MA 241 Honors REVIEW
SHEET FOR TEST 3
-Know the solution to the logistic equation on p. 534 box 4 (Remember in class we had M=C)
-Examples p. 538 # 7, 10
-Know how to find solutions to the auxiliary equation of ayÕÕ+byÕ+cy=0 for all 3 cases.
-Be able to solve initial and boundary value problems
-Be able to prove Theorem 3 (we did this proof in class)
-Be able to prove x*exp(rx) is a
solution to ayÕÕ+byÕ+cy=0 if r is a repeated root (we did this proof in class).
-Examples #1, 3,5,7,17,25
-Be able to find the complementary solution
-Find the particular solution using the Method of Undetermined Coefficients
-Understand the Superposition Principle
-Use the complementary and particular to find the general solution
- Examples #1-17 odd (Note: #13, 15,17 donÕt require you to find the values of the coefficients)
-Look at the WS for 7.7/7.8
-Be able to use the techniques from 7.7 and 7.8 to solve problems involving springs.
-Know the 3 different types of damping
-Examples 1,3,5. Also be able to do the problems we worked in class. For instance, know what to do if you were given force in pounds, etc.
-Be able to find the limit of a sequence and justify your result
-Examples p. 562 #1, 3, 5, 13,15,19, 25,33,45
-Be able to apply the Monotonic Sequence Theorem ex p.563 # 54,55,56
-Be able to determine if a given series is convergent
-Know when a geometric series is convergent and what it converges to p. 567
-Know about the Harmonic Series
-Know the Test for Divergence
-Know how to deal with Telescoping series
-Examples p. 573 #1,7,9, 13,15, 19, 25,31,33,39,47,60,61,62