1. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Bernoulli Equations: Homogeneous Equations; Numerical Methods a. (18.2.1), Bernoulli equation, pp. 1099, 1100 (18.2.1), Bernoulli equation, pp. 1099, 1100 b. Homogeneous equations, p. 1101 Homogeneous equations, p. 1101 c. Euler method, p. 1104, figure 18.2.2 Euler method, p. 1104, figure 18.2.2 d. Runge-Kutta method, p. 1105 Runge-Kutta method, p. 1105 Exact Equations a. Exact differential equation, (18.3.1), p. 1108 Exact differential equation, (18.3.1), p. 1108 b. (18.3.2), p. 1111 (18.3.2), p. 1111 c. (18.3.3), p. 1112 (18.3.3), p. 1112 The Equation y”+ay’+by=0 a. (18.4.1), p. 1113 (18.4.1), p. 1113 b. Characteristic equation pp. 1113, 1114 Characteristic equation pp. 1113, 1114 c. Existence and uniqueness theorem, p. 1115 Existence and uniqueness theorem, p. 1115 d. Wronskian, p. 1116 Wronskian, p. 1116 e. Theorem 18.4.4, p. 1116 Theorem 18.4.4, p. 1116 f. Theorem 18.4.5, p. 1117 Theorem 18.4.5, p. 1117 g. Theorem 18.4.6, p. 1118 Theorem 18.4.6, p. 1118 The Equation y”+ay’+by=  (x) a. The complete equation, (18.5.1), p. 1123 The complete equation, (18.5.1), p. 1123 b. (18.5.2), p. 1123 (18.5.2), p. 1123 c. (18.5.3), p. 1123 (18.5.3), p. 1123 d. (18.5.4), p. 1123 (18.5.4), p. 1123 e. Variation of parameters, (18.5.6), p. 1125 Variation of parameters, (18.5.6), p. 1125 Chapter 18: Elementary Differential Equations Mechanical Vibrations a. Simple harmonic motion, (18.6.1), p. 1130 Simple harmonic motion, (18.6.1), p. 1130 b. General solution, (18.6.2), p. 1131 General solution, (18.6.2), p. 1131 c. Period, frequency, amplitude, phase shift, p. 1131 Period, frequency, amplitude, phase shift, p. 1131 d. Figure 18.6.1, p. 1131 Figure 18.6.1, p. 1131 e. Damped vibrations, (18.6.3), p. 1134 Damped vibrations, (18.6.3), p. 1134 f. Underdamped, overdamped, critically damped, (18.6.4-6), p. 1135 Underdamped, overdamped, critically damped, (18.6.4-6), p. 1135 g. Forced vibrations, (18.6.7-8), p. 1136 Forced vibrations, (18.6.7-8), p. 1136

2. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Bernoulli Equations: Homogeneous Equations; Numerical Methods (18.2.1), Bernoulli equations, pp. 1099, 1100

3. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Bernoulli Equations: Homogeneous Equations; Numerical Methods Homogeneous equations, p. 1101

4. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Bernoulli Equations: Homogeneous Equations; Numerical Methods Euler method, p. 1104, figure 18.2.2

5. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Bernoulli Equations: Homogeneous Equations; Numerical Methods Runge-Kutta method, p. 1105

6. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Exact Equations Exact differential equation, (18.3.1), p. 1108

7. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Exact Equations (18.3.2), p. 1111

8. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Exact Equations (18.3.3), p. 1112

9. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=0 (18.4.1), p. 1113

10. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=0 Characteristics equation pp. 1113, 1114

11. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=0 Existence and uniqueness theorem, p. 1115

12. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=0 Wronskian, p. 1116

13. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=0 Theorem 18.4.4, p. 1116

14. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=0 Theorem 18.4.5, p. 1117

15. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=0 Theorem 18.4.6, p. 1118

16. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=φ(x) The complete equation, (18.5.1), p. 1123

17. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=φ(x) (18.5.2), p. 1123

18. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=φ(x) (18.5.3), p. 1123

19. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=φ(x) (18.5.4), p. 1123

20. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. The Equation y”+ay’+by=φ(x) Variation of parameters, (18.5.6), p. 1125

21. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Mechanical Vibrations Simple harmonic motion, (18.6.1), p. 1130

22. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Mechanical Vibrations General solution, (18.6.2), p. 1131

23. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Mechanical Vibrations Period, frequency, amplitude, phase shift, p. 1131

24. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Mechanical Vibrations Figure 18.6.1. p. 1131

25. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Mechanical Vibrations Damped vibrations, (18.6.3), p. 1134

26. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Mechanical Vibrations Underdamped, overdamped, critically damped, (18.6.4-6), p. 1135

27. Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Mechanical Vibrations Forced vibrations, (18.6.7-8), p. 1136