MATH 266: Elementary Differential Equations
(3-0) Cr. 3. F.S.SS.
Prereq: Minimum of C- in MATH 166 or MATH 166H
Solution methods for ordinary differential equations. First order equations, linear equations, constant coefficient equations. Eigenvalue methods for systems of first order linear equations. Introduction to stability and phase plane analysis.
MATH 267: Elementary Differential Equations and Laplace Transforms
(4-0) Cr. 4. F.S.SS.
Differential Equations And Boundary Value Problems, Pearson, 5th edition with access to MyMathLab online homework platform
Edwards, Penney, and Calvis
MATH 266 and 267 are enrolled in the Iowa State University Immediate Access Program. The price charged through this program covers one semester access to the digital content, that is, the e-book and online homework platform, which will be automatically charged to your U-Bill shortly before classes begin. A print copy of the text can also be purchased, and a loose-leaf version of the text will also become available in the third week of the semester.
Math 267 contains all the topics from Math266, plus two additional topics.
Math 266 and 267
- First Order ODEs
- Sections 1.1–1.2, 1.3 (Optional), and 1.4-1.6
- Applications of the 1st Order ODEs
- Sections 2.1-2.2
- Higher Order Linear ODEs
- Sections 3.1-3.5
- Intro. to Systems of ODEs
- Sections 4.1-4.2
- Linear Systems of ODEs
- Sections 5.1-5.2, 5.3 (Optional), and 5.5-5.7
- Nonlinear Systems and Phenomena
- Sections 6.1-6.2 (Optional)
Math 267 only
- Laplace Transform Methods
- Sections 7.1-7.6
- Power Series Methods
- Sections 8.1-8.2
Objectives for Math 266
Be able to identify types of differential equations and use appropriate methods to solve them.
- Be able to use the method of integrating factors to solve first order linear equations.
- Be able to separate variables and compute integrals in solving first order separable equations.
- Know how to find a general solution of a linear second order constant coefficient homogeneous differential equation by seeking exponential solutions.
- Be able to use the method of undetermined coefficients to find a particular solution of a linear second order constant coefficient nonhomogeneous differential equation.
- Be able to find a general solution of a linear second order constant coefficient nonhomogeneous equation.
- Be able to solve an initial value problem associated with a linear second order constant coefficient homogeneous or nonhomogeneous equation.
- Be able to extend the methods used for linear second order constant coefficient equations to higher order linear constant coefficient equations, both homogeneous and non-homogeneous.
- Be able to use the eigenvalue-eigenvector method to find general solutions of linear first order constant coefficient systems of differential equations of size 2 or 3.
- Be able to find a fundamental matrix for linear first order constant coefficient system of differential equations of size 2 or 3.
- Be able to use the method of variation of parameters to find a particular solution of a nonhomogeneous linear first order constant coefficient system of size 2.
Learn how differential equations are used to model physical systems and other applied problems. These could include the following types of problems.
- Be able to formulate and use elementary models for population dynamics, such as the logistic equation, to describe transient and steady state behavior.
- Be able to work with models for the linear motion of objects using assumptions on the velocity and acceleration of the object.
- Be able to set up and solve a problem involving stirred tank reactor dynamics.
- Be able to use Newton’s second law to set up a model for a simple spring-mass system; and use appropriate methods to obtain the solution of the model problem.
- Be able to use models for continuous compounding of interest to describe elementary savings and loan problems.
Gain an elementary understanding of the theory of ordinary differential equations.
- Understand statements on existence and uniqueness of solutions.
- Understand the role of linear independence of solutions in finding general solutions of differential equations.
- Understand what constitutes a general solution of a differential equation.
- Understand the concept of stability as it relates to equilibrium solutions.
Objectives of Math 267
All of the above objectives for Math 266, and in addition
- Be able to use the method of Laplace transforms to solve linear second order constant coefficient homogeneous and nonhomogeneous equations.
- Be able to use series methods to find a power series solution of a linear second order variable coefficient homogeneous equation about an ordinary point.