110 Study Guide I

# 110 Study Guide I - MATH 110 Don Lawrence Study Guide for...

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MATH 110 Don Lawrence Study Guide for Exam I The exam will cover homeworks 1 through 4; calculators will be allowed. I try to make study guides complete, but there is no guarantee – I might think of something later that I forgot to include. Also look at homeworks, quizzes, handouts, labs, and class notes. Topics Modeling (building a DE or IVP) o Define your functions and variables o Constant rate of change ( 47 = y ) o Proportional rate of change ( y y 47 . = ), including interest compounded continuously, unconstrained population growth, etc. o Jointly proportional rate of change ( kAB y = ) o Newton’s law of cooling o Constrained population growth o SIR o Approximate a constant k in an IVP Extract information from an IVP or DE o Tangent line and linear approximation, given any presentation of the data (slope and point) that allows you to find a tangent line (most likely given an IVP, but see also problems 8 and 11 on Homework #2) o Euler’s method On an IVP On a system of IVPs Know how to use Excel to do Euler’s method Successive approximation Stop when consecutive approximations are the same, rounded to a specified number of digits; use the latter of the two as your approximation Why successive approximation is better than a single approximation Error in Euler is approximately proportional to t (♣) Richardson extrapolation Understand how to derive the formula, starting with fact ♣ Be able to apply it given a list of successive approximations o Know that a max or min of a function happens when its derivative is zero; use this fact to extract from a DE information about where maxes/mins happen (e.g., where an epidemic

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110 Study Guide I - MATH 110 Don Lawrence Study Guide for...

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