# Science:Math Exam Resources/Courses/MATH215

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 MATH215

## MATH 215/255

Since both MATH 215 and 255 have the same curriculum and same exams, we are listing everything here under the title MATH215 only but all the content is intended for MATH255 students as well.

## General Course Info

Visit the course main page here.

## First order equations

Integrals as solutions 1.1

Slope fields and unique existence 1.2

Separable equations 1.3

Linear equations and the integrating factor 1.4

Exact equations (notes)

Autonomous equations 1.6

Numerical methods: Euler’s method 1.7

## Second order linear equations

Second order linear ODEs (method of reduction of order) 2.1

Constant coefficient second order linear ODEs (2.2 and notes)

Mechanical vibrations 2.4

Nonhomogeneous equations (undetermined coefficients and variation of parameters) 2.5

Forced oscillations and resonance 2.6

## Laplace transforms

Definition and examples 6.1

Transforms of derivatives and ODEs 6.2

Convolution 6.3

Dirac delta and impulse response 6.4

## 4. Linear systems

Introduction to systems of ODEs 3.1–3.3

Eigenvalue method 3.4

Two dimensional systems and their vector fields 3.5

Second order systems and applications 3.6

Multiple eigenvalues 3.7

Matrix exponentials 3.8

Nonhomogeneous systems 3.9

## Nonlinear autonomous planar systems

Critical points and linearization 8.1

Stability and classification of isolated critical points 8.2

Applications 8.3

## All Topics in this Course in Alphabetical Order

MER CH flag, MER CS flag, MER RQ flag, MER RT flag, MER Tag Initial value problem---MER QGQ flag, MER RH flag, MER RS flag, MER RT flag, MER Tag Separation of variables---MER QGQ flag, MER RH flag, MER RS flag, MER RT flag, MER Tag Critical points and intervals of increase and decrease---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Linear ordinary differential equation---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Linear ordinary differential equation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Higher-order differential equation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Exact differential equation, Pages with math errors---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Exact differential equation---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Steady state and equilibrium---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Laplace transforms---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Higher-order differential equation, MER Tag Laplace transforms---MER QGH flag, MER QGQ flag, MER QGS flag, MER QGT flag, MER Tag Laplace transforms---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Laplace transforms---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Laplace transforms---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Laplace transform---MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Eigenvalues and eigenvectors---

Day of final exam: Monday, December 15th at 3:30pm

## Available Midterm Exams

Year   Instructor   Midterm number   pdf
2014   Lindstrom 1 of 3
2014   Lindstrom 2 of 3
2014   Lindstrom 3 of 3