Syllabus

MATH 2255 Lectures MWF Place CH 0218 , 11.30 AM- 12. 25 PM (This page will be updated and adjusted to reflect the pace of the course; please check it regularly.) Purpose of the course: The course is an introduction to the most basic concepts and methods in solving ordinary differential equations. Upon completion of this course students should know some applications of ordinary differential equations in engineering, physics and biology. Text book: Elementary differential equations and boundary value Problems, by W.E.Boyce and R.C. DiPrima, (8th edition, blue cover- custom unbound edition) or Text book: Elementary differential equations and boundary value Problems, by W.E.Boyce and R.C. DiPrima, (9th edition) In view of the complexity of the material discussed a continuous class attendance is STRONGLY RECOMMENDED. Grading policy: Two midterms, each graded with 100 pts. One miter 50 pts. Final exam graded with 200 pts. Home work assignment 50 pts. SYLLABUS: Will be updated and adjusted to reflect the pace of the course Ch 1 Introduction: 1.3 Classification of differential equations. Ch 2. First Order Differential Equations: 2.1 Linear Equations with variable coefficients, 2.2 Separable equations, 2.3 Modeling with first order equation (Only Example 4 about Escape velocity) 2.4 Difference between linear and nonlinear equations, 2.5 Autonomous equations and Population Dynamics, 2.6 Exact equations and integrating factors, 2.7 Numerical approximation, Euler Method, 2.8 The existence and uniqueness theorem. (7 lectures) Ch 3 Second order Linear equations: 3.1 3.2 3.3 3.4 3.5 3.6

Homogeneous equations with constant coefficients, Solutions of linear homogeneous equations; the Wronskian Complex roots of the characteristic equations, Repeated roots, reduction of the order, Nonhomogeneous equations, Method of undetermined coefficients, Variation of parameters. 1

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3.7 Mechanical and Electrical vibrations 3.8 Forced vibrations (6 lectures) Midterm 1. Most likely February 7 or February 10 Ch 4 Higher Order Linear Equations: 4.1 General theory of n−th order linear equations, 4.2 Homogeneous equations with constant coefficients, 4.3 The method of undetermined coefficients, 4.4 The method of variation of parameters. (6 lectures) Ch 6 The Laplace Transform: 6.1 Definition of the Laplace transform, 6.2 Solution of the initial value problems, 6.3 Step functions, 6.4 Differential equations with discontinuous forcing, 6.5 Functions, 6.6 Impulse functions, 6.6 The convolution integral. (7 lectures) Midterm 2. Most likely March 7 or March 17. Ch 5. Series Solutions of Second order linear equations: 5.1 Review of power series, 5.2 Series solutions near ordinary point (part 1), 5.3 Series solutions near ordinary point (part 2), 5.4 Regular singular points, 5.5 Euler equations, 5.6 Series solutions near regular singular point (part 1), 5.7 Bessel functions (8 lectures) Midterm 3. Most likely April 7. The remaining class hours will be occupied by exams and review of the material. FINAL EXAM, Friday April 25-th 12-1.45 PM Home work assignments. Grader: Raeyong Kim email: [email protected] Office : MA 458 , Office Phone : 292-1482 Only the problems within parentheses are supposed to be evaluated. Please write down the solutions in clean and well organized manner. You should drop your assignment at the end of the week (Friday) in the envelope No 1 on the door of my office (MW 752) and collect the graded work next week from envelope No 2. 1.1: 1, 3, 4, 7, 25 (difficult), 1.2: 1, 3, 7, 8, 12, 17.

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1.3: 1, 7, (( 9, 14, 17 )), 21, 23, 25, 27 2.1: 6,7,10,11 13, ((15,17, 19 , 21, 24, 28)), 38 In problem 21-24 ignore part a) 2.2: 2, 5, 6, 8, 13, ((17, 22, 26, 28)), 31, 35 2.3: ((20, 22, 26)), 30 2.4: all odd problems from 1 to 12, ((21)), 27, ((29, 31)) 2.5: 1, 3, ((5)), 9, ((13)), 16, ((17)), 18, 19 2.6: ((7)), 12, 15, ((19)), 21, ((25)), 27, 32 2.8: ((1, 3, 11)), 15, 16, 17 page 132/144 edition 9. pqge 131 edition 8 ((1, 8, 22,31 )) 2.8: ((1, 3, 11)), 15, 16, 17 page 132/144 edition 9. pqge 131 edition 8 ((1, 8, 22,31 )) 3.1: 5, 7, ((20, 22, 26, 28)) 3.2: 2, 5, 10, ((12, 17, 23, 25, 28)), 30, 33, 35 3.3: 7,9, ((11, 12, ))13, 15, 17, 19, ((23, 25, 27)), 32 3.4: 1, 5, 9, ((7, 10,)) 13, 15, ((17, 20, 21, 23,)) 27, 29 Problems for midterm 1 to review (from text book) page page 41: 16,17,28,29 page 76: 28,29 page 89: 15 page 100: 15 21 25 page 144: 12,15 page 155: 9,11, 36 page 163: 25,26 page 172: 10, 15 3.5: ((7, 9)), 11, 13, 17, 19, ((25, 26, )) 27, 31, 33, 34 3.6: 1, 5, 9, 11, ((15, 16, 18)), 21, 22, 23, 28 3.7: ((7,11)), 14, 18, 28, 30 4.1: 5, 9, ((10, 14, 16,)) 17, 20, 23, 24 4.2: 11, 15, ((18, 21, 27)), 28, 30, 33, 36, ((38 )) 4.3: 1, ((5, 6 )), 11, 12, ((17 )) 4.4: 1, ((5 )), 9, ((11)), 12, ((13, 15)), 17 6.1: ((5, 9, )) 10, 15, 21, 26, 19, ((23)) 6.2: 2, 4, 8, ((12, 17, 23)), 27, 32, 6.3: 13, ((14,)) 15, 21, 23, ((37, 38,)) 40 6.5: 5, 8, ((11, 15, ))16, ((17)) 6.6: 5, 7, 9, 10, ((16, 17, 20,)) 22

Office hours: MWF 1PM - 2PM Dan Burghelea, MW 752 e-mail [email protected] Tel 614-292-5259