Resolucion De Ecuaciones

Contents
CHAPTER 1: Introduction 1
EXERCISES 1.1: Background, page 5 . . . . . . . . . . . . . . . . . . . . . . . . . . 1
EXERCISES 1.2: Solutions and Initial Value Problems, page 14 . . . . . . . . . . . 3
EXERCISES 1.3: Direction Fields, page 22 . . . . . . . . . . . . . . . . . . . . . . . 10
EXERCISES 1.4: The ApproximationMethod of Euler, page 28 . . . . . . . . . . . 17
CHAPTER 2:First Order Differential Equations 27
EXERCISES 2.2: Separable Equations, page 46 . . . . . . . . . . . . . . . . . . . . 27
EXERCISES 2.3: Linear Equations, page 54 . . . . . . . . . . . . . . . . . . . . . . 41
EXERCISES 2.4: Exact Equations, page 65 . . . . . . . . . . . . . . . . . . . . . . 59
EXERCISES 2.5: Special Integrating Factors, page 71 . . . . . . . . . . . . . . . . . 72EXERCISES 2.6: Substitutions and Transformations, page 78 . . . . . . . . . . . . 79
REVIEWPROBLEMS: page 81 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
CHAPTER 3: Mathematical Models and Numerical Methods Involving First
Order Equations 103
EXERCISES 3.2: Compartmental Analysis, page 98 . . . . . . . . . . . . . . . . . . 103
EXERCISES 3.3: Heating and Cooling of Buildings, page 107. . . . . . . . . . . . 116
EXERCISES 3.4: NewtonianMechanics, page 115 . . . . . . . . . . . . . . . . . . . 123
EXERCISES 3.5: Electrical Circuits, page 122 . . . . . . . . . . . . . . . . . . . . . 137
EXERCISES 3.6: Improved Euler’sMethod, page 132 . . . . . . . . . . . . . . . . . 139
EXERCISES 3.7: Higher Order Numerical Methods: Taylor and Runge-Kutta, page 142 153
CHAPTER 4: LinearSecond Order Equations 167
EXERCISES 4.1: Introduction: The Mass-Spring Oscillator, page 159 . . . . . . . . 167
EXERCISES 4.2: Homogeneous Linear Equations; The General Solution, page 167 . 169
EXERCISES 4.3: Auxiliary Equations with Complex Roots, page 177 . . . . . . . . 177
iiiContents
CHAPTER 1: Introduction 1
EXERCISES 1.1: Background, page 5 . . . . . . . . . . . . . . . . . . . . . .. . . . 1
EXERCISES 1.2: Solutions and Initial Value Problems, page 14 . . . . . . . . . . . 3
EXERCISES 1.3: Direction Fields, page 22 . . . . . . . . . . . . . . . . . . . . . . . 10
EXERCISES 1.4: The ApproximationMethod of Euler, page 28 . . . . . . . . . . . 17
CHAPTER 2: First Order Differential Equations 27
EXERCISES 2.2: Separable Equations, page 46 . . . . . . . . . . . . . . . . . .. . 27
EXERCISES 2.3: Linear Equations, page 54 . . . . . . . . . . . . . . . . . . . . . . 41
EXERCISES 2.4: Exact Equations, page 65 . . . . . . . . . . . . . . . . . . . . . . 59
EXERCISES 2.5: Special Integrating Factors, page 71 . . . . . . . . . . . . . . . . . 72
EXERCISES 2.6: Substitutions and Transformations, page 78 . . . . . . . . . . . . 79
REVIEWPROBLEMS: page 81 . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 90
CHAPTER 3: Mathematical Models and Numerical Methods Involving First
Order Equations 103
EXERCISES 3.2: Compartmental Analysis, page 98 . . . . . . . . . . . . . . . . . . 103
EXERCISES 3.3: Heating and Cooling of Buildings, page 107 . . . . . . . . . . . . 116
EXERCISES 3.4: NewtonianMechanics, page 115 . . . . . . . . . . . . . . . . . . . 123EXERCISES 3.5: Electrical Circuits, page 122 . . . . . . . . . . . . . . . . . . . . . 137
EXERCISES 3.6: Improved Euler’sMethod, page 132 . . . . . . . . . . . . . . . . . 139
EXERCISES 3.7: Higher Order Numerical Methods: Taylor and Runge-Kutta, page 142 153
CHAPTER 4: Linear Second Order Equations 167
EXERCISES 4.1: Introduction: The Mass-Spring Oscillator, page 159 . . . . . . . . 167EXERCISES 4.2: Homogeneous Linear Equations; The General Solution, page 167 . 169
EXERCISES 4.3: Auxiliary Equations with Complex Roots, page 177 . . . . . . . . 177
iiiContents
CHAPTER 1: Introduction 1
EXERCISES 1.1: Background, page 5 . . . . . . . . . . . . . . . . . . . . . . . . . . 1
EXERCISES 1.2: Solutions and Initial Value Problems, page 14 . . . . . . . . . . . 3
EXERCISES 1.3:...