The Mathematical Mechanic : Using Physical Reasoning to Solve Problems /

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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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Detalles Bibliográficos
Autor principal: Levi, Mark (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2022]
Colección:Princeton Science Library ; 139
Temas:
Mathematical physics.
Problem solving.
MATHEMATICS / General.
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.
Acceso en línea:Texto completo
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Tabla de Contenidos:
  • 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

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