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vi | |
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viii | |
Acknowledgements |
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x | |
Introduction |
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1 | (1) |
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1 Defining Chamber Music in the Early Nineteenth Century |
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6 | (17) |
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2 Celebrating Haydn, Cultivating Opera |
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23 | (37) |
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3 Selling String Quartets in Beethoven's Vienna |
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60 | (31) |
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4 Locating String Quartets in Beethoven's Vienna |
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91 | (30) |
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5 Early Nineteenth-Century Performance and Criticism |
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121 | (26) |
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6 Sociability, Showmanship, and Study: `Quartet Friends' |
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147 | (29) |
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7 The String Quartet and the Listener |
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176 | (22) |
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8 Schubert's Song, Beethoven's Theatricality |
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198 | |
Epilogue: Constructing `Viennese Chamber Music' |
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222 | (11) |
Bibliography |
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233 | (12) |
Index |
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245 | (312) |
Preface |
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v | |
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Chapter 1 First-Order Differential Equations |
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1 | (67) |
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1.1 Definition of Differential Equations |
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1 | (9) |
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1.2 Slope Fields and Solution Curves |
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10 | (3) |
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1.3 Separation of Variables |
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13 | (6) |
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1.4 First-Order Linear DEs |
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19 | (8) |
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1.5 The Substitution Methods |
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27 | (11) |
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1.5.1 Polynomial Substitution |
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27 | (2) |
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29 | (1) |
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30 | (8) |
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38 | (5) |
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43 | (22) |
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65 | (3) |
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Chapter 2 Mathematical Models |
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68 | (81) |
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2.1 Newton's Law of Cooling |
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68 | (4) |
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2.2 Torricelli's Law for Draining |
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72 | (7) |
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79 | (13) |
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79 | (1) |
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2.3.2 General Population Equation |
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80 | (2) |
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2.3.3 The Logistic Equation |
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82 | (4) |
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2.3.4 Doomsday vs. Extinction |
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86 | (6) |
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2.4 Acceleration-Velocity Model |
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92 | (31) |
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2.4.1 Newton's Laws of Motion |
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92 | (2) |
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2.4.2 Velocity and Acceleration Models |
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94 | (1) |
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2.4.3 Air Resistance Model |
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95 | (18) |
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2.4.4 Gravitational Acceleration |
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113 | (10) |
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2.5 Windy Day Plane Landing |
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123 | (8) |
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131 | (5) |
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2.7 River Ferryboat-Docking Problem |
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136 | (5) |
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2.8 Equation for Compound Interest |
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141 | (8) |
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Chapter 3 Linear DEs Of Higher Order |
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149 | (62) |
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3.1 Classifications of Linear DEs |
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149 | (6) |
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155 | (9) |
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164 | (23) |
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3.3.1 DEs with Constant Coefficients |
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164 | (11) |
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3.3.2 DEs with Variable Coefficients |
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175 | (12) |
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3.4 Inhomogeneous Linear DEs |
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187 | (24) |
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3.4.1 Method of Undetermined Coefficients |
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187 | (10) |
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3.4.2 Variation of Parameters |
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197 | (14) |
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Chapter 4 Systems Of Linear DEs |
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211 | (51) |
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4.1 Basics of System of DEs |
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211 | (3) |
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4.2 First-Order Systems and Applications |
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214 | (8) |
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4.2.1 One Block and One Spring |
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214 | (2) |
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4.2.2 Two Blocks and Two Springs |
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216 | (1) |
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4.2.3 Kirchhoff Circuit Laws |
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217 | (5) |
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4.3 The Substitution Method |
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222 | (5) |
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227 | (5) |
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4.5 The Eigen-Analysis Method |
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232 | (24) |
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4.6 Examples of Systems of DEs |
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256 | (6) |
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256 | (3) |
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259 | (3) |
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Chapter 5 Laplace Transforms |
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262 | (53) |
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262 | (2) |
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5.2 Properties of Laplace Transforms |
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264 | (21) |
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5.2.1 Laplace Transforms for Polynomials |
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265 | (3) |
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5.2.2 The Translator Property |
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268 | (4) |
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5.2.3 Transforms of Step and Delta Functions |
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272 | (4) |
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5.2.4 The t-multiplication Property |
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276 | (3) |
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279 | (1) |
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5.2.6 Differentiation and Integration Property |
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280 | (5) |
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5.3 Inverse Laplace Transforms |
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285 | (5) |
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5.4 The Convolution of Two Functions |
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290 | (5) |
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295 | (20) |
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APPENDIX A SOLUTIONS TO PROBLEMS |
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315 | (232) |
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Chapter 1 First-Order DEs |
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315 | (1) |
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315 | (5) |
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1.2 Slope Fields and Solution Curves |
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320 | (1) |
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1.3 Separation of Variables |
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321 | (6) |
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1.4 First-Order Linear DEs |
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327 | (10) |
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337 | (20) |
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357 | (7) |
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364 | (12) |
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Chapter 2 Mathematical Models |
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376 | (1) |
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2.1 Newton's Law of Cooling |
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376 | (1) |
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2.2 Torricelli's Law for Draining |
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377 | (8) |
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385 | (8) |
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2.4 Acceleration-Velocity Model |
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393 | (20) |
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2.5 Windy Day Plane Landing |
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413 | (9) |
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422 | (2) |
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2.7 River Ferryboat-Docking Problem |
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424 | (3) |
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2.8 Equation for Compound Interest |
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427 | (8) |
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Chapter 3 Linear DEs of Higher Order |
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435 | (1) |
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3.1 Classification of Linear DEs |
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435 | (2) |
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437 | (7) |
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444 | (14) |
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3.4 Inhomogeneous Linear DEs |
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458 | (23) |
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Chapter 4 Systems of Linear DEs |
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481 | (1) |
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4.1 Basics of System of DEs |
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481 | (1) |
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4.2 First-Order Systems and Applications |
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482 | (5) |
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487 | (6) |
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493 | (8) |
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4.5 The Eigen-Analysis Method |
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501 | (8) |
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509 | (1) |
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Chapter 5 Laplace Transforms |
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510 | (1) |
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5.2 Properties of Laplace Transforms |
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510 | (6) |
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5.3 Inverse Laplace Transforms |
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516 | (3) |
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5.4 The Convolution of Two Functions |
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519 | (2) |
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521 | (26) |
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APPENDIX B LAPLACE TRANSFORMS |
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547 | (4) |
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Selected Laplace Transforms |
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547 | (1) |
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Selected Properties of Laplace Transforms |
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548 | (3) |
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APPENDIX C BASIC FORMULAS |
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551 | (2) |
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553 | (4) |
References |
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557 | (2) |
Index |
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559 | |