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 Homogeneous equations, p c. Euler method, p. 1104, figure Euler method, p. 1104, figure d. Runge-Kutta method, p Runge-Kutta method, p Exact Equations a. Exact differential equation, (18.3.1), p Exact differential equation, (18.3.1), p b. (18.3.2), p (18.3.2), p c. (18.3.3), p (18.3.3), p The Equation y”+ay’+by=0 a. (18.4.1), p (18.4.1), p b. Characteristic equation pp. 1113, 1114 Characteristic equation pp. 1113, 1114 c. Existence and uniqueness theorem, p Existence and uniqueness theorem, p d. Wronskian, p Wronskian, p e. Theorem , p Theorem , p f. Theorem , p Theorem , p g. Theorem , p Theorem , p The Equation y”+ay’+by=  (x) a. The complete equation, (18.5.1), p The complete equation, (18.5.1), p b. (18.5.2), p (18.5.2), p c. (18.5.3), p (18.5.3), p d. (18.5.4), p (18.5.4), p e. Variation of parameters, (18.5.6), p Variation of parameters, (18.5.6), p Chapter 18: Elementary Differential Equations Mechanical Vibrations a. Simple harmonic motion, (18.6.1), p Simple harmonic motion, (18.6.1), p b. General solution, (18.6.2), p General solution, (18.6.2), p c. Period, frequency, amplitude, phase shift, p Period, frequency, amplitude, phase shift, p d. Figure , p Figure , p e. Damped vibrations, (18.6.3), p Damped vibrations, (18.6.3), p f. Underdamped, overdamped, critically damped, ( ), p Underdamped, overdamped, critically damped, ( ), p g. Forced vibrations, ( ), p Forced vibrations, ( ), p. 1136

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

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

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

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

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

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

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

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

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

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

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

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 , p. 1116

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 , p. 1117

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 , p. 1118

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

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

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

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

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

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

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

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

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

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

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, ( ), p. 1135

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