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Exponential functions. --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions
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Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision and Robotics. The most commonly used norm in the approximation by linear combinations of exponentials is the l2 norm (sum of squares of residuals), in which case one obtains a nonlinear separable least squares problem. A number of different methods have been proposed through the years to solve these types of problems and new applications appear
Exponential functions. --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions
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eebo-0018
Fireworks --- Geometry --- Mensuration --- Roots, Numerical --- Numerical roots --- Cube root --- Exponents (Algebra) --- Square root --- Measuring --- Mensuration --- Mathematics --- Technology --- Metrology --- Physical measurements --- Mathematics, Greek --- Pyrotechnics --- Pyrotechnists
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This single-volume compilation of three books centers on Hyperbolic Functions, an introduction to the relationship between the hyperbolic sine, cosine, and tangent, and the geometric properties of the hyperbola. The development of the hyperbolic functions, in addition to those of the trigonometric (circular) functions, appears in parallel columns for comparison. A concluding chapter introduces natural logarithms and presents analytic expressions for the hyperbolic functions.The second book, Configuration Theorems, requires only the most elementary background in plane and solid geometry. It dis
Exponential functions --- Geometry, Projective --- Polygons --- Polyhedra --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Polyhedral figures --- Polyhedrons --- Geometry, Solid --- Shapes --- Polygonal figures --- Geometry, Plane --- Projective geometry --- Geometry, Modern --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions
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The Role of Mathematics in Science aims to illustrate the many ways in which mathematical methods have helped discovery in science. It is aimed at a group of readers who are interested in mathematics beyond the level of high school. The authors occasionally use some calculus and more intricate arguments. The book should appeal to college students and general readers with some background in mathematics. The authors state that, 'If we succeed in giving an impression of the beauty and power of mathematical reasoning in science, the purpose of our work will have been achieved.' This book includes the laws of levers and inclined planes, the laws of exponential versus limited population growth, ray optics, and relativity.
Exponential functions. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- Mathematical physics. --- Mathematics. --- Science. --- Natural science --- Natural sciences --- Science of science --- Sciences --- Math --- Science --- Physical mathematics --- Physics --- Mathematics
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This book presents a functional approach to the construction, use and approximation of Green's functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics.
Green's functions. --- Exponential functions. --- Mathematical physics. --- Physical mathematics --- Physics --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Mathematics
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Mathematical statistics --- Sufficient statistics --- Distribution (Probability theory) --- Exponential functions --- 519.24 --- 519.221 --- Statistics, Sufficient --- Sampling (Statistics) --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Special statistical applications and models --- Foundations of statistical theory --- 519.221 Foundations of statistical theory --- 519.24 Special statistical applications and models
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The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Nonlinear systems. --- Exponential functions. --- Functions, Exponential --- Hyperbolic functions --- Systems, Nonlinear --- Mathematics. --- Fourier analysis. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Mathematical physics. --- Partial Differential Equations. --- Fourier Analysis. --- Mathematical Physics. --- Applications of Mathematics. --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- System theory --- Differential equations, partial. --- Math --- Science --- Analysis, Fourier --- Mathematical analysis --- Partial differential equations --- Engineering --- Engineering analysis --- Physical mathematics --- Physics --- Mathematics
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FOURIER ANALYSIS --- Moment problems (Mathematics) --- Exponential functions --- Control theory --- Distributed parameter systems --- Fourier analysis --- 517.98 --- Calculus, Operational --- Analysis, Fourier --- Mathematical analysis --- Functions, Exponential --- Hyperbolic functions --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- Systems, Distributed parameter --- Engineering systems --- System analysis --- Dynamics --- Machine theory --- 517.98 Functional analysis and operator theory --- Functional analysis and operator theory
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