MATH 307 I: INTRODUCTION TO DIFFERENTIAL EQUATIONS

Exams

See the syllabus for administrative information. More practice exams may be found in Andy Loveless' Math 307 Exam Archive.

Final

Topics for the final:

• 3.4: reduction of order
• 3.5: non-homogeneous DE's
• 3.6: variation of parameters
• 3.7: unforced vibrations
• 3.8: forced vibrations
• 6.1: Laplace transforms (only the parts discussed in lecture; this section is very technical, and we skipped most of it)
• 6.2: Laplace transforms and IVP's
• 6.3: Step functions
• 6.4: Discontinuous forcing

Below are three practice finals with solutions. We have two exams instead of three, so keep that in mind when going through old exams. Our final is not cumulative and will focus on material from after the midterm.

• Here's the final from the last time I taught Math 307 without solutions; with solutions. Here are some statistics. This equation sheet was included in that exam.

• Practice final A; solutions. Ignore 6 (it's a bonus question).
• Practice final B; solutions. Skip 1, 4, and 8.

Midterm

Here's the midterm without solutions; with solutions. Here's some summary statistics.

Topics for the midterm:

• 2.2: separable equations
• 2.3: first order equations, modeling
• 2.4: first order existence/uniqueness
• 2.5: autonomous equations
• 2.6: integrating factors
• 2.7: Euler's method
• 2.8: Picard iteration
• 3.1: homogeneous constant coefficient second order equations, distinct real roots
• 3.2: second order existence/uniqueness, Wronskians
• 3.3: complex roots
• 3.4: repeated roots

Here are some practice midterms with solutions. We have only one midterm instead of the standard two, so some material traditionally on midterm 2 will be on our midterm---hence the second two practice midterms come in pairs.

• Here's the midterm from the last time I taught Math 307 without solutions; with solutions. Here are some statistics. This equation sheet was included in that exam.
• Practice midterm A1; solutions.
• Practice midterm A2; solutions. 1(b): replace 4 cos(3t) with 0; stop after 2.
• Practice midterm B1; solutions. Skip 1(b).
• Practice midterm B2; solutions. 1(a): replace 2t e^t with 0; stop after 1.