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Solution Manual for Fundamentals of Differential Equations 9th Edition Nagle / All Chapters Full Complete 2023
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Solution Manual for Fundamentals of Differential Equations 9th Edition Nagle / All Chapters Full Complete 2023

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  • May 26, 2023
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Fundamentals of Differential Equations 9th Edition Nagle Solutions Manual Contents Notes to the Instructor 1 Supplements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Computer Labs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Group Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Technical Writing Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Student Presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Homework Assignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Syllabus Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Numerical, Graphical, and Qualitative Methods . . . . . . . . . . . . . . . . . . 3 Engineering/Physics Applications . . . . . . . . . . . . . . . . . . . . . . . . . 5 Biology/Ecology Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Economics Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Supplemental Group Projects 10 Detailed Solutions & Answers to Even -Numbered Problems 23 CHAPTER 1 Introduction 23 Exercises 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Exercises 1.2 Solutions and Initial Value Problems . . . . . . . . . . . . . . . 24 Exercises 1.3 Direction Fields . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Exercises 1.4 The Approximation Method of Euler . . . . . . . . . . . . . . . 31 Review Problems Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 CHAPTER 2 First Order Differential Equations 43 Exercises 2.2 Separable Equations . . . . . . . . . . . . . . . . . . . . . . . . 43 Exercises 2.3 Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Exercises 2.4 Exact Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Exercises 2.5 Special Integrating Factors . . . . . . . . . . . . . . . . . . . . 66 Exercises 2.6 Substitutions and Transformations . . . . . . . . . . . . . . . . 72 Review Problems Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 ii Contents Tables ................................ ................................ ................................ .............................. 82 Figures ................................ ................................ ................................ ............................. 82 CHAPTER 3 Mathematical Models and Numerical Methods Involving First Order Equations 85 Exercises 3.2 Compartmental Analysis ................................ ................................ ........ 85 Exercises 3.3 Heating and Cooling of Buildings ................................ .......................... 93 Exercises 3.4 Newtonian Mechanics ................................ ................................ ............. 99 Exercises 3.5 Electrical Circuits ................................ ................................ .................. 108 Exercises 3.6 Improved Euler’s Method ................................ ................................ ..... 109 Exercises 3.7 Higher -Order Numerical Methods: Taylor and Runge -Kutta ............. 109 Tables ................................ ................................ ................................ ............................ 111 Figures ................................ ................................ ................................ ........................... 112 CHAPTER 4 Linear Second Order Equations 113 Exercises 4.1 Introduction: The Mass -Spring Oscillator ................................ ........... 113 Exercises 4.2 Homogeneous Linear Equations: The General Solution ..................... 115 Exercises 4.3 Auxiliary Equations with Complex Roots ................................ ............ 123 Exercises 4.4 Nonhomogeneous Equations: The Method of Undetermined Coefficients ................................ ................................ ................................ ...................... 131 Exercises 4.5 The Superposition Principle and Undetermined Coefficients Revisited ................................ ................................ ................................ ..................... 136 Exercises 4.6 Variation of Parameters ................................ ................................ ........ 148 Exercises 4.7 Variable -Coefficient Equations ................................ ............................. 155 Exercises 4.8 Qualitative Considerations for Variable -Coefficient and Nonlinear Equations ................................ ................................ ................................ .................... 168 Exercises 4.9 A Closer Look at Free Mechanical Vibrations ................................ .. 171 Exercises 4.10 A Closer Look at Forced Mechanical Vibrations ............................ 177 Review Problems Answers ................................ ................................ .......................... 182 Figures ................................ ................................ ................................ ........................... 184 CHAPTER 5 Introduction to Systems and Phase Plane Analysis 189 Exercises 5.2 Elimination Method for Systems with Constant Coefficients ............. 189 Exercises 5.3 Solving Systems and Higher –Order Equations Numerically ............... 191 Exercises 5.4 Introduction to the Phase Plane ................................ .......................... 192 Exercises 5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models ................................ ................................ ................................ ........................ 194 Exercises 5.6 Coupled Mass –Spring Systems ................................ ............................. 194 Exercises 5.7 Electrical Systems ................................ ................................ ................. 195 Exercise s 5.8 Dynamical Systems , Poincar`e Maps, and Chaos ................................ . 195 Review Problems Answers ................................ ................................ .......................... 196 Tables ................................ ................................ ................................ ............................ 197 Contents iii Figures ................................ ................................ ................................ ........................... 199 CHAPTER 6 Theory of Higher -Order Linear Differential Equations 205 Exercises 6.1 Basic Theory of Linear Differential Equations ................................ .... 205 Exercises 6.2 Homogeneous Linear Equations with Constant Coefficients ............... 206 Exercises 6.3 Undetermined Coefficients and the Annihilator Method ..................... 206 Exercises 6.4 Method of Variation of Parameters ................................ ........................ 207 Review Problems Answers ................................ ................................ .......................... 208 CHAPTER 7 Laplace Transforms 209 Exercises 7.2 Definition of the Laplace Transform ................................ .................... 209 Exercises 7.3 Properties of the Laplace Transform ................................ ................... 213 Exercises 7.4 Inverse Laplace Transform ................................ ................................ .... 219 Exercises 7.5 Solving Initial Value Problems ................................ ............................. 227 Exercises 7.6 Transforms of Discontinuous Functions ................................ ............... 236 Exercises 7.7 Transforms of Periodic and Power Functions ................................ ...... 245 Exercises 7.8 Convolution ................................ ................................ ........................... 250 Exercises 7.9 Impulses and the Dirac Delta Function ................................ ............... 258 Exercises 7.10 Solving Linear Systems with Laplace Transforms ............................. 263 Review Problems Answers ................................ ................................ .......................... 273 Figures ................................ ................................ ................................ ........................... 274 CHAPTER 8 Series Solutions of Differential Equations 279 Exercises 8.1 Introduction: The Taylor Polynomial Approximation ........................ 279 Exercises 8.2 Power Series and Analytic Functions ................................ ................... 280 Exercises 8.3 Power Series Solutions to Linear Differential Equations ..................... 281 Exercises 8.4 Equations with Analytic Coefficients ................................ ................... 282 Exercises 8.5 Cauchy -Euler (Equidimensional) Equations Revisited ........................ 283 Exercises 8.6 Method of Frobenius ................................ ................................ ................ 283 Exercises 8.7 Finding a Second Linearly Independent Solution ................................ 285 Exercises 8.8 Special Functions ................................ ................................ .................. 286 Review Problems Answers ................................ ................................ .......................... 287 Figures ................................ ................................ ................................ ........................... 288 CHAPTER 9 Matrix Methods for Linear Systems 289 Exercises 9.1 Introduction ................................ ................................ .......................... 289 Exercises 9.2 Review 1: Linear Algebraic Equations ................................ ................. 289 Exercises 9.3 Review 2: Matrices and Vectors ................................ .......................... 290 Exercises 9.4 Linear Systems in Normal Form ................................ .......................... 293 Exercises 9.5 Homogeneous Linear Systems with Constant Coefficients .................. 295 Exercises 9.6 Complex Eigenvalues ................................ ................................ ............ 297 Exercises 9.7 Nonhomogeneous Linear Systems ................................ ........................ 298

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