Math 246: Recommended Problems from the Textbook (8th edition)

These problems will be similar to problems of the exams and the final exam. But they will not be collected or graded. Note that partial solutions to the problems are in the back of the textbook.

Section 1.1 (Introduction), p.7

1-4

Section 2.1 (Linear Equations), p. 39

only find the general solution: 1, 2, 6, 10
13, 14, 16, 18

Section 2.2 (Separable Equations), p. 47

1,2,3,4,9,10,13,21

Section 2.3 (Modeling with First Order Equations), p. 59:

1,3,5,28,29

Section 2.4 (Differences between Linear and Nonlinear Equations, p. 75

1, 2, 3, 22

Section 2.5 (Autonomous Equations and Population Dynamics), p. 88

3,4,5,9,10,11,20

Section 2.6 (Exact Equations and Integrating Factors), p. 99

1,2,3,7,10,13,19. For which of those problems can you find the solution in explicit form?

Section 2.7, 8.1, 8.2, 8.3, 8.6 (Numerical Methods)

problems

Section 3.1 (Homogeneous Equations with Constant Coefficients), p. 142

1,5,8,9,10

Section 3.4 (Complex Roots), p.164

7,9,12,17,21

Section 3.5 (Repeated Roots), p. 172

1,11,12,13,14

Section 3.6 (Method of Undetermined Coefficients), p. 184

1, 3, 6,7; only (a) for: 19,20,23

Section 3.7 (Variation of Parameters), p. 190

5,7,10

Section 3.8 (Mechanical and Electrical Vibrations), p. 203

1, 2, 5, 11, 17
Note: For some strange reason the book does not tell you directly what the spring constant k is. The weight W is the force with which mass is pulled by earth's gravity. It is related to the mass M by W = M g , where g = 9.81 m s^-2 = 32 ft s^-2.

• "A spring is stretched a distance of D by a force of F"
  means that the spring constant is k = F/D.
• "A mass weighing W stretches a spring a distance D"
  means that the spring constant is k = W/D.
• "A mass of M stretches a spring a distance D"
  means that the spring constant is k = Mg/D.

For the exams I will only give you problems without units, and I will tell you directly what the spring constant k is.

Section 3.9 (Forced Vibrations), p. 214

1, 9, 12, 17 (use formulas (6), (7) for d)

Section 6.2 (Solution of IVP using the Laplace Transform), p. 322

11, 12, 22; 21, 23

Section 6.3 (Step Functions), p. 329

1, 2, 7, 8, 11,16, 18

Section 6.4 (Discontinuous Forcing Functions), p. 337

1, 5, 9, 10

Section 6.5 (Impulse Funcions), p. 344

1,4,5

Section 7.5 (Homogeneous Systems of First Order Linear Equation)

2, 3, 5, 7

Section 7.6 (Complex Eigenvalues)

1, 4, 6

Section 7.8 (Repeated Eigenvalues)

1, 2

Section 9.1 (The Phase Plane: Linear Systems)

do parts (a), (b), (c) in all problems: 1, 2, 5, 7, 10, 11

Section 9.3 (Almost Linear Systems)

(do parts (a), (b), (c) in all problems, sketch a phase portrait close to each critical point): 5, 6, 7, 8, 10, 12