C Edward Sandifer
The Early Mathematics of Leonhard Euler
C Edward Sandifer
The Early Mathematics of Leonhard Euler
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Describes Euler’s early mathematical works - the 50 mathematical articles he wrote before he left St. Petersburg in 1741 to join the Academy of Frederick the Great in Berlin. These works contain some of Euler’s greatest mathematics: the Konigsburg bridge problem, his solution to the Basel problem, his first proof of the Euler-Fermat theorem. Also presented are important results that we seldom realize are due to Euler: that mixed partial derivatives are equal, our f(x) notation, and the integrating factor in differential equations. The book is a portrait of the world’s most exciting mathematics…mehr
Describes Euler’s early mathematical works - the 50 mathematical articles he wrote before he left St. Petersburg in 1741 to join the Academy of Frederick the Great in Berlin. These works contain some of Euler’s greatest mathematics: the Konigsburg bridge problem, his solution to the Basel problem, his first proof of the Euler-Fermat theorem. Also presented are important results that we seldom realize are due to Euler: that mixed partial derivatives are equal, our f(x) notation, and the integrating factor in differential equations. The book is a portrait of the world’s most exciting mathematics between 1725 and 1741, rich in technical detail, woven with connections within Euler’s work and with the work of other mathematicians in other times and places, laced with historical context.
Produktdetails
- Produktdetails
- Verlag: Cambridge University Press
- Seitenzahl: 414
- Erscheinungstermin: 15. März 2007
- Englisch
- Abmessung: 262mm x 183mm x 27mm
- Gewicht: 875g
- ISBN-13: 9780883855591
- ISBN-10: 0883855593
- Artikelnr.: 22577939
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- 06621 890
- Verlag: Cambridge University Press
- Seitenzahl: 414
- Erscheinungstermin: 15. März 2007
- Englisch
- Abmessung: 262mm x 183mm x 27mm
- Gewicht: 875g
- ISBN-13: 9780883855591
- ISBN-10: 0883855593
- Artikelnr.: 22577939
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- 06621 890
Preface
Part I. 1725–1727: 1. Construction of isochronal curves in any kind of resistant
2. Method of finding reciprocal algebraic trajectories
Part II. 1728: 3. Solution to problems of reciprocal trajectories
4. A new method of reducing innumerable differential equations of the second degree to equations of the first degree: Integrating factor
Part III. 1729–1731: 5. On transcendental progressions, or those for which the general term cannot be given algebraically
6. On the shortest curve on a surface that joins any two given points
7. On the summation of innumerably many progressions
Part IV. 1732: 8. General methods for summing progressions
9. Observations on theorems that Fermat and others have looked at about prime numbers
10. An account of the solution of isoperimetric problems in the broadest sense
Part V. 1733: 11. Construction of differential equations which do not admit separation of variables
12. Example of the solution of a differential equation without separation of variables
13. On the solution of problems of Diophantus about integer numbers
14. Inferences on the forms of roots of equations and of their orders
15. Solution of the differential equation axn dx = dy + y2dx
Part VI. 1734: 16. On curves of fastest descent in a resistant medium
17. Observations on harmonic progressions
18. On an infinity of curves of a given kind, or a method of finding equations for an infinity of curves of a given kind
19. Additions to the dissertation on infinitely many curves of a given kind
20. Investigation of two curves, the abscissas of which are corresponding arcs and the sum of which is algebraic
Part VII. 1735: 21. On sums of series of reciprocals
22. A universal method for finding sums which approximate convergent series
23. Finding the sum of a series from a given general term
24. On the solution of equations from the motion of pulling and other equations pertaining to the method of inverse tangents
25. Solution of a problem requiring the rectification of an ellipse
26. Solution of a problem relating to the geometry of position
Part VIII. 1736: 27. Proof of some theorems about looking at prime numbers
28 Further universal methods for summing series
29. A new and easy way of finding curves enjoying properties of maximum or minimum
Part IX. 1737: 30. On the solution of equations
31. An essay on continued fractions
32. Various observations about infinite series
33. Solution to a geometric problem about lunes formed by circles
Part X. 1738: 34. On rectifiable algebraic curves and algebraic reciprocal trajectories
35. On various ways of closely approximating numbers for the quadrature of the circle
36. On differential equations which sometimes can be integrated
37. Proofs of some theorems of arithmetic
38. Solution of some problems that were posed by the celebrated Daniel Bernoulli
Part XI. 1739: 39. On products arising from infinitely many factors
40. Observations on continued fractions
41. Consideration of some progressions appropriate for finding the quadrature of the circle
42. An easy method for computing sines and tangents of angles both natural and artificial
43. Investigation of curves which produce evolutes that are similar to themselves
44. Considerations about certain series
Part XII. 1740: 45. Solution of problems in arithmetic of finding a number, which, when divided by given numbers leaves given remainders
46. On the extraction of roots of irrational quantities: gymnastics with radical signs
Part XIII. 1741: 47. Proof of the sum of this series 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/ 36 + etc
48. Several analytic observations on combinations
49. On the utility of higher mathematics
Topically related articles
Index
About the author.
Part I. 1725–1727: 1. Construction of isochronal curves in any kind of resistant
2. Method of finding reciprocal algebraic trajectories
Part II. 1728: 3. Solution to problems of reciprocal trajectories
4. A new method of reducing innumerable differential equations of the second degree to equations of the first degree: Integrating factor
Part III. 1729–1731: 5. On transcendental progressions, or those for which the general term cannot be given algebraically
6. On the shortest curve on a surface that joins any two given points
7. On the summation of innumerably many progressions
Part IV. 1732: 8. General methods for summing progressions
9. Observations on theorems that Fermat and others have looked at about prime numbers
10. An account of the solution of isoperimetric problems in the broadest sense
Part V. 1733: 11. Construction of differential equations which do not admit separation of variables
12. Example of the solution of a differential equation without separation of variables
13. On the solution of problems of Diophantus about integer numbers
14. Inferences on the forms of roots of equations and of their orders
15. Solution of the differential equation axn dx = dy + y2dx
Part VI. 1734: 16. On curves of fastest descent in a resistant medium
17. Observations on harmonic progressions
18. On an infinity of curves of a given kind, or a method of finding equations for an infinity of curves of a given kind
19. Additions to the dissertation on infinitely many curves of a given kind
20. Investigation of two curves, the abscissas of which are corresponding arcs and the sum of which is algebraic
Part VII. 1735: 21. On sums of series of reciprocals
22. A universal method for finding sums which approximate convergent series
23. Finding the sum of a series from a given general term
24. On the solution of equations from the motion of pulling and other equations pertaining to the method of inverse tangents
25. Solution of a problem requiring the rectification of an ellipse
26. Solution of a problem relating to the geometry of position
Part VIII. 1736: 27. Proof of some theorems about looking at prime numbers
28 Further universal methods for summing series
29. A new and easy way of finding curves enjoying properties of maximum or minimum
Part IX. 1737: 30. On the solution of equations
31. An essay on continued fractions
32. Various observations about infinite series
33. Solution to a geometric problem about lunes formed by circles
Part X. 1738: 34. On rectifiable algebraic curves and algebraic reciprocal trajectories
35. On various ways of closely approximating numbers for the quadrature of the circle
36. On differential equations which sometimes can be integrated
37. Proofs of some theorems of arithmetic
38. Solution of some problems that were posed by the celebrated Daniel Bernoulli
Part XI. 1739: 39. On products arising from infinitely many factors
40. Observations on continued fractions
41. Consideration of some progressions appropriate for finding the quadrature of the circle
42. An easy method for computing sines and tangents of angles both natural and artificial
43. Investigation of curves which produce evolutes that are similar to themselves
44. Considerations about certain series
Part XII. 1740: 45. Solution of problems in arithmetic of finding a number, which, when divided by given numbers leaves given remainders
46. On the extraction of roots of irrational quantities: gymnastics with radical signs
Part XIII. 1741: 47. Proof of the sum of this series 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/ 36 + etc
48. Several analytic observations on combinations
49. On the utility of higher mathematics
Topically related articles
Index
About the author.
Preface
Part I. 1725–1727: 1. Construction of isochronal curves in any kind of resistant
2. Method of finding reciprocal algebraic trajectories
Part II. 1728: 3. Solution to problems of reciprocal trajectories
4. A new method of reducing innumerable differential equations of the second degree to equations of the first degree: Integrating factor
Part III. 1729–1731: 5. On transcendental progressions, or those for which the general term cannot be given algebraically
6. On the shortest curve on a surface that joins any two given points
7. On the summation of innumerably many progressions
Part IV. 1732: 8. General methods for summing progressions
9. Observations on theorems that Fermat and others have looked at about prime numbers
10. An account of the solution of isoperimetric problems in the broadest sense
Part V. 1733: 11. Construction of differential equations which do not admit separation of variables
12. Example of the solution of a differential equation without separation of variables
13. On the solution of problems of Diophantus about integer numbers
14. Inferences on the forms of roots of equations and of their orders
15. Solution of the differential equation axn dx = dy + y2dx
Part VI. 1734: 16. On curves of fastest descent in a resistant medium
17. Observations on harmonic progressions
18. On an infinity of curves of a given kind, or a method of finding equations for an infinity of curves of a given kind
19. Additions to the dissertation on infinitely many curves of a given kind
20. Investigation of two curves, the abscissas of which are corresponding arcs and the sum of which is algebraic
Part VII. 1735: 21. On sums of series of reciprocals
22. A universal method for finding sums which approximate convergent series
23. Finding the sum of a series from a given general term
24. On the solution of equations from the motion of pulling and other equations pertaining to the method of inverse tangents
25. Solution of a problem requiring the rectification of an ellipse
26. Solution of a problem relating to the geometry of position
Part VIII. 1736: 27. Proof of some theorems about looking at prime numbers
28 Further universal methods for summing series
29. A new and easy way of finding curves enjoying properties of maximum or minimum
Part IX. 1737: 30. On the solution of equations
31. An essay on continued fractions
32. Various observations about infinite series
33. Solution to a geometric problem about lunes formed by circles
Part X. 1738: 34. On rectifiable algebraic curves and algebraic reciprocal trajectories
35. On various ways of closely approximating numbers for the quadrature of the circle
36. On differential equations which sometimes can be integrated
37. Proofs of some theorems of arithmetic
38. Solution of some problems that were posed by the celebrated Daniel Bernoulli
Part XI. 1739: 39. On products arising from infinitely many factors
40. Observations on continued fractions
41. Consideration of some progressions appropriate for finding the quadrature of the circle
42. An easy method for computing sines and tangents of angles both natural and artificial
43. Investigation of curves which produce evolutes that are similar to themselves
44. Considerations about certain series
Part XII. 1740: 45. Solution of problems in arithmetic of finding a number, which, when divided by given numbers leaves given remainders
46. On the extraction of roots of irrational quantities: gymnastics with radical signs
Part XIII. 1741: 47. Proof of the sum of this series 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/ 36 + etc
48. Several analytic observations on combinations
49. On the utility of higher mathematics
Topically related articles
Index
About the author.
Part I. 1725–1727: 1. Construction of isochronal curves in any kind of resistant
2. Method of finding reciprocal algebraic trajectories
Part II. 1728: 3. Solution to problems of reciprocal trajectories
4. A new method of reducing innumerable differential equations of the second degree to equations of the first degree: Integrating factor
Part III. 1729–1731: 5. On transcendental progressions, or those for which the general term cannot be given algebraically
6. On the shortest curve on a surface that joins any two given points
7. On the summation of innumerably many progressions
Part IV. 1732: 8. General methods for summing progressions
9. Observations on theorems that Fermat and others have looked at about prime numbers
10. An account of the solution of isoperimetric problems in the broadest sense
Part V. 1733: 11. Construction of differential equations which do not admit separation of variables
12. Example of the solution of a differential equation without separation of variables
13. On the solution of problems of Diophantus about integer numbers
14. Inferences on the forms of roots of equations and of their orders
15. Solution of the differential equation axn dx = dy + y2dx
Part VI. 1734: 16. On curves of fastest descent in a resistant medium
17. Observations on harmonic progressions
18. On an infinity of curves of a given kind, or a method of finding equations for an infinity of curves of a given kind
19. Additions to the dissertation on infinitely many curves of a given kind
20. Investigation of two curves, the abscissas of which are corresponding arcs and the sum of which is algebraic
Part VII. 1735: 21. On sums of series of reciprocals
22. A universal method for finding sums which approximate convergent series
23. Finding the sum of a series from a given general term
24. On the solution of equations from the motion of pulling and other equations pertaining to the method of inverse tangents
25. Solution of a problem requiring the rectification of an ellipse
26. Solution of a problem relating to the geometry of position
Part VIII. 1736: 27. Proof of some theorems about looking at prime numbers
28 Further universal methods for summing series
29. A new and easy way of finding curves enjoying properties of maximum or minimum
Part IX. 1737: 30. On the solution of equations
31. An essay on continued fractions
32. Various observations about infinite series
33. Solution to a geometric problem about lunes formed by circles
Part X. 1738: 34. On rectifiable algebraic curves and algebraic reciprocal trajectories
35. On various ways of closely approximating numbers for the quadrature of the circle
36. On differential equations which sometimes can be integrated
37. Proofs of some theorems of arithmetic
38. Solution of some problems that were posed by the celebrated Daniel Bernoulli
Part XI. 1739: 39. On products arising from infinitely many factors
40. Observations on continued fractions
41. Consideration of some progressions appropriate for finding the quadrature of the circle
42. An easy method for computing sines and tangents of angles both natural and artificial
43. Investigation of curves which produce evolutes that are similar to themselves
44. Considerations about certain series
Part XII. 1740: 45. Solution of problems in arithmetic of finding a number, which, when divided by given numbers leaves given remainders
46. On the extraction of roots of irrational quantities: gymnastics with radical signs
Part XIII. 1741: 47. Proof of the sum of this series 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/ 36 + etc
48. Several analytic observations on combinations
49. On the utility of higher mathematics
Topically related articles
Index
About the author.