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E-grāmata: Math Tools: 500+ Applications in Science and Arts

  • Formāts: PDF+DRM
  • Izdošanas datums: 13-Sep-2017
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319669601
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Math Tools: 500+ Applications in Science and ArtsPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 13-Sep-2017
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319669601
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In this book, topics such as algebra, trigonometry, calculus and statistics are brought to life through over 500 applications ranging from biology, physics and chemistry to astronomy, geography and music.

With over 600 illustrations emphasizing the beauty of mathematics, Math Tools complements more theoretical textbooks on the market, bringing the subject closer to the reader and providing a useful reference to students. By highlighting the ubiquity of mathematics in practical fields, the book will appeal not only to students and teachers, but to anyone with a keen interest in mathematics and its applications.

Recenzijas

Glaeser's offering is essentially an encyclopedia of applied mathematics problems. useful resource for anyone searching for interesting applications of various topics in elementary mathematics. Recommended. Lower-division undergraduates, faculty, and general readers. (D. S. Larson, Choice, Vol. 55 (11), July, 2018) The book is clearly written and is a valuable source for interested readers. This volume is warmly recommended to the graduate students. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, mathematical physics, and applied analysis. The clarity and breadth of this book make it a welcome addition to the personal library of every mathematician. (Teodora-Liliana Rdulescu, zbMATH 1386.00002, 2018) All materials are given in a very concise and precise form, showing amazing findings of human mind and offering a fascinating and enjoyable reading . The book serves to popularization of mathematics among students and can be very interesting and useful to professional researchers as well. (Stan Lipovetsky, Technometrics, Vol. 60 (2), 2018)

1 Introduction
1(6)
2 Equations, systems of equations
7(60)
2.1 The fundamentals of numbers and equations
8(15)
2.2 Linear equations
23(4)
2.3 Systems of linear equations
27(9)
2.4 Quadratic equations
36(5)
2.5 Algebraic equations of higher degree
41(5)
2.6 Further applications
46(21)
3 Proportions and similar objects
67(52)
3.1 Similarity of planar figures
68(6)
3.2 Similarity of spatial objects
74(4)
3.3 On small scales not as on large scales
78(13)
3.4 Centrifugal and gravitational forces
91(6)
3.5 Further applications
97(22)
4 Angles and trigonometry
119(56)
4.1 The family of Pythagorean theorems
120(5)
4.2 Radian measure
125(6)
4.3 Sine, cosine, tangent
131(14)
4.4 The scalene triangle
145(9)
4.5 Further applications
154(21)
5 Vector analysis
175(62)
5.1 Elementary vector operations
176(12)
5.2 Dot product and cross product
188(5)
5.3 Intersecting lines and planes
193(4)
5.4 Distances, angles, areas, volumes
197(10)
5.5 Reflection
207(9)
5.6 Further Applications
216(21)
6 Functions and their derivatives
237(60)
6.1 Real functions and their inverses
238(6)
6.2 Power, exponential, and logarithmic functions
244(14)
6.3 The derivative function of a real function
258(5)
6.4 Differentiation rules
263(16)
6.5 Differentiating with a computer
279(2)
6.6 Solving equations of the form f(x) = 0
281(6)
6.7 Further applications
287(10)
7 Curves and surfaces
297(70)
7.1 Rigid body motions
298(14)
7.2 Matrix calculations and some applications
312(3)
7.3 Parametrization of curves
315(26)
7.4 Envelopes
341(9)
7.5 Surfaces
350(8)
7.6 Further applications
358(9)
8 Infinitesimal calculus
367(70)
8.1 Calculation with infinitesimal quantities
368(3)
8.2 Curve sketching
371(3)
8.3 Optimization problems
374(7)
8.4 Series expansion
381(8)
8.5 Integration as the inverse of differentiation
389(6)
8.6 Interpretations of the definite integrals
395(18)
8.7 Numerical integration
413(7)
8.8 Further applications
420(17)
9 Statistics and probability calculus
437(64)
9.1 Descriptive statistics
438(8)
9.2 Probability -- computing with chance
446(7)
9.3 The probability concept
453(6)
9.4 Conditional and independent events
459(8)
9.5 Combinatorics
467(8)
9.6 Fallacies, traps of reasoning, and apparent contradictions
475(7)
9.7 Probability distributions
482(9)
9.8 Further applications
491(10)
A Music and mathematics
501(18)
A.1 Basic approach, fundamentals of natural science
502(3)
A.2 System formation
505(2)
A.3 Tuning instruments -- intonation
507(5)
A.4 Numerical symbolism
512(1)
A.5 Harmonics (basic fundamental research)
513(2)
A.6 Numerical examples
515(4)
B Numbers
519(34)
B.1 Numerology
520(4)
B.2 Rational and irrational numbers
524(3)
B.3 Famous irrational numbers
527(3)
B.4 The Fibonacci numbers
530(3)
B.5 Imaginary and complex numbers
533(20)
Index 553
Georg Glaeser received his PhD and habilitation in geometry from the Vienna University of Technology. Since 1998, he has been full professor of geometry at the University of Applied Arts Vienna. He is a passionate natural photographer and the author and coauthor of more than a dozen books on geometry, mathematics, computational geometry, computer graphics, photography, and several books about evolution.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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