# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 22B: Differential Equations
Approved: 2000-09-01 (revised 2011-07-01, Bruno Nachtergaele)

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Elementary Differential Equations and Boundary Value Problems, 9th Edition, by Boyce/DiPrima (Wiley; \$157.12 via Amazon.com)
Search by ISBN on Amazon: 978-0470383346

Suggested Schedule:

 Lecture(s) Sections Comments/Topics 1 and 2 1.1-3 Introduction and terminology, direction fields, discussion and solution of some ODE 3 2.1 Linear equations; integrating factors 4 2.2 Separable equations 5 2.3-4 Modeling, mechanics; Linear versus non-linear equations 6 2.5 Autonomous equations; Population dynamics 7 2.7 Numerical approximation; Euler’s method 8 2.8 Existence and uniqueness theorem 9 2.9 First order difference equations 10 3.1 Homogeneous 2nd order equations with constant coefficients 11 and 12 3.2-3 Fundamental solutions, linear independence, Wronskian 13 3.4 Complex roots 14 3.5 Repeated roots; Reduction of order 15 3.6 Nonhomogeneous equations; Method of undetermined coefficients 16 3.7 Variation of parameters 17 3.8-9 Applications to oscillating systems 18 6.1 Laplace Transform, definition 19 6.2 Solution of initial value problems with Laplace Transform 20 7.1 Systems of linear ODE, introduction 21 7.2-3 Review of related linear algebra 22 7.4 Basic theory of first order linear systems 23 7.5 Homogeneous linear systems with constant coefficients 24 7.6 Complex eigenvalues 25 7.7 Fundamental matrices 26 7.8 Repeated eigenvalues 27 7.9 Nonhomogeneous linear systems 28 Applications and review