Beschreibung
xv, 391-812, xxii p. Das Exemplar ist in einem sehr guten und sauberen Zustand ohne Anstreichungen. / The copy is in a very good and clean condition without markings. -- Contents -- 18. Mathematics as of 1700, 391 -- 1. The Transformation of Mathematics, 391 -- 2. Mathematics and Science, 394 -- 3. Communication Among Mathematicians, 396 -- 4. The Prospects for the -- Eighteenth Century, 398 -- 19. Calculus in the Eighteenth Century, 400 -- 1. Introduction, 400 2 -- . The Function Concept, 403 -- 3. The Technique of Integration -- and Complex Quantities, 406 -- 4. Elliptic Integrals, 411 -- 5. Further Special Functions, -- 422 6. The Calculus of Functions of Several Variables, 425 -- 7. The Attempts to -- Supply Rigor in the Calculus, 426 -- 20. Infinite Series, 436 -- 1. Introduction, 436 -- 2. Initial Work on Infinite Series, 436 -- 3. The Expansion of -- Functions, 440 4. The Manipulation of Series, 422 5. Trigonometric Series, 454 -- 6. Continued Fractions, 459 7 -- . The Problem of Convergence and Divergence, 460 -- 21. Ordinary Differential Equations in the Eighteenth Century, 468 -- 1. Motivations, 468 -- 2. First Order Ordinary Differential Equations, 471 -- 3. Singular Solutions, 476 4 -- . Second Order Equations and the Riccati Equations, 478 -- 5. Higher Order Equations, -- 484 6. The Method of Series, 488 -- 7. Systems of -- Differential Equations, 490 -- 8. Summary, 499 -- 22. Partial Differential Equations in the Eighteenth Century, 502 -- 1. Introduction, 502 -- 2. The Wave Equation, 503 -- 3. Extensions of the Wave Equation, -- 515 4. Potential Theory, -- 522 5. First Order -- Partial Differential Equations, 531 -- 6. Monge and the Theory of Characteristics, 536 -- 7. Monge and the Nonlinear Second -- Order Equations, 538 8. Systems of First Order -- Partial Differential Equations, 540 -- 9. The Rise of the Mathematical Subject, 542 -- 23. Analytic and Differential Geometry in the Eighteenth Century, 544 -- 1. Introduction, 544 -- 2. Basic Analytic Geometry, 544 -- 3. Higher Plane Curves, 547 -- 4. The Curves, 557 -- Beginnings of Differential Geometry, 544 -- 5. Plane Curves, 555 -- 6. Space -- 7. The Theory of Surfaces, 562 -- 8. The Mapping Problem, 570 -- 24. The Calculus of Variations in the Eighteenth Century, 573 -- 3. The Principle of -- 1. The Initial Problems, 573 Least Action -- 2. The Early Work of Euler, 577 -- , 579 4. The Methodology of Lagrange, 582 -- Action, 587 -- 6. The Second Variation, 589 -- 5. Lagrange and Least -- 25. Algebra in the Eighteenth Century, 592 -- 1. Status of the Number System, 592 3. Determinants and Elimination Theory, 606 -- 2. The Theory of Equations, 597 -- 4. The Theory of Numbers, 608 -- 26. Mathematics as of 1800, 614 -- 1. The Rise of Analysis, 614 2. The Motivation for the Eighteenth-Century Work, -- 616 3. The Problem of Proof, 617 4. The Metaphysical Basis, 619 5. The Expansion -- of Mathematical Activity, 621 6. A Glance Ahead, 623 -- 27. Functions of a Complex Variable, 626 -- 1. Introduction, 626 2. The Beginnings of Complex Function Theory, 626 3. The -- Geometrical Representation of Complex Numbers, 628 4. The Foundation Function Theory, 632 5. Weierstrass's Approach to Function Theory, 642 6. Elliptic Functions, 644 7. Hyperelliptic Integrals and Abel's Theorem, 651 8. Riemann and -- of Complex -- Multiple-Valued Functions, 655 9. Abelian Integrals and Functions, 663 -- 10. Conformal Mapping, 666 11. The Representation of Functions and Excepional -- Values, 667 -- 28. Partial Differential Equations in the Nineteenth Century, 671 -- 1. Introduction, 671 2. The Heat Equation and Fourier Series, 671 3. Closed -- Solutions; the Fourier Integral, 679 4. The Potential Equation and Green's Theorem, Equation, 690 7. Systems of Partial Differential Equations, 696 8. Existence -- 681 5. Curvilinear Coordinates, 687 6. The Wave Equation and the Reduced Wave -- Theorems, 699 -- 29. Ordinary Differential Equations in the Nineteenth Century, 709 -- 1. Introduction, 709.
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