MA 241 REVIEW SHEET FOR TEST 3

• Take the practice test at www4.ncsu.edu/~lakurtz/241.html

• 7.5 The Logistic Equation

-Know the solution to the logistic equation on p. 539 box 4 (Remember in class we had K=C)

-Examples p. 543 # 7, 10

• 7.7 Second Order Linear Differential Equations

http://stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-2ndOrderLinearEqns_Stu.pdf

-Know how to find solutions to the auxiliary equation of ax’’+bx’+cx=0 for all 3 cases.

-Be able to solve initial and boundary value problems.

-Examples #1, 3,5,7,17,25

• 7.8 Nonhomogeneous Linear Equations http://stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-NonhomgenLinEqns_Stu.pdf

-Be able to find the complementary solution

-Find the particular solution using the Method of Undetermined Coefficients

-Use the complementary and particular to find the general solution

- Examples #1-15 odd (Note: #13 &15 don’t require you to find the values of the coefficients)

• 7.9 Applications of Second-Order Differential Equations

http://stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-AppsOf2ndOrders_Stu.pdf

-Be able to use the techniques from 7.7 and 7.8 to solve problems involving springs.

-Examples 1,3,5. Also be able to do easier versions of problems we worked in class. For instance, know what to do if you were given force in pounds, etc.

• 8.1 Sequences

-Be able to the limit of a sequence and justify your result

-Examples p. 565 #1, 3, 5, 13,19

• 8.2 Series

-Be able to determine if a given series is convergent

-Know when a geometric series is convergent and what it converges to p. 569

-Know about the Harmonic Series

-Know the Test for Divergence

-Examples p. 574 #1,9, 13,15,17