The Mathematical Mechanic : : Using Physical Reasoning to Solve Problems / / Mark Levi.
Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Ma...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2023] ©2023 |
Year of Publication: | 2023 |
Language: | English |
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Physical Description: | 1 online resource (216 p.) :; 56 halftones. 66 line illus. 1 table. |
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Levi, Mark, author. aut http://id.loc.gov/vocabulary/relators/aut The Mathematical Mechanic : Using Physical Reasoning to Solve Problems / Mark Levi. Princeton, NJ : Princeton University Press, [2023] ©2023 1 online resource (216 p.) : 56 halftones. 66 line illus. 1 table. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Princeton Science Library ; 139 Frontmatter -- Contents -- Preface -- 1 INTRODUCTION -- 2 THE PYTHAGOREAN THEOREM -- 3 MINIMA AND MAXIMA -- 4 INEQUALITIES BY ELECTRIC SHORTING -- 5 CENTER OF MASS: PROOFS AND SOLUTIONS -- 6 GEOMETRY AND MOTION -- 7 COMPUTING INTEGRALS USING MECHANICS -- 8 THE EULER-LAGRANGE EQUATION VIA STRETCHED SPRINGS -- 9 LENSES, TELESCOPES, AND HAMILTONIAN MECHANICS -- 10 A BICYCLE WHEEL AND THE GAUSS-BONNET THEOREM -- 11 COMPLEX VARIABLES MADE SIMPLE(R) -- APPENDIX: PHYSICAL BACKGROUND -- BIBLIOGRAPHY -- INDEX restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist.Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can. Did you know it's possible to derive the Pythagorean theorem by spinning a fish tank filled with water? Or that soap film holds the key to determining the cheapest container for a given volume? Or that the line of best fit for a data set can be found using a mechanical contraption made from a rod and springs? Levi demonstrates how to use physical intuition to solve these and other fascinating math problems. More than half the problems can be tackled by anyone with precalculus and basic geometry, while the more challenging problems require some calculus. This one-of-a-kind book explains physics and math concepts where needed, and includes an informative appendix of physical principles.The Mathematical Mechanic will appeal to anyone interested in the little-known connections between mathematics and physics and how both endeavors relate to the world around us. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 29. Mai 2023) MATHEMATICS / General. bisacsh Addition. Analytic function. Angular acceleration. Angular velocity. Axle. Calculation. Capacitor. Cartesian coordinate system. Cauchy's integral formula. Center of mass (relativistic). Center of mass. Centroid. Ceva's theorem. Clockwise. Complex analysis. Complex number. Conservation of energy. Convex curve. Curvature. Curve. Cylinder (geometry). Derivative. Diameter. Differential geometry. Dimension. Division by zero. Dot product. Eigenvalues and eigenvectors. Electric current. Equation. Euler's formula. Euler–Lagrange equation. Fermat's principle. Friction. Fundamental theorem of calculus. Gaussian curvature. Generating function. Geodesic curvature. Geometry. Gravity. Green's theorem. Heat flux. Hinge. Hooke's law. Horizontal plane. Hypotenuse. Inductance. Instant. Kinetic energy. Line integral. Linear map. Mathematics. Mechanics. Moment of inertia. Newton's laws of motion. Normal (geometry). Ohm's law. Optics. Partial derivative. Potential energy. Proportionality (mathematics). Pythagorean theorem. Quadratic function. Quantity. Rectangle. Resistor. Right angle. Right triangle. Second law of thermodynamics. Semicircle. Series and parallel circuits. Sign (mathematics). Slinky. Snell's law. Soap bubble. Soap film. Special case. Spring (device). Stiffness. Summation. Surface area. Surface tension. Tangent space. Tangent. Telescope. Theorem. Thought experiment. Tractrix. Trapezoid. Trigonometric functions. Two-dimensional gas. Uncertainty principle. Unit circle. Unit vector. Vacuum. Variable (mathematics). Vector field. Voltage drop. Voltage. Wavefront. Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 English 9783111319292 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 9783111318912 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2023 English 9783111319209 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2023 9783111318608 ZDB-23-DMA Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2023 9783110749748 print 9780691242057 https://doi.org/10.1515/9780691244174?locatt=mode:legacy https://www.degruyter.com/isbn/9780691244174 Cover https://www.degruyter.com/document/cover/isbn/9780691244174/original |
language |
English |
format |
eBook |
author |
Levi, Mark, Levi, Mark, |
spellingShingle |
Levi, Mark, Levi, Mark, The Mathematical Mechanic : Using Physical Reasoning to Solve Problems / Princeton Science Library ; Frontmatter -- Contents -- Preface -- 1 INTRODUCTION -- 2 THE PYTHAGOREAN THEOREM -- 3 MINIMA AND MAXIMA -- 4 INEQUALITIES BY ELECTRIC SHORTING -- 5 CENTER OF MASS: PROOFS AND SOLUTIONS -- 6 GEOMETRY AND MOTION -- 7 COMPUTING INTEGRALS USING MECHANICS -- 8 THE EULER-LAGRANGE EQUATION VIA STRETCHED SPRINGS -- 9 LENSES, TELESCOPES, AND HAMILTONIAN MECHANICS -- 10 A BICYCLE WHEEL AND THE GAUSS-BONNET THEOREM -- 11 COMPLEX VARIABLES MADE SIMPLE(R) -- APPENDIX: PHYSICAL BACKGROUND -- BIBLIOGRAPHY -- INDEX |
author_facet |
Levi, Mark, Levi, Mark, |
author_variant |
m l ml m l ml |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Levi, Mark, |
title |
The Mathematical Mechanic : Using Physical Reasoning to Solve Problems / |
title_sub |
Using Physical Reasoning to Solve Problems / |
title_full |
The Mathematical Mechanic : Using Physical Reasoning to Solve Problems / Mark Levi. |
title_fullStr |
The Mathematical Mechanic : Using Physical Reasoning to Solve Problems / Mark Levi. |
title_full_unstemmed |
The Mathematical Mechanic : Using Physical Reasoning to Solve Problems / Mark Levi. |
title_auth |
The Mathematical Mechanic : Using Physical Reasoning to Solve Problems / |
title_alt |
Frontmatter -- Contents -- Preface -- 1 INTRODUCTION -- 2 THE PYTHAGOREAN THEOREM -- 3 MINIMA AND MAXIMA -- 4 INEQUALITIES BY ELECTRIC SHORTING -- 5 CENTER OF MASS: PROOFS AND SOLUTIONS -- 6 GEOMETRY AND MOTION -- 7 COMPUTING INTEGRALS USING MECHANICS -- 8 THE EULER-LAGRANGE EQUATION VIA STRETCHED SPRINGS -- 9 LENSES, TELESCOPES, AND HAMILTONIAN MECHANICS -- 10 A BICYCLE WHEEL AND THE GAUSS-BONNET THEOREM -- 11 COMPLEX VARIABLES MADE SIMPLE(R) -- APPENDIX: PHYSICAL BACKGROUND -- BIBLIOGRAPHY -- INDEX |
title_new |
The Mathematical Mechanic : |
title_sort |
the mathematical mechanic : using physical reasoning to solve problems / |
series |
Princeton Science Library ; |
series2 |
Princeton Science Library ; |
publisher |
Princeton University Press, |
publishDate |
2023 |
physical |
1 online resource (216 p.) : 56 halftones. 66 line illus. 1 table. |
contents |
Frontmatter -- Contents -- Preface -- 1 INTRODUCTION -- 2 THE PYTHAGOREAN THEOREM -- 3 MINIMA AND MAXIMA -- 4 INEQUALITIES BY ELECTRIC SHORTING -- 5 CENTER OF MASS: PROOFS AND SOLUTIONS -- 6 GEOMETRY AND MOTION -- 7 COMPUTING INTEGRALS USING MECHANICS -- 8 THE EULER-LAGRANGE EQUATION VIA STRETCHED SPRINGS -- 9 LENSES, TELESCOPES, AND HAMILTONIAN MECHANICS -- 10 A BICYCLE WHEEL AND THE GAUSS-BONNET THEOREM -- 11 COMPLEX VARIABLES MADE SIMPLE(R) -- APPENDIX: PHYSICAL BACKGROUND -- BIBLIOGRAPHY -- INDEX |
isbn |
9780691244174 9783111319292 9783111318912 9783111319209 9783111318608 9783110749748 9780691242057 |
url |
https://doi.org/10.1515/9780691244174?locatt=mode:legacy https://www.degruyter.com/isbn/9780691244174 https://www.degruyter.com/document/cover/isbn/9780691244174/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
510 - Mathematics |
dewey-full |
510 |
dewey-sort |
3510 |
dewey-raw |
510 |
dewey-search |
510 |
doi_str_mv |
10.1515/9780691244174?locatt=mode:legacy |
oclc_num |
1353269125 |
work_keys_str_mv |
AT levimark themathematicalmechanicusingphysicalreasoningtosolveproblems AT levimark mathematicalmechanicusingphysicalreasoningtosolveproblems |
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ids_txt_mv |
(DE-B1597)635579 (OCoLC)1353269125 |
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hierarchy_parent_title |
Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2023 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2023 Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2023 |
is_hierarchy_title |
The Mathematical Mechanic : Using Physical Reasoning to Solve Problems / |
container_title |
Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 English |
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tag="653" ind1=" " ind2=" "><subfield code="a">Two-dimensional gas.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Uncertainty principle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Unit circle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Unit vector.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vacuum.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Variable (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vector field.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Voltage drop.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Voltage.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Wavefront.</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield 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