Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 7.6 (p. 421)- Transforms of Discontinuous Functions) 3. Find the Laplace transform of a b a a bb a abb where a b ab a b Ans: OE Express the function using step function
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 7.5 (p. 409)- Solving Initial Value Problems 11. Solve the DE ab ab Let In terms of ab ab ab ab ab ab aba b a b ab
ab a ba b a b a b a b a b aba b ab a b 23. Note: we
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 7.4 (p. 400)- Inverse Laplace Transform
21. Find the inverse transform of ab a ba b a ba b
a ba b a b a b a b ab Therefore a abb Determine a abb if ab ab aba b ab a
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 7.3 (p. 391)- Properties of Laplace Transforms 3. To find a b note that a b a b where ab a b a b a b To find a b note that a b a b where ab a b a b a b a b a b To find
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 7.2 (p. 385)- Definition of Laplace Transform 1. ab (
" (
where a b (
"
3.
assuming a b (
(
ab
ab
4.
(
ab
where ab ab ab ab ( assuming a b a b
9.
a b oe
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 4.10 (p. 246)- Forced Mechanical Vibrations 3. where ab and ab a b ab ab Ans: An 8-kg mass is attached to a spring hanging from the ceiling, thereby causing the spring
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 4.9 (p. 238)- Free Mechanical Vibrations 1. ab ab
a b where is quadrant containing the point ^ which is 4. Therefore ab Ans: ^ 3. There are 4 parts. Part 1= where ab
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 4.5 (p. 201)- The Superposition Principle
21. Find a general solution to the DE a b a b a b ab and a b . We need the factor. a b a b a b =
a b a b a b ignore terms wit
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 4.4 (p. 195)- Nonhomogeneous Eq's: The Method of Undetermined Coefficients For questions 1, 3, and 5, does the method of undetermined coeff's apply to the DE? 1. 3. the
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 4.3 (p. 186)- Auxiliary Equations with Complex Roots 5. Find a general solution to the DE a b The general solution is S < 17. Find a general solution to the eqution
a
Fundamentals of Differential Eqautions by Nagle, Saff, and Snider 7th edition) Section 4.2 (p. 176)- Homogeneous Linear Equations: the General Solution 5. Find a general solution to the DE a b is a root of mult. 2 the general solution is 15. Solve the ini
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 3.2 (p. 104)- Compartmental Analysis 1. 0
.5 kg of salt
ab amt. of salt in tank; ab
input rate output rate ab I.F. The solution to DE is ( Therefore ab and ab ab
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 2.5 (p. 71)- Special Integrating Factors 2. a b a b
ab Therefore there is an integrating factor depending upon x alone. The DE is not separable, not linear, and
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 2.4 (p. 65)- Exact Differential Equations 3. a b a b The DE is exact but it is not separable and not linear. 5. a b DE is exact DE is linear with x as dep. variable! 9.
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 2.3 (p. 54)- Linear Differential Equations 1. Is the DE separable, linear, neither, or both? DE is Linear. It is not separable. 3. a b ^ a b DE is separable. a b a b DE
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 2.2 (p. 46)- Background 12.
^
a b
^
a b a b
15.
19.
ab
a b ab
24.
a b a b
34.
(Thermometer Problem) At time 0, and a b use because a) k k
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 1.4 (p. 28)- The Approximation Method of Euler 1. a b yab Estimate at the pts where and using New old + slope at old pt
3
3 (2
3 ) ( .1) = 2.7 2.7) ( .1) = 2.511 2.511
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition)
Section 1.3 (p. 22)- Direction Fields Draw the iscolines with their direction markers and sketch several solutions including the curve satisfying the initial conditions. 12. ab
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 1.2 (p. 14)- Solutions and Initial Value Problems 1. b) ab a b a b c) ab defined on a b OE OE where where a b a b -
3.
4.
7.
14. Show that ab is a solution to 20. a)
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 2.6 (p. 78)- Substitutions and Bernoulli's Equation 11. a b DE has homogeneous coef's Let a b a b
kk and 15.
Let a b a b a b
ab
Fundamentals of Differential Equations by Nagle, Saff, and Snider 7th edition) Section 1.1 (p. 5)- Background 1. ODE, 2nd order, linear, is dep. var. and is indep. var.
3.
a b a b ODE, 1st order, non-linear, is dep. var. and is indep. var. PDE, 2nd order