The Lesbian Mistress and Her Pet

__**Elementary Differential Equations and Boundary Value Problems 11e**__, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. Cover 1 Title Page 5 Copyright 6 Dedication 7 The Authors 8 Preface 9 Brief Contents 12 Contents 13 CHAPTER 1: Introduction 15 1.1. Some Basic Mathematical Models; Direction Fields 15 Problems 22 1.2. Solutions of Some Differential Equations 23 Problems 29 1.3. Classification of Differential Equations 30 Problems 36 References 37 CHAPTER 2: First-Order Differential Equations 38 2.1. Linear Differential Equations; Method of Integrating Factors 38 Problems 45 2.2. Separable Differential Equations 47 Problems 52 2.3. Modeling with First-Order Differential Equations 53 Problems 61 2.4. Differences Between Linear and Nonlinear Differential Equations 65 Problems 71 2.5 Autonomous Differential Equations and Population Dynamics 72 Problems 81 2.6. Exact Differential Equations and Integrating Factors 84 Problems 89 2.7. Numerical Approximations: Euler’s Method 90 Problems 96 2.8. The Existence and Uniqueness Theorem 97 Problems 104 2.9. First-Order Difference Equations 105 Problems 113 Chapter Review Problems 114 References 115 CHAPTER 3: Second-Order Linear Differential Equations 117 3.1. Homogeneous Differential Equations with Constant Coefficients 117 Problems 123 3.2. Solutions of Linear Homogeneous Equations; the Wronskian 124 Problems 133 3.3. Complex Roots of the Characteristic Equation 134 Problems 139 3.4. Repeated Roots; Reduction of Order 141 Problems 146 3.5. Nonhomogeneous Equations; Method of Undetermined Coefficients 147 Problems 155 3.6. Variation of Parameters 156 Problems 160 3.7. Mechanical and Electrical Vibrations 161 Problems 171 3.8. Forced Periodic Vibrations 173 Problems 181 References 182 CHAPTER 4: Higher-Order Linear Differential Equations 183 4.1. General Theory of nth Order Linear Differential Equations 183 Problems 187 4.2. Homogeneous Differential Equations with Constant Coefficients 188 Problems 194 4.3. The Method of Undetermined Coefficients 195 Problems 198 4.4. The Method of Variation of Parameters 199 Problems 202 References 202 CHAPTER 5: Series Solutions of Second-Order Linear Equations 203 5.1. Review of Power Series 203 Problems 209 5.2. Series Solutions Near an Ordinary Point, Part I 209 Problems 218 5.3. Series Solutions Near an Ordinary Point, Part II 219 Problems 223 5.4. Euler Equations; Regular Singular Points 225 Problems 232 5.5. Series Solutions Near a Regular Singular Point, Part I 233 Problems 237 5.6. Series Solutions Near a Regular Singular Point, Part II 238 Problems 243 5.7. Bessel’s Equation 244 Problems 253 References 254 CHAPTER 6: The Laplace Transform 255 6.1. Definition of the Laplace Transform 255 Problems 261 6.2. Solution of Initial Value Problems 262 Problems 269 6.3. Step Functions 271 Problems 276 6.4. Differential Equations with Discontinuous Forcing Functions 278 Problems 282 6.5. Impulse Functions 284 Problems 287 6.6. The Convolution Integral 289 Problems 293 References 294 CHAPTER 7: Systems of First-Order Linear Equations 295 7.1. Introduction 295 Problems 298 7.2. Matrices 300 Problems 307 7.3. Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors 309 Problems 317 7.4. Basic Theory of Systems of First-Order Linear Equations 318 Problems 322 7.5. Homogeneous Linear Systems with Constant Coefficients 323 Problems 332 7.6. Complex-Valued Eigenvalues 333 Problems 341 7.7 Fundamental Matrices 343 Problems 350 7.8. Repeated Eigenvalues 351 Problems 357 7.9. Nonhomogeneous Linear Systems 359 Problems 365 References 367 CHAPTER 8: Numerical Methods 368 8.1. The Euler or Tangent Line Method 368 Problems 375 8.2. Improvements on the Euler Method 377 Problems 380 8.3. The Runge-Kutta Method 381 Problems 384 8.4. Multistep Methods 385 Problems 389 8.5. Systems of First-Order Equations 390 Problems 392 8.6. More on Errors; Stability 392 Problems 400 References 401 CHAPTER 9: Nonlinear Differential Equations and Stability 402 9.1. The Phase Plane: Linear Systems 402 Problems 411 9.2. Autonomous Systems and Stability 412 Problems 420 9.3. Locally Linear Systems 421 Problems 429 9.4. Competing Specie 431 Problems 440 9.5. Predator - Prey Equations 442 Problems 447 9.6. Liapunov’s Second Method 449 Problems 457 9.7. Periodic Solutions and Limit Cycles 458 Problems 466 9.8. Chaos and Strange Attractors: The Lorenz Equations 468 Problems 474 References 475 CHAPTER 10: Partial Differential Equations and Fourier Series 477 10.1. Two-Point Boundary Value Problems 477 Problems 482 10.2. Fourier Series 483 Problems 490 10.3. The Fourier Convergence Theorem 491 Problems 495 10.4. Even and Odd Functions 496 Problems 501 10.5. Separation of Variables; Heat Conduction in a Rod 502 Problems 509 10.6. Other Heat Conduction Problems 510 Problems 516 10.7. The Wave Equation: Vibrations of an Elastic String 518 Problems 526 10.8. Laplace’s Equation 528 Problems 534 A. APPENDIX 536 B. APPENDIX 540 References 542 CHAPTER 11: Boundary Value Problems and Sturm-Liouville Theory 543 11.1. The Occurrence of Two-Point Boundary Value Problems 543 Problems 547 11.2 Sturm-Liouville Boundary Value Problems 549 Problems 557 11.3. Nonhomogeneous Boundary Value Problems 559 Problems 567 11.4. Singular Sturm-Liouville Problems 570 Problems 575 11.5. Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion 576 Problems 578 11.6. Series of Orthogonal Functions: Mean Convergence 580 Problems 585 References 586 Answers to Problems 587 Chapter 1 587 Section 1.1, page 8 587 Section 1.2, page 15 587 Section 1.3, page 22 587 Chapter 2 588 Section 2.1, page 31 588 Section 2.2, page 38 588 Section 2.3, page 47 588 Section 2.4, page 57 589 Section 2.5, page 67 589 Section 2.6, page 75 590 Section 2.7, page 82 590 Section 2.8, page 90 590 Section 2.9, page 99 590 Miscellaneous Problems, page 100 591 Chapter 3 591 Section 3.1, page 109 591 Section 3.2, page 119 591 Section 3.3, page 125 592 Section 3.4, page 132 592 Section 3.5, page 141 593 Section 3.6, page 146 593 Section 3.7, page 157 593 Section 3.8, page 167 594 Chapter 4 594 Section 4.1, page 173 594 Section 4.2, page 180 594 Section 4.3, page 184 595 Section 4.4, page 188 595 Chapter 5 595 Section 5.1, page 195 595 Section 5.2, page 204 596 Section 5.3, page 209 596 Section 5.4, page 218 597 Section 5.5, page 223 597 Section 5.6, page 229 598 Section 5.7, page 239 598 Chapter 6 599 Section 6.1, page 247 599 Section 6.2, page 255 599 Section 6.3, page 262 599 Section 6.4, page 268 600 Section 6.5, page 273 600 Section 6.6, page 279 600 Chapter 7 601 Section 7.1, page 284 601 Section 7.2, page 293 601 Section 7.3, page 303 602 Section 7.4, page 308 602 Section 7.5, page 318 603 Section 7.6, page 327 603 Section 7.7, page 336 604 Section 7.8, page 343 604 Section 7.9, page 351 605 Chapter 8 606 Section 8.1, page 361 606 Section 8.2, page 366 606 Section 8.3, page 370 607 Section 8.4, page 375 607 Section 8.5, page 378 607 Section 8.6, page 386 607 Chapter 9 608 Section 9.1, page 397 608 Section 9.2, page 406 608 Section 9.3, page 415 608 Section 9.4, page 426 609 Section 9.5, page 433 610 Section 9.7, page 452 611 Section 9.8, page 460 611 Chapter 10 611 Section 10.1, page 468 611 Section 10.2, page 476 612 Section 10.3, page 481 612 Section 10.4, page 487 613 Section 10.5, page 495 614 Section 10.6, page 502 614 Section 10.7, page 512 615 Section 10.8, page 520 615 Section 11.1, page 533 616 Section 11.2, page 543 616 Section 11.3, page 553 617 Section 11.4, page 561 618 Section 11.5, page 564 618 Section 11.6, page 571 618 Index 620 EULA 625 Elementary Differential Equations and Boundary Value Problems 11e , like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11 th edition includes new problems, updated figures and examples to help motivate students. The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations. Elementary Differential Equations And Boundary Value Problems 11e, Like Its Predecessors, Is Written From The Viewpoint Of The Applied Mathematician, Whose Interest In Differential Equations May Sometimes Be Quite Theoretical, Sometimes Intensely Practical, And Often Somewhere In Between. The Authors Have Sought To Combine A Sound And Accurate (but Not Abstract) Exposition Of The Elementary Theory Of Differential Equations With Considerable Material On Methods Of Solution, Analysis, And Approximation That Have Proved Useful In A Wide Variety Of Applications. While The General Structure Of The Book Remains Unchanged, Some Notable Changes Have Been Made To Improve The Clarity And Readability Of Basic Material About Differential Equations And Their Applications. In Addition To Expanded Explanations, The 11th Edition Includes New Problems, Updated Figures And Examples To Help Motivate Students. The Program Is Primarily Intended For Undergraduate Students Of Mathematics, Science, Or Engineering, Who Typically Take A Course On Differential Equations During Their First Or Second Year Of Study. The Main Prerequisite For Engaging With The Program Is A Working Knowledge Of Calculus, Gained From A Normal Two Or Three Semester Course Sequence Or Its Equivalent. Some Familiarity With Matrices Will Also Be Helpful In The Chapters On Systems Of Differential Equations. Boyce's Elementary Differential Equations and Boundary Value Problems, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, this edition includes new problems, updated figures and examples to help motivate students.The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations Maintaining a contemporary approach, flexible chapter construction, clear exposition and outstanding problems, this book focuses both on the theory and the practical applications of differential equations as they apply to engineering and the sciences.