%PDF-1.4 5 0 obj << /S /GoTo /D (chapter.1) >> endobj 8 0 obj (1 Introduction) endobj 9 0 obj << /S /GoTo /D (section.1.1) >> endobj 12 0 obj (1.1 Preliminaries) endobj 13 0 obj << /S /GoTo /D (section.1.2) >> endobj 16 0 obj (1.2 Sample Application of Differential Equations) endobj 17 0 obj << /S /GoTo /D (chapter.2) >> endobj 20 0 obj (2 First Order Ordinary Differential Equations) endobj 21 0 obj << /S /GoTo /D (section.2.1) >> endobj 24 0 obj (2.1 Separable Equations) endobj 25 0 obj << /S /GoTo /D (section.2.2) >> endobj 28 0 obj (2.2 Exact Differential Equations) endobj 29 0 obj << /S /GoTo /D (section.2.3) >> endobj 32 0 obj (2.3 Integrating Factors) endobj 33 0 obj << /S /GoTo /D (section.2.4) >> endobj 36 0 obj (2.4 Linear First Order Equations) endobj 37 0 obj << /S /GoTo /D (section.2.5) >> endobj 40 0 obj (2.5 Substitutions) endobj 41 0 obj << /S /GoTo /D (subsection.2.5.1) >> endobj 44 0 obj (2.5.1 Bernoulli Equation) endobj 45 0 obj << /S /GoTo /D (subsection.2.5.2) >> endobj 48 0 obj (2.5.2 Homogeneous Equations) endobj 49 0 obj << /S /GoTo /D (subsection.2.5.3) >> endobj 52 0 obj (2.5.3 Substitution to Reduce Second Order Equations to First Order) endobj 53 0 obj << /S /GoTo /D (chapter.3) >> endobj 56 0 obj (3 Applications and Examples of First Order ode's) endobj 57 0 obj << /S /GoTo /D (section.3.1) >> endobj 60 0 obj (3.1 Orthogonal Trajectories) endobj 61 0 obj << /S /GoTo /D (section.3.2) >> endobj 64 0 obj (3.2 Exponential Growth and Decay) endobj 65 0 obj << /S /GoTo /D (section.3.3) >> endobj 68 0 obj (3.3 Population Growth) endobj 69 0 obj << /S /GoTo /D (section.3.4) >> endobj 72 0 obj (3.4 Predator-Prey Models) endobj 73 0 obj << /S /GoTo /D (section.3.5) >> endobj 76 0 obj (3.5 Newton's Law of Cooling) endobj 77 0 obj << /S /GoTo /D (section.3.6) >> endobj 80 0 obj (3.6 Water Tanks) endobj 81 0 obj << /S /GoTo /D (section.3.7) >> endobj 84 0 obj (3.7 Motion of Objects Falling Under Gravity with Air Resistance) endobj 85 0 obj << /S /GoTo /D (section.3.8) >> endobj 88 0 obj (3.8 Escape Velocity) endobj 89 0 obj << /S /GoTo /D (section.3.9) >> endobj 92 0 obj (3.9 Planetary Motion) endobj 93 0 obj << /S /GoTo /D (section.3.10) >> endobj 96 0 obj (3.10 Particle Moving on a Curve) endobj 97 0 obj << /S /GoTo /D (chapter.4) >> endobj 100 0 obj (4 Linear Differential Equations) endobj 101 0 obj << /S /GoTo /D (section.4.1) >> endobj 104 0 obj (4.1 Homogeneous Linear Equations) endobj 105 0 obj << /S /GoTo /D (subsection.4.1.1) >> endobj 108 0 obj (4.1.1 Linear Differential Equations with Constant Coefficients) endobj 109 0 obj << /S /GoTo /D (section.4.2) >> endobj 112 0 obj (4.2 Nonhomogeneous Linear Equations) endobj 113 0 obj << /S /GoTo /D (chapter.5) >> endobj 116 0 obj (5 Second Order Linear Equations) endobj 117 0 obj << /S /GoTo /D (section.5.1) >> endobj 120 0 obj (5.1 Reduction of Order) endobj 121 0 obj << /S /GoTo /D (section.5.2) >> endobj 124 0 obj (5.2 Undetermined Coefficients) endobj 125 0 obj << /S /GoTo /D (subsection.5.2.1) >> endobj 128 0 obj (5.2.1 Shortcuts for Undetermined Coefficients) endobj 129 0 obj << /S /GoTo /D (section.5.3) >> endobj 132 0 obj (5.3 Variation of Parameters) endobj 133 0 obj << /S /GoTo /D (chapter.6) >> endobj 136 0 obj (6 Applications of Second Order Differential Equations) endobj 137 0 obj << /S /GoTo /D (section.6.1) >> endobj 140 0 obj (6.1 Motion of Object Hanging from a Spring) endobj 141 0 obj << /S /GoTo /D (section.6.2) >> endobj 144 0 obj (6.2 Electrical Circuits) endobj 145 0 obj << /S /GoTo /D (chapter.7) >> endobj 148 0 obj (7 Higher Order Linear Differential Equations) endobj 149 0 obj << /S /GoTo /D (section.7.1) >> endobj 152 0 obj (7.1 Undetermined Coefficients) endobj 153 0 obj << /S /GoTo /D (section.7.2) >> endobj 156 0 obj (7.2 Variation of Parameters) endobj 157 0 obj << /S /GoTo /D (section.7.3) >> endobj 160 0 obj (7.3 Substitutions: Euler's Equation) endobj 161 0 obj << /S /GoTo /D (chapter.8) >> endobj 164 0 obj (8 Power Series Solutions to Linear Differential Equations) endobj 165 0 obj << /S /GoTo /D (section.8.1) >> endobj 168 0 obj (8.1 Introduction) endobj 169 0 obj << /S /GoTo /D (section.8.2) >> endobj 172 0 obj (8.2 Background Knowledge Concerning Power Series) endobj 173 0 obj << /S /GoTo /D (section.8.3) >> endobj 176 0 obj (8.3 Analytic Equations) endobj 177 0 obj << /S /GoTo /D (section.8.4) >> endobj 180 0 obj (8.4 Power Series Solutions: Levels of Success) endobj 181 0 obj << /S /GoTo /D (section.8.5) >> endobj 184 0 obj (8.5 Level 1: Finding a finite number of coefficients) endobj 185 0 obj << /S /GoTo /D (section.8.6) >> endobj 188 0 obj (8.6 Level 2: Finding the recursion relation) endobj 189 0 obj << /S /GoTo /D (section.8.7) >> endobj 192 0 obj (8.7 Solutions Near a Singular Point) endobj 193 0 obj << /S /GoTo /D (section.8.8) >> endobj 196 0 obj (8.8 Functions Defined via Differential Equations) endobj 197 0 obj << /S /GoTo /D (subsection.8.8.1) >> endobj 200 0 obj (8.8.1 Chebyshev Equation) endobj 201 0 obj << /S /GoTo /D (subsection.8.8.2) >> endobj 204 0 obj (8.8.2 Legendre Equation) endobj 205 0 obj << /S /GoTo /D (subsection.8.8.3) >> endobj 208 0 obj (8.8.3 Airy Equation) endobj 209 0 obj << /S /GoTo /D (subsection.8.8.4) >> endobj 212 0 obj (8.8.4 Laguerre's Equation) endobj 213 0 obj << /S /GoTo /D (subsection.8.8.5) >> endobj 216 0 obj (8.8.5 Bessel Equation) endobj 217 0 obj << /S /GoTo /D (chapter.9) >> endobj 220 0 obj (9 Linear Systems) endobj 221 0 obj << /S /GoTo /D (section.9.1) >> endobj 224 0 obj (9.1 Preliminaries) endobj 225 0 obj << /S /GoTo /D (section.9.2) >> endobj 228 0 obj (9.2 Computing e\136T) endobj 229 0 obj << /S /GoTo /D (section.9.3) >> endobj 232 0 obj (9.3 The 2x2 Case in Detail) endobj 233 0 obj << /S /GoTo /D (section.9.4) >> endobj 236 0 obj (9.4 The Non-Homogeneous Case) endobj 237 0 obj << /S /GoTo /D (section.9.5) >> endobj 240 0 obj (9.5 Phase Portraits) endobj 241 0 obj << /S /GoTo /D (subsection.9.5.1) >> endobj 244 0 obj (9.5.1 Real Distinct Eigenvalues) endobj 245 0 obj << /S /GoTo /D (subsection.9.5.2) >> endobj 248 0 obj (9.5.2 Complex Eigenvalues) endobj 249 0 obj << /S /GoTo /D (subsection.9.5.3) >> endobj 252 0 obj (9.5.3 Repeated Real Roots) endobj 253 0 obj << /S /GoTo /D (chapter.10) >> endobj 256 0 obj (10 Existence and Uniqueness Theorems) endobj 257 0 obj << /S /GoTo /D (section.10.1) >> endobj 260 0 obj (10.1 Picard's Method) endobj 261 0 obj << /S /GoTo /D (section.10.2) >> endobj 264 0 obj (10.2 Existence and Uniqueness Theorem for First Order ODE's) endobj 265 0 obj << /S /GoTo /D (section.10.3) >> endobj 268 0 obj (10.3 Existence and Uniqueness Theorem for Linear First Order ODE's) endobj 269 0 obj << /S /GoTo /D (section.10.4) >> endobj 272 0 obj (10.4 Existence and Uniqueness Theorem for Linear Systems) endobj 273 0 obj << /S /GoTo /D (chapter.11) >> endobj 276 0 obj (11 Numerical Approximations) endobj 277 0 obj << /S /GoTo /D (section.11.1) >> endobj 280 0 obj (11.1 Euler's Method) endobj 281 0 obj << /S /GoTo /D (subsection.11.1.1) >> endobj 284 0 obj (11.1.1 Error Bounds) endobj 285 0 obj << /S /GoTo /D (section.11.2) >> endobj 288 0 obj (11.2 Improved Euler's Method) endobj 289 0 obj << /S /GoTo /D (section.11.3) >> endobj 292 0 obj (11.3 Runge-Kutta Methods) endobj 293 0 obj << /S /GoTo /D [294 0 R /Fit ] >> endobj 296 0 obj << /Length 259 /Filter /FlateDecode >> stream xڍN0E /zbdɈ)`1@AtLQE86ɏLCv;蛱n^0HESbL-.8tZ5$@LAc}Sg&uoT7v4훮!NRau+9{>Uv..lSUc"1EavM>unS's(oR6reor?^endstream endobj 294 0 obj << /Type /Page /Contents 296 0 R /Resources 295 0 R /MediaBox [0 0 612 792] /Parent 305 0 R >> endobj 297 0 obj << /D [294 0 R /XYZ 106.8692 686.127 null] >> endobj 298 0 obj << /D [294 0 R /XYZ 106.8692 668.127 null] >> endobj 295 0 obj << /Font << /F17 301 0 R /F37 304 0 R >> /ProcSet [ /PDF /Text ] >> endobj 308 0 obj << /Length 117 /Filter /FlateDecode >> stream x}ͱ 1>_\I *Xo'VrߚB"cb )YR1ɳwVjawҴq{Ͳl~kْRcLQSnP_l([o+;endstream endobj 307 0 obj << /Type /Page /Contents 308 0 R /Resources 306 0 R /MediaBox [0 0 612 792] /Parent 305 0 R >> endobj 309 0 obj << /D [307 0 R /XYZ 160.6675 686.127 null] >> endobj 306 0 obj << /Font << /F8 312 0 R >> /ProcSet [ /PDF /Text ] >> endobj 315 0 obj << /Length 2220 /Filter /FlateDecode >> stream xK