krainaksiazek geometric integration theory 20107058

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Geometric Integration Theory - 2845339415

319,99 zł

Geometric Integration Theory

Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Geometry

This Self-contained And Accessible Textbook Introduces Geometric Measure Theory Through The Notion Of Currents. Motivating Key Ideas With Examples And Figures, This Book Is A Comprehensive Introduction Ideal For Both Self-study And For Use In The Classroo


The Mathematics of Classical and Quantum Physics - 2826676408

100,66 zł

The Mathematics of Classical and Quantum Physics Dover Publications

Książki / Literatura obcojęzyczna

VOLUME ONE 1 Vectors in Classical Physics Introduction 1.1 Geometric and Algebraic Definitions of a Vector 1.2 The Resolution of a Vector into Components 1.3 The Scalar Product 1.4 Rotation of the Coordinate System: Orthogonal Transformations 1.5 The Vector Product 1.6 A Vector Treatment of Classical Orbit Theory 1.7 Differential Operations on Scalar and Vector Fields *1.8 Cartesian-Tensors 2 Calculus of Variations Introduction 2.1 Some Famous Problems 2.2 The Euler-Lagrange Equation 2.3 Some Famous Solutions 2.4 Isoperimetric Problems - Constraints 2.5 Application to Classical Mechanics 2.6 Extremization of Multiple Integrals 2.7 Invariance Principles and Noether's Theorem 3 Vectors and Matrics Introduction 3.1 "Groups, Fields, and Vector Spaces" 3.2 Linear Independence 3.3 Bases and Dimensionality 3.4 Ismorphisms 3.5 Linear Transformations 3.6 The Inverse of a Linear Transformation 3.7 Matrices 3.8 Determinants 3.9 Similarity Transformations 3.10 Eigenvalues and Eigenvectors *3.11 The Kronecker Product 4. Vector Spaces in Physics Introduction 4.1 The Inner Product 4.2 Orthogonality and Completeness 4.3 Complete Ortonormal Sets 4.4 Self-Adjoint (Hermitian and Symmetric) Transformations 4.5 Isometries-Unitary and Orthogonal Transformations 4.6 The Eigenvalues and Eigenvectors of Self-Adjoint and Isometric Transformations 4.7 Diagonalization 4.8 On The Solvability of Linear Equations 4.9 Minimum Principles 4.10 Normal Modes 4.11 Peturbation Theory-Nondegenerate Case 4.12 Peturbation Theory-Degenerate Case 5. Hilbert Space-Complete Orthonormal Sets of Functions Introduction 5.1 Function Space and Hilbert Space 5.2 Complete Orthonormal Sets of Functions 5.3 The Dirac d-Function 5.4 Weirstrass's Theorem: Approximation by Polynomials 5.5 Legendre Polynomials 5.6 Fourier Series 5.7 Fourier Integrals 5.8 Sphereical Harmonics and Associated Legendre Functions 5.9 Hermite Polynomials 5.10 Sturm-Liouville Systems-Orthogaonal Polynomials 5.11 A Mathematical Formulation of Quantum Mechanics VOLUME TWO 6 Elements and Applications of the Theory of Analytic Functions Introduction 6.1 Analytic Functions-The Cauchy-Riemann Conditions 6.2 Some Basic Analytic Functions 6.3 Complex Integration-The Cauchy-Goursat Theorem 6.4 Consequences of Cauchy's Theorem 6.5 Hilbert Transforms and the Cauchy Principal Value 6.6 An Introduction to Dispersion Relations 6.7 The Expansion of an Analytic Function in a Power Series 6.8 Residue Theory-Evaluation of Real Definite Integrals and Summation of Series 6.9 Applications to Special Functions and Integral Representations 7 Green's Function Introduction 7.1 A New Way to Solve Differential Equations 7.2 Green's Functions and Delta Functions 7.3 Green's Functions in One Dimension 7.4 Green's Functions in Three Dimensions 7.5 Radial Green's Functions 7.6 An Application to the Theory of Diffraction 7.7 Time-dependent Green's Functions: First Order 7.8 The Wave Equation 8 Introduction to Integral Equations Introduction 8.1 Iterative Techniques-Linear Integral Operators 8.2 Norms of Operators 8.3 Iterative Techniques in a Banach Space 8.4 Iterative Techniques for Nonlinear Equations 8.5 Separable Kernels 8.6 General Kernels of Finite Rank 8.7 Completely Continuous Operators 9 Integral Equations in Hilbert Space Introduction 9.1 Completely Continuous Hermitian Operators 9.2 Linear Equations and Peturbation Theory 9.3 Finite-Rank Techniques for Eigenvalue Problems 9.4 the Fredholm Alternative for Completely Continuous Operators 9.5 The Numerical Solutions of Linear Equations 9.6 Unitary Transformations 10 Introduction to Group Theory Introduction 10.1 An Inductive Approach 10.2 The Symmetric Groups 10.3 "Cosets, Classes, and Invariant Subgroups" 10.4 Symmetry and Group Representations 10.5 Irreducible Representations 10.6 "Unitary Representations, Schur's Lemmas, and Orthogonality Relations" 10.7 The Determination of Group Representations 10.8 Group Theory in Physical Problems General Bibliography Index to Volume One Index to Volume Two


Calculus of Variations - 2826704446

431,00 zł

Calculus of Variations Cambridge University Press

Książki / Literatura obcojęzyczna

This textbook on the calculus of variations leads the reader from the basics to modern aspects of the theory. One-dimensional problems and the classical issues like Euler-Lagrange equations are treated, as are Noether's theorem, Hamilton-Jacobi theory, and in particular geodesic lines, thereby developing some important geometric and topological aspects. The basic ideas of optimal control theory are also given. The second part of the book deals with multiple integrals. After a review of Lebesgue integration, Banach and Hilbert space theory and Sobolev spaces (with complete and detailed proofs), there is a treatment of the direct methods and the fundamental lower semicontinuity theorems. Subsequent chapters introduce the basic concepts of the modern calculus of variations, namely relaxation, Gamma convergence, bifurcation theory and minimax methods based on the Palais


The Scientific Papers of Sir George Darwin - 2138985955

224,95 zł

The Scientific Papers of Sir George Darwin Cambridge Univeristy Press

Księgarnia / Cambridge University Press / Badania planet

The Scientific Papers of Sir George Darwin: Volume 4 Periodic Orbits and Miscellaneous Papers Autor: George Howard DarwinSir George Darwin (1845–1912) was the second son and fifth child of Charles Darwin. After studying mathematics at Cambridge he read for the Bar, but soon returned to science and to Cambridge, where in 1883 he was appointed Plumian Professor of Astronomy and Experimental Philosophy. His family home is now the location of Darwin College. His work was concerned primarily with the effect of the sun and moon on tidal forces on Earth, and with the theoretical cosmogony which evolved from practical observation: he formulated the fission theory of the formation of the moon (that the moon was formed from still-molten matter pulled away from the Earth by solar tides). This volume of his collected papers covers periodic orbits and some miscellaneous papers, including two investigating the health statistics of the marriage of first cousins – of interest to a member of a dynasty in which such marriages were common. Spis treści: Preface Part I. Periodic orbits: 1. Periodic orbits 2. On certain discontinuities connected with periodic orbits 3. On certain families of periodic orbits Part II. The Tides: 4. The tides Part III. Miscellaneous Papers in Chronological Order: 5. On some proposed forms of slide-rule 6. An application of Peaucellier's cell 7. The mechanical description of equipotential lines 8. On a mechanical representation of the second elliptic integral 9. On maps of the world 10. A geometric puzzle 11. A geometric illustration of the potential of a distant centre of force 12. On graphical interpolation and integration 13. On a theorem in spherical harmonic analysis 14. On fallible measures of variable quantities, and on the treatment of meteorological observations 15. On the horizontal thrust of a mass of sand 16. On the formation of ripple-mark in sand 17. Note on Mr Davison's paper on the straining of the Earth's crust in cooling 18. On the mechanical conditions of a swarm of meteorites, and on theories of cosmogony 19. On the perturbation of a comet in the neighbourhood of a planet 20. The Eulerian notation of the Earth's axis 21. The analogy between Lesage's theory of gravitation and the repulsion of light Part IV. Papers on Tides: 22. The tidal observations of the British Antarctic Expedition, 1907 23. On a mistake in the instructions for the use of a certain apparatus in tidal reductions 24. Geological time 25. Presentation of the Medal of the Royal Astronomical Society to M. Henri PoincarĂŠ 26. Cosmical evolution Appendix: 27. Marriages between first cousins in England and their effects 28. Note on the marriages of first cousins Index.dla: academic researchers, graduate students isbn9781108004473stron628Data publikacji20/07/20094 b/w illus.Paperback244 x 170 mm


Mathematics and the Imagination - 2842080323

84,47 zł

Mathematics and the Imagination Dover Publications

Książki / Literatura obcojęzyczna

Introduction I. NEW NAMES FOR OLD Easy words for hard ideas Transcendental Non-simple curve Simple curve Simple group Bolsheviks and giraffes Turbines Turns and slides Circles and cycles Patho-circles Clocks Hexagons and parhexagons "Radicals, hyperradicals, and ultraradicals (nonpolitical)" New numbers for the nursery Googol and googolplex Miracle of the rising book The mathescope II. BEYOND THE GOOGOL Counting?the language of number "Counting, matching, and "Going to Jerusalem" Cardinal numbers Cosmic chess and googols The sand reckoner Mathematical induction The infinite and its progeny Zeno Puzzles and quarrels Bolzano Galileo's puzzle Cantor Measuring the measuring rod The whole is no greater than some of its parts The first transfinite?Alepho Arithmetic for morons Common sense hits a snag Cardinality madman The tortoise unmasked Motionless motion Private life of a number The house that Cantor built III. "Pie, i, e (PIE)" Chinamen and chandeliers Twilight of common sense "Pie, i, e" Squaring the circle and its cousins Mathematical impossibility "Silk purse, sow's ear, ruler and compass" Rigor mortis Algebraic equations and transcendental numbers Galois and Greek epidemics Cube duplicators and angle trisectors Biography of pie "Infancy: Archimedes, the Bible, the Egyptians" "Adolescence: Vieta, Van Ceulen" "Maturity: Wallis, Newton, Leibniz" "Old Age: Dase, Richter, Shanks" Victim of schizophrenia Boon to insurance companies (e) Logarithms or tricks of the trade Mr. Briggs is surprised Mr. Napier explains "Biography of e; or e, the banker's boon" Pituitary gland of mathematics: the exponential function (i) "Humpty Dumpty, Doctor or Semantics" Imaginary numbers "The v-1, or "Where am I?" " "Biography of i, the self-made amphibian" "Omar Khayyám, Cardan, Bombelli, and Gauss" i and Soviet Russia Program music of mathematics "Breakfast in bed; or, How to become a great mathematician" Analytic geometry Geometric representation of i Complex plane "A famous formula, faith, and humility" IV. ASSORTED GEOMETRIES?PLANE AND FANCY The talking fish and St. Augustine A new alphabet High priests and mumbo jumbo Pure and applied mathematics Euclid and Texas Mathematical tailors Geometry?a game "Ghosts, table-tipping, and the land of the dead" Fourth-dimension flounders Henry More to the rescue Fourth-dimension?a new gusher A cure for arthritis Syntax suffers a setback The physicist's delight Dimensions and manifolds Distance formulae Scaling blank walls Four-dimensional geometry defined Moles and tesseracts A four-dimensional fancy Romance of flatland Three-dimensional cats and two-dimensional kings Gallant Gulliver and the gloves Beguiling voices and strange footprints Non-Euclidean geometry Space credos and millinery Private and public space Rewriting our textbooks The prince and the Boethians The flexible fifth The mathematicians unite?nothing to lose but their chains Lobachevsky breaks a link Riemann breaks another Checks and double checks in mathematics The tractrix and the pseudosphere Great circles and bears The skeptic persists?and is stepped on Geodesics Seventh Day Adventists Curvature Lobachevskian Eiffel Towers and Riemannian Holland Tunnels V. PASTIMES OF PAST AND PRESENT TIMES Puzzle acorns and mathematical oaks Charlemagne and crossword puzzles "Mark Twain and the "farmer's daughter" The syntax of puzzles Carolyn Flaubert and the cabin boy "A wolf, a goat, and a head of cabbage" Brides and cuckolds I'll be switched "Poisson, the misfit" "High finance; or, The international beer wolf" Lions and poker players The decimal system Casting out nines "Buddha, God, and the binary scale" "The march of culture; or, Russia, the home of the binary system" The Chinese rings The tower of Hanoi "The ritual of Benares: or, Charley horse in the Orient" "Nim, Sissa Ben Dahir, and Josephus" Bismarck plays the boss The 15 puzzle plague The spider and the fly A nightmare of relatives The magic square Take a number from 1 to 10 Fermat's last theorem Mathematics' lost legacy VI. PARADOX LOST AND PARADOX REGAINED Great paradoxes and distant relatives Three species of paradox Paradoxes strange but true Wheels that move faster on top than on bottom The cycloid family "The curse of transportation; or, How locomotives can't make up their minds" Reformation of geometry Ensuing troubles Point sets?the Arabian Nights of mathematics Hausdorff spins a tall tale Messrs. Banach and Tarski rub the magic lamp Baron Munchhausen is stymied by a pea Mathematical fallacies "Trouble from a bubble; or, Dividing by zero" The infinite?troublemaker par excellence Geometrical fallacies Logical paradoxes?the folk tales of mathematics Deluding dialectics of the poacher and the prince; of the introspective barber; of the number 111777; of this book and Confucius; of the Hon. Bertrand Russell "Scylla and Charybdis; or, What shall poor mathematics d "Twits Napoleon, who does" The Marquis de Condorcet has high hopes M. le Marquis omits a factor and loses his head Fourier of the Old Guard Dr. Darwin of the New The syllogism scraps a standby Mr. Socrates may not die "Ring out the old logic, ring in the new" VIII. RUBBER-SHEET GEOMETRY Seven bridges over a stein of beer Euler shivers Is warmed by news from home Invents topology Dissolves the dilemma of Sunday strollers Babies' cribs and Pythagoreans Talismen and queer figures Position is everything in topology Da Vinci and Dali Invariants Transformations The immutable derby "Competition for the caliph's cup; or, Sifting out the suitors by science" Mr. Jordan's theorem Only seems idiotic Deformed circles Old facts concerning Times Square and a balloonist's head Eccentric deportment of several distinguished gentlemen at Princeton Their passion for pretzels Their delving in doughnuts Enforced modesty of readers and authors The ring Lachrymose recital around a Paris pissoir "Who staggered how many times around the walls of what?" In and out the doughnut Gastric surgery?from doughnut to sausage in a single cut N-dimensional pretzels The Möbius strip Just as black as it is painted Foments industrial discontent Never takes sides Bane of painter and paintpot alike The iron rings "Mathematical cotillion; or, How on earth do I get rid of my partner?" "Topology?the pinnacle of perversity; or, Removing your vest without your coat" Down to earth?map coloring Four-color problem Euler's theorem The simplest universal law Brouwer's puzzle The search for invariants IX. CHANGE AND CHANGEABILITY The calculus and cement Meaning of change and rate of change Zeno and the movies "Flying Arrow" local?stops at all points" Geometry and genetics The arithmetic men dig pits Lamentable analogue of the boomerang History of the calculus Kepler Fermat Story of the great rectangle Newton and Leibniz Archimedes and the limit "Shrinking and swelling; or, "Will the circle go the limit?" Brief dictionary of mathematics and physics "Military idyll; or, The speed of the falling bomb" The calculus at work The derivative Higher derivatives and radius of curvature Laudable scholarship of automobile engineers The third derivative as a shock absorber The derivative finds its mate Integration Kepler and the bungholes "Measuring lengths; or, The yawning regress" Methods of approximation Measuring areas under curves Method of rectangular strips The definite Indefinite On the inverse of the other "The outline of history and the descent of man: or, y=ex" Sickly curves and orchidaceous ones The snowflake Infinite perimeters and postage stamps Anti-snowflake Super-colossal pathological specimen?the curve that fills space The unbelievable crisscross EPILOGUE. MATHEMATICS AND THE IMAGINATION


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