MATH 334: Differential Equations
MATH 334 Homepage

Welcome, please note that the offical syllabus is linked here. Please note this webpage is where test solutions and further assignments are to be posted. For your convenience, I have provided a few links to points further down this page.


I. Course Contact Information:


II. Useful Materials and Links:



III. Additional Examples:

These notes show you what I expect you already saw in calculus II. We do review some of these materials in this course:
  • Chapter 10: Introduction to Differential Equations
  • Chapter 11: Sequences and Series
  • Chapter 12: Basics of Power Series
  • Chapter 13: Power Series Techniques




  • IV. Test Reviews and Solutions:
    I will post reviews and solutions for our course here once it's time.

    Test Solutions from this Semester:

    Test Reviews: (will appear here soon )


    V. Course Notes:

    Sorry these took so long to put up this summer. The first few pages are blank at the moment because I plan to add an introduction and overview once I've written all the notes. The notes are finished for the summer. I may add notes on Chapter 10 if I find it is needed. At the present there are 40+ pages of Practice Homework solutions on Chapter 10. Beyond that, the text is in many ways better than my notes in this course so I recommend that you read it.

    Notes that are covered by Test I ( if at all ):
    Notes that are covered by Test II ( if at all ):
    Notes that are covered by Test III ( if at all ):
    Notes that are covered by Test IV ( if at all ):


    VI. Bonus Point Policy:
    It is possible to earn bonus points by asking particularly good questions or suggesting corrections to errors in notes and materials on the course website. This does not include spelling or grammatical errors, those are provided for your amusement.


    VII. Problem Sets and Practice Homework List with Selected Solutions:
    There are 4 Problem Sets which will be collected. These consist about 70% of standard example problems which are not terribly difficult once you understand the concept and about 30% that is harder and/or abstract. I have provided solutions for problems like the standard examples. The practice homework is not collected but it is representative of the skill set I expect you should assimilate as the course unfolds. This summer Problem Set IV and Test IV are identical. Test IV is 100% takehome. The final exam covers those things covered by Tests I,II, III as well as theory which I hope you have assimilated by the end of the course.

    (these links will work once I post the assignments for this semester)

    (the * problems indicate the problem is explicitly about a real-world application. However, all the problems in this course are real world since you are in the real world and you will be doing the problems. Besides that obvious comment, all the mathematics mentioned in this course is used in engineering, physics and much much more... if you want to see more of that add a physics minor or an engineering major. My focus is math.)

    Section # My Lecture Notes Solutions Assignment Description / Hints / Mathematica helps
    Sec. 2.2 [13-23] PH-[1-3] 9, 11, 15, 21, 25, 35* separation of variables
    Sec. 2.3 [24-28] PH-[4-6] 7, 9, 11, 15, 21, 23* integrating factor method
    Sec. 2.4 [24-28] PH-[7-9] 11, 13, 17, 23, 29 exact equations
    Sec. 2.5 [29-37] PH-[10-13] 7, 9, 11, 13 special integrating factors
    Sec. 2.6 [29-37] PH-[14-16] 9, 15, 17, 41 transformation tricks
    Sec. 3.4 [41-45] PH-[17-21] 1*, 5*, 19*, 23*, 33*, 35* Newtonian Mechanics
    Sec. 4.2 [46-55] PH-[22-23] 1, 5, 13, 17, 27, 29 homogeneous constant coefficient ordinary differential equations with real roots
    Sec. 4.3 [46-55] PH-[24-26] 1, 5, 13, 21, 32*, 33*, 35* homogeneous constant coefficient ordinary differential equations with complex roots
    Sec. 6.2 [46-55] PH-[27-30] 1, 9, 13, 15, 17, 35* higher order homogeneous constant coefficient ODEs.
    Event Test I Sept. 8 Sections 2.2, 2.3, 2.4, 2.5, 2.6, 3.4, 4.2, 4.3, 6.2 solutions of first order differential equations and homogeneous constant coefficient ODEs.
    Sec. 6.1 [56-65] PH-[31-33] 1, 5, 7, 9, 17, 23 theory of linear ODEs.
    Sec. 6.3 [75-88] PH-[34-37] 5, 11, 13, 15, 17, 21, 23, 25, 27 annihilators; a way to find the particular solution.
    Sec. 4.4 [75-88] PH-[38-39] 9, 11, 15, 17, 21, 23, 27, 31 undetermined coefficients ( section 6.3 justifies where the guess for the particular solution comes from).
    Sec. 4.5 [91-93] PH-[40-43] 1, 3, 17, 21, 25, 29, 43* superposition principle.
    Sec. 4.6 [89-90] PH-[44-48] 1, 5, 15 variation of parameters ( for things not covered by undetermined coefficients)
    Sec. 4.7 [94-101] PH-[49-50] 45, 47 variable coeffcients.
    Sec. 4.9 [102-108] PH-[51-52] 3, 5, 9*, 11* [use math software for #3 and 5] springs and vibrations.
    Sec. 4.10 [102-108] PH-[53-58] 9*, 11* forced vibrations.
    Sec. 5.7 [102-108] PH-[59-62] 3*, 5*, 7*, 9*, 11*, 13* RLC circuits and the analogy to springs with forced vibrations
    Event Test II Sept. 29 Sections 6.1, 6.3, 4.4, 4.5, 4.6, 4.7, 4.9, 4.10, 5.7 solutions of nonhomogeneous constant coefficient ODEs and select applications to springs and RLC circuits, variable coefficient DEqns.
    Sec. 7.2 [109-114] PH-[63-64] 9, 13, 15, 17, 19, 21, 23 Laplace Transformations
    Sec. 7.3 [115-121] PH-[65-66] 5, 7, 11, 13, 15, 17, 19, 25 Properties of Laplace Transformations
    Sec. 7.4 [122-126] PH-[67-71] 1, 3, 21, 23, 27, 33, 35 Inverse Laplace Transformations
    Sec. 7.5 [127-133] PH-[72-76] 3, 9, 11, 35 How to solve differential equations via Laplace Transformations
    Sec. 7.6 [134-140] PH-[77-81] 5, 7, 9, 11, 17, 19, 33, 39, 59 discontinuous functions (this is most interesting feature of the Laplace method in my opinion)
    Sec. 7.8 [145-154] PH-[82-84] 1, 5, 29 Dirac Delta "functions"
    Sec. 8.2 [155-160] PH-[85-89] 1, 5, 9, 11, 15, 25, 29, 31, 33 power series refresher
    Sec. 8.3 [161-165] PH-[90-97] 1, 9, 13, 17, 19, 21, 27 power series solutions to DEqns
    Sec. 8.4 [166-170] PH-[98-103] 7, 11, 13, 17, 21, 31* analytic coefficients
    Sec. 8.5 [94-101] PH-[104-105] 1, 5, 13 Cauchy-Euler Problem
    Sec. 8.6 [171-178] PH-[106-114] 1, 17, 21, 23, 25, 27, 33, 41 Frobenius method
    Sec. 8.7 [171-178] PH-[106-114] 5, 11, 15 (note to self, find Ginny solution) finding a second linearly independent solution
    Event Test III Nov. 3 Sections 7.2, 7.3, 7.4, 7.5, 7.6, 7.8, 8.2, 8.3, 8.4, 8.6, 8.7 Laplace transform and series solutions to ODEs
    Sec. 10.2 . PH-[118-126] 1, 5, 9, 13, 15, 21, 23, 29, 33 separation of variables for PDEs with nice boundary conditions
    Sec. 10.3 . PH-[127-132] 1, 5, 7, 9, 11, 13, 19, 21, 29 Fourier series
    Sec. 10.4 . PH-[133-134] 5, 13, 17 Fourier cosine and sine series
    Sec. 10.5 . PH-[135-144] 3, 7, 15 the heat equation
    Sec. 10.6 . PH-[145-149] 1, 13, 15 the wave equation
    Sec. 10.7 . PH-[150-161] 1, 3, 7, 9, 11 Laplace's equation
    Event Test IV take-home Sections 10.2, 10.3, 10.4, 10.5, 10.6, 10.7 PDEs with nice solutions.




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    7 . PH-[150-161] 1, 3, 7, 9, 11 Laplace's equation Event Test IV take-home Sections 10.2, 10.3, 10.4, 10.5, 10.6, 10.7 PDEs with nice solutions.




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