Mathematics 254

Introduction to Ordinary Differential Equations

Summer I 2016

Course Syllabus

The textbook is Fundamentals of Differential Equations (Eighth Edition) by R. Nagle, E. Saff, and A. Snider.

session	date	topic	text pages	assignment
1	6Jun	Introduction Calculus Review		Integration Review
2	7Jun	1.1 Background 1.2 Solutions and Initial Value Problems	1-5 6-14	1.1 4,6,11,14,16 1.2 4,7,11,15,18,20
3	8Jun	1.3 Direction Fields Calculus Pre-Test	15-22	1.3 2,7
4	9Jun	1.4 The Approximation Method of Euler Chapter 1 group projects	23-28	1.4 2,3,15
5	10Jun	2.1 Introduction: Motion of a Falling Body 2.2 Separable Equations 2.3 Linear Equations	35-37 38-45 45-54	2.2 17,19,23,25,34 2.3 7,8,10,21,37
6	13Jun	2.4 Exact Equations 3.1 Mathematical Modeling	55-63 89-90	2.4 1-5, 11-15
7	14Jun	3.2 Compartmental Analysis 4.1 Introduction: The Mass-Spring Oscillator	91-100 153-157	3.2 2,5 4.1 3,4,5
8	15Jun	Exam 1 Chapter 2 group projects
9	16Jun	4.2 Homogeneous Linear Equations	158-166	4.2 13-18
10	17Jun	4.3 Auxiliary Equations with Complex Roots 4.4 Nonhomogeneous Equations	167-174 175-181	4.3 21-25,32,33 4.4 13-15, 27-30
11	20Jun	4.6 Variation of Parameters 4.9 A Closer Look at Free Mechanical Vibrations	189-192 214-222	4.6 9,10 4.9 1-3
12	21Jun	4.10 A Closer Look at Forced Mechanical Vibrations Chapter 4 group projects	223-230
13	22Jun	5.4 Introduction to the Phase Plane	263-275	5.4 1,3,5,7,11,12
14	23Jun	5.5 Applications to Biomathematics 5.6 Coupled Mass-Spring Systems	276-284 285-290	5.5 2,3,6 5.6 1,2,7
15	24Jun	8.1 Introduction: Taylor Polynomial Approximations 8.2 Power Series and Analytic Functions 8.3 Power Series Solutions	422-426 427-435 436-445	8.1 1,4,10 8.2 4,5,11 8.3 14,15,16,23,24
16	27Jun	Exam 2 Chapter 5 group projects
17	28Jun	8.4 Equations with Analytic Coefficients 8.6 Method of Frobenius	436-445 455-466	8.4 1,4,8,9 8.6 4,7,8
18	29Jun	9.1 Introduction 9.2 Linear Algebraic Equations Chapter 8 group projects	455-466 502-505	9.1 1,5,6,10 9.2 1,3,7,9
19	30Jun	9.3 Matrices and Vectors 9.4 Linear Systems in Normal Form	506-516 517-525	9.3 6, 9,12,27 9.4 5,8
20	1Jul	9.5 Homogeneous Linear Systems 9.6 Complex Eigenvalues	526-537 538-542	9.5 1,2,4,12 9.6 1.5.6,13
21	5Jun	9.7 Nonhomogeneous Linear Systems Chapter 9 group projects	543-549
22	6Jul	Review
23	7Jul	Final Examination