文档介绍：Contents
CHAPTER 1: Introduction 1
EXERCISES : Background, page 5 . ......................... 1
:SolutionsandInitialValueProblems,page14 ........... 3
:DirectionFields,page22 ....................... 10
:TheApproximationMethodofEuler,page28 ........... 17
CHAPTER 2: First Order Differential Equations 27
:SeparableEquations,page46 .................... 27
:LinearEquations,page54 ...................... 41
:ExactEquations,page65 ...................... 59
:SpecialIntegratingFactors,page71 ................. 72
EXERCISES : Substitutions and Transformations, page 78 ............ 79
REVIEWPROBLEMS:page81 ............................. 90
CHAPTER 3: Mathematical Models and Numerical Methods Involving First
Order Equations 103
,page98 .................. 103
:HeatingandCoolingofBuildings,page107 ............ 116
:NewtonianMechanics,page115 ................... 123
:ElectricalCircuits,page122 ..................... 137
:ImprovedEuler’sMethod,page132 ................. 139
EXERCISES : Higher Order Numerical Methods: Taylor and Runge-Kutta, page 142 153
CHAPTER 4: Linear Second Order Equations 167
EXERCISES : Introduction: The Mass-Spring Oscillator, page 159 ........ 167
EXERCISES : Homogeneous Linear Equations; The General Solution, page 167 . 169
EXERCISES : Auxiliary Equations plex Roots, page 177 ........ 177
iii
EXERCISES : Nonhomogeneous Equations: The Method of Undetermined
Coefficients,page186 ................................. 189
EXERCISES : The Superposition Principle and Undetermined Coefficients
Revisited,page192 ................................... 196
:VariationofParameters,page197 .................. 211
EXERCISES : Qualitative Considerations for Variable-Coefficient and Nonlinear
Equations,page208 ...........................