74,99 zł

The Fundamental Theorems Of The Differential Calculus (Classic Reprint)

Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Calculus & mathematical analysis>Calculus

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Sklep: Gigant.pl

532,42 zł

Advanced Calculus Birkhauser Boston Inc

Książki / Literatura obcojęzyczna

In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus. He begins with a lucid discussion of differential forms and quickly moves to the fundamental theorems of calculus and Stokes theorem. The result is genuine mathematics, both in spirit and content, and an exciting choice for an honors or graduate course or indeed for any mathematician in need of a refreshingly informal and flexible reintroduction to the subject. For all these potential readers, the author has made the approach work in the best tradition of creative mathematics.§This affordable softcover reprint of the 1994 edition presents the diverse set of topics from which advanced calculus courses are created in beautiful unifying generalization. The author emphasizes the use of differential forms in linear algebra, implicit differentiation in higher dimensions using the calculus of differential forms, and the method of Lagrange multipliers in a general but easy-to-use formulation. There are copious exercises to help guide the reader in testing understanding. The chapters can be read in almost any order, including beginning with the final chapter that contains some of the more traditional topics of advanced calculus courses. In addition, it is ideal for a course on vector analysis from the differential forms point of view.§The professional mathematician will find here a delightful example of mathematical literature; the student fortunate enough to have gone through this book will have a firm grasp of the nature of modern mathematics and a solid framework to continue to more advance studies.§The most important feature is that it is fun it is fun to read the exercises, it is fun to read the comments printed in the margins, it is fun simply to pick a random spot in the book and begin reading. This is the way mathematics should be presented, with an excitement and liveliness that show why we are interested in the subject. § The American Mathematical Monthly (First Review) §An inviting, unusual, high-level introduction to vector calculus, based solidly on differential forms. Superb exposition: informal but sophisticated, down-to-earth but general, geometrically rigorous, entertaining but serious. Remarkable diverse applications, physical and mathematical. § The American Mathematical Monthly (1994) Based on the Second Edition §

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120,59 zł

Calculus Dover Publications Inc.

Książki / Literatura obcojęzyczna

1. Sequences2. Functions of a Single Variable3. Limit of a Function4. Differential Calculus for Functions of a Single Variable5. Fundamental Theorems of the Differential Calculus6. Applications of Differential Calculus7. The Differential8. The Indefinite Integral9. The Definite Integral10. Applications of the Definite Integral11. Infinite Series12. Various Problems Solutions, Hints, Answers. Index. List of Greek Letters.

Sklep: Libristo.pl

404,89 zł

Calculus: Concepts and Methods Cambridge University Press

Książki / Literatura obcojęzyczna

The pebbles used in ancient abacuses gave their name to the calculus, which today is a fundamental tool in business, economics, engineering and the sciences. This introductory book takes readers gently from single to multivariate calculus and simple differential and difference equations. Unusually the book offers a wide range of applications in business and economics, as well as more conventional scientific examples. Ideas from univariate calculus and linear algebra are covered as needed, often from a new perspective. They are reinforced in the two-dimensional case, which is studied in detail before generalisation to higher dimensions. Although there are no theorems or formal proofs, this is a serious book in which conceptual issues are explained carefully using numerous geometric devices and a wealth of worked examples, diagrams and exercises. Mathematica has been used to generate many beautiful and accurate, full-colour illustrations to help students visualise complex mathematical objects. This adds to the accessibility of the text, which will appeal to a wide audience among students of mathematics, economics and science.

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94,93 zł

Variational Principles of Mechanics Dover Publications

Książki / Literatura obcojęzyczna

Introduction 1. The variational approach to mechanics 2. The procedure of Euler and Lagrange 3. Hamilton's procedure 4. The calculus of variations 5. Comparison between the vectorial and the variational treatments of mechanics 6. Mathematical evaluation of the variational principles 7. Philosophical evaluation of the variational approach to mechanics I. The Basic Concepts of Analytical Mechanics 1. The Principal viewpoints of analytical mechanics 2. Generalized coordinates 3. The configuration space 4. Mapping of the space on itself 5. Kinetic energy and Riemannian geometry 6. Holonomic and non-holonomic mechanical systems 7. Work function and generalized force 8. Scleronomic and rheonomic systems. The law of the conservation of energy II. The Calculus of Variations 1. The general nature of extremum problems 2. The stationary value of a function 3. The second variation 4. Stationary value versus extremum value 5. Auxiliary conditions. The Lagrangian lambda-method 6. Non-holonomic auxiliary conditions 7. The stationary value of a definite integral 8. The fundamental processes of the calculus of variations 9. The commutative properties of the delta-process 10. The stationary value of a definite integral treated by the calculus of variations 11. The Euler-Lagrange differential equations for n degrees of freedom 12. Variation with auxiliary conditions 13. Non-holonomic conditions 14. Isoperimetric conditions 15. The calculus of variations and boundary conditions. The problem of the elastic bar III. The principle of virtual work 1. The principle of virtual work for reversible displacements 2. The equilibrium of a rigid body 3. Equivalence of two systems of forces 4. Equilibrium problems with auxiliary conditions 5. Physical interpretation of the Lagrangian multiplier method 6. Fourier's inequality IV. D'Alembert's principle 1. The force of inertia 2. The place of d'Alembert's principle in mechanics 3. The conservation of energy as a consequence of d'Alembert's principle 4. Apparent forces in an accelerated reference system. Einstein's equivalence hypothesis 5. Apparent forces in a rotating reference system 6. Dynamics of a rigid body. The motion of the centre of mass 7. Dynamics of a rigid body. Euler's equations 8. Gauss' principle of least restraint V. The Lagrangian equations of motion 1. Hamilton's principle 2. The Lagrangian equations of motion and their invariance relative to point transformations 3. The energy theorem as a consequence of Hamilton's principle 4. Kinosthenic or ignorable variables and their elimination 5. The forceless mechanics of Hertz 6. The time as kinosthenic variable; Jacobi's principle; the principle of least action 7. Jacobi's principle and Riemannian geometry 8. Auxiliary conditions; the physical significance of the Lagrangian lambda-factor 9. Non-holonomic auxiliary conditions and polygenic forces 10. Small vibrations about a state of equilibrium VI. The Canonical Equations of motion 1. Legendre's dual transformation 2. Legendre's transformation applied to the Lagrangian function 3. Transformation of the Lagrangian equations of motion 4. The canonical integral 5. The phase space and the space fluid 6. The energy theorem as a consequence of the canonical equations 7. Liouville's theorem 8. Integral invariants, Helmholtz' circulation theorem 9. The elimination of ignorable variables 10. The parametric form of the canonical equations VII. Canonical Transformations 1. Coordinate transformations as a method of solving mechanical problems 2. The Lagrangian point transformations 3. Mathieu's and Lie's transformations 4. The general canonical transformation 5. The bilinear differential form 6. The bracket expressions of Lagrange and Poisson 7. Infinitesimal canonical transformations 8. The motion of the phase fluid as a continuous succession of canonical transformations 9. Hamilton's principal function and the motion of the phase fluid VIII. The Partial differential equation of Hamilton-Jacobi 1. The importance of the generating function for the problem of motion 2. Jacobi's transformation theory 3. Solution of the partial differential equation by separation 4. Delaunay's treatment of separable periodic systems 5. The role of the partial differential equation in the theories of Hamilton and Jacobi 6. Construction of Hamilton's principal function with the help of Jacobi's complete solution 7. Geometrical solution of the partial differential equation. Hamilton's optico-mechanical analogy 8. The significance of Hamilton's partial differential equation in the theory of wave motion 9. The geometrization of dynamics. Non-Riemannian geometrics. The metrical significance of Hamilton's partial differential equation IX. Relativistic Mechanics 1. Historical Introduction 2. Relativistic kinematics 3. Minkowski's four-dimensional world 4. The Lorentz transformations 5. Mechanics of a particle 6. The Hamiltonian formulation of particle dynamics 7. The potential energy V 8. Relativistic formulation of Newton's scalar theory of gravitation 9. Motion of a charged particle 10. Geodesics of a four-dimensional world 11. The planetary orbits in Einstein's gravitational theory 12. The gravitational bending of light rays 13. The gravitational red-shirt of the spectral lines Bibliography X. Historical Survey XI. Mechanics of the Continua 1. The variation of volume integrals 2. Vector-analytic tools 3. Integral theorems 4. The conservation of mass 5. Hydrodynamics of ideal fluids 6. The hydrodynamic equations in Lagrangian formulation 7. Hydrostatics 8. The circulation theorem 9. Euler's form of the hydrodynamic equations 10. The conservation of energy 11. Elasticity. Mathematical tools 12. The strain tensor 13. The stress tensor 14. Small elastic vibrations 15. The Hamiltonization of variational problems 16. Young's modulus. Poisson's ratio 17. Elastic stability 18. Electromagnetism. Mathematical tools 19. The Maxwell equations 20. Noether's principle 21. Transformation of the coordinates 22. The symmetric energy-momentum tensor 23. The ten conservation laws 24. The dynamic law in field theoretical derivation Appendix I; Appendix II; Bibliography; Index

Sklep: Libristo.pl

120,89 zł

Variational Principles of Mechanics Dover Publications Inc.

Książki / Literatura obcojęzyczna

Introduction 1. The variational approach to mechanics 2. The procedure of Euler and Lagrange 3. Hamilton's procedure 4. The calculus of variations 5. Comparison between the vectorial and the variational treatments of mechanics 6. Mathematical evaluation of the variational principles 7. Philosophical evaluation of the variational approach to mechanicsI. The Basic Concepts of Analytical Mechanics 1. The Principal viewpoints of analytical mechanics 2. Generalized coordinates 3. The configuration space 4. Mapping of the space on itself 5. Kinetic energy and Riemannian geometry 6. Holonomic and non-holonomic mechanical systems 7. Work function and generalized force 8. Scleronomic and rheonomic systems. The law of the conservation of energyII. The Calculus of Variations 1. The general nature of extremum problems 2. The stationary value of a function 3. The second variation 4. Stationary value versus extremum value 5. Auxiliary conditions. The Lagrangian lambda-method 6. Non-holonomic auxiliary conditions 7. The stationary value of a definite integral 8. The fundamental processes of the calculus of variations 9. The commutative properties of the delta-process 10. The stationary value of a definite integral treated by the calculus of variations 11. The Euler-Lagrange differential equations for n degrees of freedom 12. Variation with auxiliary conditions 13. Non-holonomic conditions 14. Isoperimetric conditions 15. The calculus of variations and boundary conditions. The problem of the elastic barIII. The principle of virtual work 1. The principle of virtual work for reversible displacements 2. The equilibrium of a rigid body 3. Equivalence of two systems of forces 4. Equilibrium problems with auxiliary conditions 5. Physical interpretation of the Lagrangian multiplier method 6. Fourier's inequalityIV. D'Alembert's principle 1. The force of inertia 2. The place of d'Alembert's principle in mechanics 3. The conservation of energy as a consequence of d'Alembert's principle 4. Apparent forces in an accelerated reference system. Einstein's equivalence hypothesis 5. Apparent forces in a rotating reference system 6. Dynamics of a rigid body. The motion of the centre of mass 7. Dynamics of a rigid body. Euler's equations 8. Gauss' principle of least restraintV. The Lagrangian equations of motion 1. Hamilton's principle 2. The Lagrangian equations of motion and their invariance relative to point transformations 3. The energy theorem as a consequence of Hamilton's principle 4. Kinosthenic or ignorable variables and their elimination 5. The forceless mechanics of Hertz 6. The time as kinosthenic variable; Jacobi's principle; the principle of least action 7. Jacobi's principle and Riemannian geometry 8. Auxiliary conditions; the physical significance of the Lagrangian lambda-factor 9. Non-holonomic auxiliary conditions and polygenic forces 10. Small vibrations about a state of equilibriumVI. The Canonical Equations of motion 1. Legendre's dual transformation 2. Legendre's transformation applied to the Lagrangian function 3. Transformation of the Lagrangian equations of motion 4. The canonical integral 5. The phase space and the space fluid 6. The energy theorem as a consequence of the canonical equations 7. Liouville's theorem 8. Integral invariants, Helmholtz' circulation theorem 9. The elimination of ignorable variables 10. The parametric form of the canonical equationsVII. Canonical Transformations 1. Coordinate transformations as a method of solving mechanical problems 2. The Lagrangian point transformations 3. Mathieu's and Lie's transformations 4. The general canonical transformation 5. The bilinear differential form 6. The bracket expressions of Lagrange and Poisson 7. Infinitesimal canonical transformations 8. The motion of the phase fluid as a continuous succession of canonical transformations 9. Hamilton's principal function and the motion of the phase fluidVIII. The Partial differential equation of Hamilton-Jacobi 1. The importance of the generating function for the problem of motion 2. Jacobi's transformation theory 3. Solution of the partial differential equation by separation 4. Delaunay's treatment of separable periodic systems 5. The role of the partial differential equation in the theories of Hamilton and Jacobi 6. Construction of Hamilton's principal function with the help of Jacobi's complete solution 7. Geometrical solution of the partial differential equation. Hamilton's optico-mechanical analogy 8. The significance of Hamilton's partial differential equation in the theory of wave motion 9. The geometrization of dynamics. Non-Riemannian geometrics. The metrical significance of Hamilton's partial differential equationIX. Relativistic Mechanics 1. Historical Introduction 2. Relativistic kinematics 3. Minkowski's four-dimensional world 4. The Lorentz transformations 5. Mechanics of a particle 6. The Hamiltonian formulation of particle dynamics 7. The potential energy V 8. Relativistic formulation of Newton's scalar theory of gravitation 9. Motion of a charged particle 10. Geodesics of a four-dimensional world 11. The planetary orbits in Einstein's gravitational theory 12. The gravitational bending of light rays 13. The gravitational red-shirt of the spectral lines BibliographyX. Historical SurveyXI. Mechanics of the Continua 1. The variation of volume integrals 2. Vector-analytic tools 3. Integral theorems 4. The conservation of mass 5. Hydrodynamics of ideal fluids 6. The hydrodynamic equations in Lagrangian formulation 7. Hydrostatics 8. The circulation theorem 9. Euler's form of the hydrodynamic equations 10. The conservation of energy 11. Elasticity. Mathematical tools 12. The strain tensor 13. The stress tensor 14. Small elastic vibrations 15. The Hamiltonization of variational problems 16. Young's modulus. Poisson's ratio 17. Elastic stability 18. Electromagnetism. Mathematical tools 19. The Maxwell equations 20. Noether's principle 21. Transformation of the coordinates 22. The symmetric energy-momentum tensor 23. The ten conservation laws 24. The dynamic law in field theoretical derivation Appendix I; Appendix II; Bibliography; Index

Sklep: Libristo.pl

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