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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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