 3.8 Forced Vibrations (no damping) 1 HIGHER ORDER LINEAR EQUATIONS 4.2 Homogeneous Equations with Constant Coefficients 1 SERIES SOLUTIONS OF SECOND ORDER LINEAR EQUATIONS 5.2 Series solutions near an ordinary point 1 THE LAPLACE TRANSFORM 6.1 Definition of the Laplace Transform 2 6.2 Solution of Initial Value Problems 2 6.3 Step Functions 1 6.4 Differential Equations with Discontinuous Forcing Functions 1 6.5 Impulse Functions 1 SYSTEMS OF FIRST ORDER LINEAR EQUATIONS 7.1 Introduction to Systems of Differential Equations 1 7.5-9 Classification of critical points and sketching phase portraits. 2 NUMERICAL METHODS 8.1 The Euler or Tangent Line Method 1 NONLINEAR DIFFERENTIAL EQUATIONS AND STABILITY 9.1 Phase portraits and stability 1 9.2 Phase portraits for Nonhomogeneous Linear systems 1 9.5 Linearize a nonlinear system at each of its critical points. Phase portrait for predator- prey equation . 1 PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES 10.1 Two Point Boundary Value Problems 1 10.2 Fourier Series 2 10.3 The Fourier Theorem 2 10.4 Even and Odd Functions 2 10.5 Separation of Variables ; Heat in a Rod 2 10.6 Other Heat Conduction Problems 2 10.7 The Wave Equation: Vibrations of an Elastic String 1 10.8 Laplace's Equation 1 Review 3 Total 59

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