• Syllabus for Math 230   (3 pages)
  
• My generic UVM syllabus 
  
• Sanctions for academic integrity violations 
  
• Why I will not compute your "current grade" 
  


• Homework  
  
• Background from Algebra, Precalculus, and Calculus I, mastery of which I expect from students in this class.
• Video:  How I expect you to do homework problems  
  
• This video was prepared for another class, but it stresses the same concepts that I expect you to use in this class.
  

• Instructions for doing extra credit Homework assignments (please read them before you attempt to do one) 
  
• Instructions for doing extra credit Project assignments 
  
• What to do if you received a low grade on a quiz  and want to improve your future grades
I really think that the above 3-step review will help you if you follow the directions.

• Preparation sheet for Test 1   
  
• Test 1 will be given after we cover Sec. 3.1.
•  Test 1 will be on DATE, from TIME pm in ROOM.
  
• Example of how NOT to prepare a formula sheet  
  
• Solutions for Test 1    
  
• Solutions for Quiz 6  
  
• Solutions for Quiz 7  
  
• Preparation sheet for Test 2  
  
• Tentatively, Test 2 will be given after we cover Sec. 3.10.
  
• Test 2 will be on Tuesday, April 18, from 6:30 pm - 7:50 pm in Lafayette L311.
  
• Solutions for Test 2      
  
• Solutions for Quiz 8  
• Preparation sheet for the Final Exam   
  

• MATHEMATICA resources
  
• Follow this link to install Mathematica on your computer.    
  
• On that page, read the (very short) instructions, click on the link "UVM Software Portal" and follow the directions there. When prompted, you will need to login with your UVM NetID.
  
• After you install Mathematica on your computer, it will ask you to Activate the program and will display a window with two Activation options: (1) with an Activation Key and (ii) through your organization. Choose the latter and sign in with your UVM credentials. In this process you will again be presented with the options to sign in with your Wolfram account or via UVM; choose the latter.
  
• Be prepared that the installation  process takes about 15+ minutes (or longer if your connection to the Internet is slow). The entire process consists of two stages, which you will be guided through by the Installer: You first download the installation package, and then the Installer installs them on your computer.
  
• On the same page, notice the link to "tutorial videos" at the end. It is a very friendly resource, which will help you if you do not feel comfortable using Mathematica. For example, Tutorial 5 in that link talks about defining and plotting functions.
  
• You will unlikely ever need Tutorials 6 and 7.
  
• An alternative, but arguably a less friendly place to get started is my own introductory lab to Mathematica: On this page, you need to open Lab 1, Part 1 and work through the first half of it up to (i.e., not including) the section "Parametric plots in 2D".

 Lecture Notes  

• Background from Algebra, Precalculus, and Calculus I, mastery of which I expect from students in this class.
  
• This document has already been listed above, after the link to Homework, but it is worth repeating.
  

 Lecture 1     Introduction 

Example 4 (direction field) worked out in detail  

 Lecture 2     Linear 1st-order differential equations 

A story of how a simple drag force model helped resolve a controversy of an atomic waste disposal problem (from M. Braun, "Differential equations and their applications," 3rd Ed., Springer, New York, 1983)

 Lecture 3     General properties of solution of 1st-order linear differential equations   

 Lecture 4     Some applications of 1st-order linear differential equations    

Description of Radiocarbon dating technique from Wikipedia 

A story about uncovering of an art forgery after World War II  using radioactive isotope dating (from M. Braun's textbook)

 Lecture 5     Separable  differential equations 

 Lecture 6     Existence and uniqueness of solution of 1st-order nonlinear  diferential equations 

 Lecture 7     Special cases when a 1st-order nonlinear differential equation can and cannot be solved  

 Lecture 8     An application of 1st-order nonlnear differential equations: The Logistic model   

 Lecture 9     Euler's method  

 Lecture 10   Introduction to 2nd-order differential equations: motivation; basic properties; linear differential equations

 Lecture 11   The general solution of a homogeneous linear 2nd-order differential equation 

 Lecture 12   Homogeneous linear differential equations with constant coefficients 

 Lecture 13   Real repeated roots; Reduction of order of a linear differential equation 

 Lecture 14   Complex roots; Oscillatory solutions of 2nd-order diffrential equations

 Lecture 15   Unforced mechanical vibrations:  Linear oscillator model revisited

Almost all realistic models of nature have damping in them, however small it may be. Without damping, one would have perpetual motion. This has been known to be impossible since the times of Isaac Newton. However, in some very sophisticated and carefully engineered systems perpetual motion is possible! Here is an example.

 Lecture 16   General solution of a linear nonhomogeneous  differential equation 

 Lecture 17   Particular solution of a nonhomogeneous 2nd-order differential equation: Method of Undetermined Coefficients

• additional worked-out Example:  (a) Determining the form of the y_p(t);  (b) Working backwards from {g(t), y_p(t)} towards  y_c(t) .
  
• Table from page 163 of textbook 
  

 Lecture 18   Particular solution of a nonhomogeneous 2nd-order differential equation: Method of Variations of Parameters 

 Lecture 19   Resonance in undamped and damped linear oscillator models 

One of the dramatic manifestations of resonance is the destruction of Tacoma Narrows Bridge in 1940. Here is a video of the event. However, a connection between that event and a resonance is far from trivial. (One obvious observation is that the resonance was not caused by a wind that blew with periodic intensity -- such winds do not exist in nature.) A critical review of various explanations of the Tacoma Bridge destruction can be found in a paper by H. Petroski, published in 1991.

Online demonstration of the phenomenon of beats 

 Lecture 20   General properties of higher-order linear differential equations 

 Lecture 21   Higher-order linear differential equations with constant coefficients             

 Lecture 22   Systems of first-order linear differential equations:  Introduction

 Lecture 23   General properties of linear systems of first-order differential equations

Proof of Abel's Theorem for n=2 

 Lecture 24   Homogeneous linear systems with constant coefficients 

 Lecture 25   Nonhomogeneous linear systems of differential equations: Method of Variation of parameters 

 Lecture 26   Laplace Transform: Motivation and Introduction 

 Lecture 27   Using Laplace Transform to solve Initial value problems