Legacy of Leonhard Euler : A Tricentennial Tribute.
Title:
Legacy of Leonhard Euler : A Tricentennial Tribute.
Author:
Debnath, Lokenath.
ISBN:
9781848165267
Personal Author:
Physical Description:
1 online resource (420 pages)
Contents:
Contents -- 1. Mathematics Before Leonhard Euler -- 1.1 Introduction -- 1.2 Pythagoras, the Pythagorean School and Euclid -- 1.3 The Major Impact of the European Renaissance on Mathematics and Science -- 1.4 The Discovery of Calculus by Newton and Leibniz -- 2. Brief Biographical Sketch and Career of Leonhard Euler -- 2.1 Euler's Early Life -- 2.2 Euler's Professional Career -- 3. Euler's Contributions to Number Theory and Algebra -- 3.1 Introduction -- 3.2 Euler's Phi Function and Cryptography -- 3.3 Euler's Other Work on Number Theory -- 3.4 Euler and Partitions of Numbers -- 3.5 Euler's Contributions to Continued Fractions -- 3.6 Euler's Contributions to Classical Algebra -- 4. Euler's Contributions to Geometry and Spherical Trigonometry -- 4.1 Introduction -- 4.2 Euler's Work in Plane Geometry -- 4.3 Incircle, Incenter and Heron's Formula for an Area of a Triangle -- 4.4 Centroid, Orthocenter and Circumcenter -- 4.5 The Euler Line and the Euler Nine-Point Circle . -- 4.6 Euler's Work on Analytic Geometry -- 4.7 Euler's Work on Di.erential Geometry -- 4.8 Spherical Trigonometry -- 5. Euler's Formula for Polyhedra, Topology and Graph Theory -- 5.1 Euler's Formula for Polyhedra -- 5.2 Graphs and Networks -- 6. Euler's Contributions to Calculus and Analysis -- 6.1 Introduction -- 6.2 Euler'sWork on Calculus -- 6.3 Euler and Elliptic Integrals -- 7. Euler's Contributions to the Infinite Series and the Zeta Function -- 7.1 Introduction -- 7.2 Euler and the Infinite Series -- 7.3 Euler's Zeta Function -- 7.4 Euler and the Fourier Series -- 7.5 Generalized Zeta Function -- 7.6 Applications of the Zeta Function to Mathematical Physics and Algebraic Geometry -- 8. Euler's Beta and Gamma Functions and Infinite Products -- 8.1 Introduction -- 8.2 Euler's Beta and Gamma Functions -- 8.3 Applications of the Euler Gamma Functions.
8.4 Euler's Contributions to Infinite Products -- 9. Euler and Differential Equations -- 9.1 Historical Introduction -- 9.2 Euler's Contributions to Ordinary Differential Equations -- 9.3 Euler's Work on Partial Differential Equations -- 9.4 Euler and the Calculus of Variations -- 10. The Euler Equations of Motion in Fluid Mechanics -- 10.1 Introduction -- 10.2 Eulerian Descriptions of Fluid Flows -- 11. Euler's Contributions to Mechanics and Elasticity -- 11.1 Introduction -- 11.2 Euler's Work on Solid Mechanics -- 11.3 Euler's Research on Elastic Curves -- 11.4 Impact of Euler's Work on Modern Aerodynamics -- 12. Euler's Work on the Probability Theory -- 12.1 Introduction -- 12.2 Euler's Work on Probability -- 12.3 Euler's Beta and Gamma Density Distributions -- 13. Euler's Contributions to Ballistics -- 13.1 Introduction -- 13.2 Euler's Research on Ballistics -- 14. Euler and his Work on Astronomy and Physics -- 14.1 Introduction -- 14.2 Euler's Contributions to Astronomy -- 14.3 Euler'sWork on Physics -- Bibliography -- Index.
Abstract:
This book primarily serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. It contains fourteen chapters describing Euler's works on number theory, algebra, geometry, trigonometry, differential and integral calculus, analysis, infinite series and infinite products, ordinary and elliptic integrals and special functions, ordinary and partial differential equations, calculus of variations, graph theory and topology, mechanics and ballistic research, elasticity and fluid mechanics, physics and astronomy, probability and statistics. The book is written to provide a definitive impression of Euler's personal and professional life as well as of the range, power, and depth of his unique contributions. This tricentennial tribute commemorates Euler the great man and Euler the universal mathematician of all time. Based on the author's historically motivated method of teaching, special attention is given to demonstrate that Euler's work had served as the basis of research and developments of mathematical and physical sciences for the last 300 years. An attempt is also made to examine his research and its relation to current mathematics and science. Based on a series of Euler's extraordinary contributions, the historical development of many different subjects of mathematical sciences is traced with a linking commentary so that it puts the reader at the forefront of current research. Erratum. Sample Chapter(s). Chapter 1: Mathematics Before Leonhard Euler (434 KB). Contents: Mathematics Before Leonhard Euler; Brief Biographical Sketch and Career of Leonhard Euler; Euler's Contributions to Number Theory and Algebra; Euler's Contributions to Geometry and Spherical Trigonometry; Euler's Formula for Polyhedra, Topology and Graph
Theory; Euler's Contributions to Calculus and Analysis; Euler's Contributions to the Infinite Series and the Zeta Function; Euler's Beta and Gamma Functions and Infinite Products; Euler and Differential Equations; The Euler Equations of Motion in Fluid Mechanics; Euler's Contributions to Mechanics and Elasticity; Euler's Work on the Probability Theory; Euler's Contributions to Ballistics; Euler and His Work on Astronomy and Physics. Readership: Undergraduate and graduate students of mathematics, mathematics education, physics, engineering and science. As well as professionals and prospective mathematical scientists.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Genre:
Electronic Access:
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