B.5 Imaginary and complex numbersġ Introduction Mathematics is “the science of numbers, quantities, and shapes and the relations between them”.1 Its history dates back almost three millennia – indeed, many insights found in this book have been known for centuries.
B.2 Rational and irrational numbers B.3 Famous irrational numbers. A.5 Harmonics (basic fundamental research). Ī Music and mathematics A.1 Basic approach, fundamentals of natural science. 9.6 Fallacies, traps of reasoning, and apparent contradictions 9.7 Probability distributions. ĩ Statistics and probability calculus 9.1 Descriptive statistics. 8.5 Integration as the inverse of differentiation 8.6 Interpretations of the definite integrals. Ĩ Infinitesimal calculus 8.1 Calculation with infinitesimal quantities. 7.2 Matrix calculations and some applications 7.3 Parametrization of curves. ħ Curves and surfaces 7.1 Rigid body motions. 6.6 Solving equations of the form f(x) = 0. 6.2 Power, exponential, and logarithmic functions 6.3 The derivative function of a real function. Ħ Functions and their derivatives 6.1 Real functions and their inverses.
5.4 Distances, angles, areas, volumes 5.5 Reflection. ĥ Vector analysis 5.1 Elementary vector operations. Ĥ Angles and trigonometry 4.1 The family of Pythagorean theorems 4.2 Radian measure. 3.3 On small scales not as on large scales 3.4 Centrifugal and gravitational forces. ģ Proportions and similar objects 3.1 Similarity of planar figures. 2.5 Algebraic equations of higher degree. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: GewerbestraCham, SwitzerlandĢ Equations, systems of equations 2.1 The fundamentals of numbers and equations. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication.
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in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The use of general descriptive names, registered names, trademarks, service marks, etc. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Library of Congress Control Number: 2017951186 Mathematics Subject Classification: 00Axx, 53Axx, 62-XX, 97U20 © Springer International Publishing AG 2017 This work is subject to copyright. Translation from the German language edition: Der mathematische Werkzeugkasten: Anwendungen in Natur und Technik by Georg Glaeser © Springer-Verlag Berlin Heidelberg 2004, 2006, 2008, 2014 All Rights Reserved. Georg Glaeser Department of Geometry University of Applied Arts Vienna Vienna Austria Math Tools 500+ Applications in Science and Arts Statistics and probability calculus (Georg Glaeser).Pages 437-500īack Matter. Infinitesimal calculus (Georg Glaeser).Pages 367-436 Vector analysis (Georg Glaeser).Pages 175-236įunctions and their derivatives (Georg Glaeser).Pages 237-296Ĭurves and surfaces (Georg Glaeser).Pages 297-366 Proportions and similar objects (Georg Glaeser).Pages 67-118Īngles and trigonometry (Georg Glaeser).Pages 119-174 Introduction (Georg Glaeser).Pages 1-6Įquations, systems of equations (Georg Glaeser).Pages 7-66
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