Second Year Calculus

Author: David M. Bressoud
Publisher: Springer Science & Business Media
ISBN: 1461209595
Format: PDF
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Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.

Advanced Calculus

Author: Harold M. Edwards
Publisher: Springer Science & Business Media
ISBN: 146120271X
Format: PDF, Docs
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This book is a high-level introduction to vector calculus based solidly on differential forms. Informal but sophisticated, it is geometrically and physically intuitive yet mathematically rigorous. It offers remarkably diverse applications, physical and mathematical, and provides a firm foundation for further studies.

Relativistic Celestial Mechanics of the Solar System

Author: Sergei Kopeikin
Publisher: John Wiley & Sons
ISBN: 3527634576
Format: PDF, Mobi
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This authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic reference frames, the celestial mechanics of N-body systems, and high-precision astrometry, navigation, and geodesy, which are then treated in the following five chapters. The final chapter provides an overview of the new field of applied relativity, based on recent recommendations from the International Astronomical Union. The book is suitable for teaching advanced undergraduate honors programs and graduate courses, while equally serving as a reference for professional research scientists working in relativity and dynamical astronomy. The authors bring their extensive theoretical and practical experience to the subject. Sergei Kopeikin is a professor at the University of Missouri, while Michael Efroimsky and George Kaplan work at the United States Naval Observatory, one of the world?s premier institutions for expertise in astrometry, celestial mechanics, and timekeeping.

Aspects of Calculus

Author: Gabriel Klambauer
Publisher: Springer Science & Business Media
ISBN: 1461395615
Format: PDF, Mobi
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This book is intended for students familiar with a beginner's version of differential and integral calculus stressing only manipulation offormulas and who are now looking for a closer study of basic concepts combined with a more creative use of information. The work is primarily aimed at students in mathematics, engineering, and science who find themselves in transition from elementary calculus to rigorous courses in analysis. In addition, this book may also be of interest to those preparing to teach a course in calculus. Instead of exposing the reader to an excess of premature abstractions that so easily can degenerate into pedantry, I felt it more useful to stress instruc tive and stimulating examples. The book contains numerous worked out examples and many of the exercises are provided with helpful hints or a solution in outline. For further exercises the interested reader may want to consult a problem book by the author entitled Problems and Propositions in Analysis (New York: Marcel Dekker, 1979). For the history of calculus I recommend the book by C. B. Boyer, The Concepts of the Calculus (New York: Dover, 1949).

Mathematical Methods of Classical Mechanics

Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 1475720637
Format: PDF
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This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

An Introduction to Celestial Mechanics

Author: Richard Fitzpatrick
Publisher: Cambridge University Press
ISBN: 1107023815
Format: PDF, ePub, Docs
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A clear, concise introduction to all the major features of solar system dynamics, ideal for a first course.

An Introduction to Fourier Analysis

Author: Russell L. Herman
Publisher: CRC Press
ISBN: 1498773710
Format: PDF, Mobi
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This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering. This introductory textbook was written with mathematics, science, and engineering students with a background in calculus and basic linear algebra in mind. It can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which cover Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables. These topics are tied together by the application of the spectral analysis of analog and discrete signals, and provide an introduction to the discrete Fourier transform. A number of examples and exercises are provided including implementations of Maple, MATLAB, and Python for computing series expansions and transforms. After reading this book, students will be familiar with: • Convergence and summation of infinite series • Representation of functions by infinite series • Trigonometric and Generalized Fourier series • Legendre, Bessel, gamma, and delta functions • Complex numbers and functions • Analytic functions and integration in the complex plane • Fourier and Laplace transforms. • The relationship between analog and digital signals Dr. Russell L. Herman is a professor of Mathematics and Professor of Physics at the University of North Carolina Wilmington. A recipient of several teaching awards, he has taught introductory through graduate courses in several areas including applied mathematics, partial differential equations, mathematical physics, quantum theory, optics, cosmology, and general relativity. His research interests include topics in nonlinear wave equations, soliton perturbation theory, fluid dynamics, relativity, chaos and dynamical systems.

A Radical Approach to Real Analysis

Author: David M. Bressoud
Publisher: MAA
ISBN: 9780883857472
Format: PDF, ePub, Docs
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Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.

Honors Calculus

Author: C. R. MacCluer
Publisher: Princeton University Press
ISBN: 0691125333
Format: PDF, Docs
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"The book introduces many topics often left to the appendixes in standard calculus textbooks and develops their connections with physics, engineering, and statistics. The author uses applications of derivatives and integrals to show how calculus is applied in these disciplines. Solutions to all exercises (even those involving proofs) are available to instructors upon request, making this book unique among texts in the field."--BOOK JACKET.