Math 2250 - 002
Midterm #1 Review
Chapter 1:
- Verify the solution of an ODE
- Use integration to solve an ODE of the form
- Given an object's acceleration, initial velocity and initial position, find it's velocity and position at any time.
- Find the general solution of a separable ODE using the separation of variables technique.
- Use an initial condition to solve for C.
- Determine whether or not a solution to an IVP exists, and, if so, whether or not it is unique.
- Determine specifically what initial conditions will guarantee that an IVP has a unique solution.
- Use the integrating factor technique to solve a first-order linear IVP.
- Derive the equations for a mixture problem to answer questions about concentration, volume and pounds of solute in a tank over time.
Fall 2011
9/29/11
Chapter 2:
- Determine the carrying capacity of a population and its base growth rate given a logistic growth equation.
- Derive a logistic growth equation given certain information about a population.
- Solve the logistic growth equation to answer questions about a population at a given time.
[this will involve partial fraction decomposition]
- Find all critical points and equilibrium solutions of an ODE.
- Draw a phase diagram for the critical points of an ODE and use it to determine which critical points are stable and unstable.
- Use Euler's method to approximate the solution to an IVP for a given step size [I won't ask you to do more than two steps on a test].
- Assuming the IVP is solvable, calculate the relative error in your approximation using
Euler's method.
- Explain why the Runge-Kutta method is better than Euler's method in terms of accuracy.

Math 2250 - 002
Midterm #1 Review
Chapter 3:
- Use the elimination method to solve a system of linear equations.
- Determine whether a system of linear equations has one solution, no solutions, or infinitely many solutions.
- Write a linear system of equations as an augmented matrix.
- Understand how to do the three types of elementary row operations and the proper notation for each type.
- Use Gaussian elimination to convert an augmented matrix into an echelon matrix.
- Use Gauss-Jordan elimination to convert an augmented matrix into a reduced echelon matrix.
- Use a reduced echelon matrix to determine whether a linear system has one solution, no solutions, or infinitely many solutions.
- Use a reduced echelon matrix to identify the free variables of the system and express all possible solutions to the system using one or more parameters.
- Addition, subtraction and scalar multiplication of matrices matrices
- Multiply two matrices.
- Find the determinant of a matrix
- Find the inverse of a matrix
Fall 2011
9/29/11
Practice Problems:
Note: I would suggest trying out at least one of each type of problem. If you need the additional practice then work through additional examples of the same problem type.
Section 1.1: 1 - 10, 17 - 26
Section 1.2: 1 - 4, 11 - 15
Section 1.3: 11 - 20
Section 1.4: 1 - 18, 19 - 28, 45 - 50
Section 1.5: 1 - 20, 35 - 37
Section 2.1: 1 - 8, 15 - 20
Section 2.2: 1 - 12, 13 - 18
Section 2.4: 1 - 6
Section 3.1: 1 - 8
Section 3.2: 11 - 16
Section 3.3: 1 - 6
Section 3.4: 1 - 4, 5 - 12
Section 3.5: 1 - 8
Section 3.6: 1 - 6