Contact Info

Email: all1@rose-hulman.edu
Office: Moench Hall DL109
Office Phone: 812-877-8716

Syllabus and other handouts

Syllabus .pdf

Projects

Project Primer .pdf
DE Trek: The N-Body Problem .pdf
Zombies! .pdf

Homework

HW1 .pdf
HW2 .pdf
HW3 .pdf
HW4 .pdf
HW5 .pdf
HW6 .pdf
HW7 .pdf

Quiz Solutions

Quiz 1 .pdf

Exams

Review 2 .pdf
Review 3 .pdf
Winter 2014 MA212
Welcome to DE 2. To the left you'll find homework, as well as quiz and exam solutions as we take them. Below I'll be posting solutions to the daily worksheets (hopefully).

Matrix arithmetic

We familiarized ourselves with matrices and operations of addition, scalar multiplication, and matrix multiplication.
Worksheet - .pdf

Systems of Linear Equations

We learned that systems of linear equations can be easily solved by putting augmented matrices into reduced echelon form.
Worksheet - .pdf

Determinants and Rank

We learned that the consistency or solvability of a system is influenced by the determinant and rank of the matrix of coefficients.
Worksheet - .pdf

Singular and Invertible Matrices

We learned that if a matrix is non-singular, then it can be ``undone'' or inverted. This is handy for solving systems like Ax=b for multiple different b. We also related these notions to those of determinant, rank, and consistency of linear systems
Worksheet - .pdf

Eigenvalues and Eigenvectors

Given a system of differential equations x' = Ax, we noticed that solutions were determined by solutions to Av = (lambda)v. This introduced us to the very important notion of eigenvalue (lambda) and eigenvector (v).
Worksheet - .pdf

Separable ODEs

We learned how to solve first order ``separable'' ODEs.
Worksheet - .pdf

Other methods for solving first order ODEs

We learned how to solve linear first order equations by integrating factors and undetermined coefficients.
Worksheet - .pdf

Linear Systems of ODEs

We introduced linear systems of ODEs and discussed what to expect from their solutions.
Worksheet - .pdf

Homogeneous Systems of ODEs with constant coefficients: distinct real eigenvalues

We discussed how to solve a 2x2 system where the matrix of coefficients has two distinct eigenvalues.
Worksheet - .pdf

Homogeneous Systems of ODEs with constant coefficients: complex eigenvalues

We discussed how to solve a 2x2 system where the matrix of coefficients has complex conjugate eigenvalues.
Worksheet - .pdf

Homogeneous Systems of ODEs with constant coefficients: repeat real eigenvalues

We discussed how to solve a 2x2 system where the matrix of coefficients has a repeat real eigenvalue.
Worksheet - .pdf

Non-Homogeneous Systems of ODEs with constant coefficients

We discussed how to solve non-homogeneous systems by the method of undetermined coefficients.
Worksheet - .pdf

Mixing Problems

We worked through a couple mixing problems (salt tank and series decay).
Worksheet - .pdf

Non-Linear Systems of Differential Equations

We discussed equilibrium points of non-linear system and paid lip-service to the process of changing variables (cartesian to polar).
Worksheet - .pdf

Classifying Equilibria on Non-Linear Systems: Via Jacobians

We discussed how to use the Jacobian (or the linearization) of a non-linear system to help classify its equilibria.
Worksheet - .pdf

Non-Linear Modeling: An Accelerating Pendulum

In class, we discussed how to model an undamped pendulum. We go a little farther in this worksheet and assume the pendulum is accelerating (for instance if it was placed in an accelerating car) and under the influence of a damping force.
Worksheet - .pdf

Non-Linear Modeling: The Forever Fall

In this example, we model the motion of a particle falling through a ``cored'' planet.
Worksheet - .pdf

Phase-Plane Method

These examples illustrate the phase-plane method. It would be a good idea to attempt the problem before reading the solution.
Worksheet - .pdf

Heat Equation

We discussed the 1-dimensional Heat Equation.
Worksheet - .pdf

Fourier Series

We discussed how to compute Fourier Series.
Worksheet - .pdf