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Analytical Mechanics for Relativity and Quantum Mechanics 2nd Revised edition [Pehme köide]

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(Emeritus Professor, Department of Physics, San Francisco State University)
  • Formaat: Paperback / softback, 652 pages, kõrgus x laius x paksus: 244x171x34 mm, kaal: 1026 g
  • Sari: Oxford Graduate Texts
  • Ilmumisaeg: 03-Mar-2016
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198766807
  • ISBN-13: 9780198766803
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Analytical Mechanics for Relativity and Quantum Mechanics 2nd Revised editionSuurem pilt
  • Formaat: Paperback / softback, 652 pages, kõrgus x laius x paksus: 244x171x34 mm, kaal: 1026 g
  • Sari: Oxford Graduate Texts
  • Ilmumisaeg: 03-Mar-2016
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198766807
  • ISBN-13: 9780198766803
Teised raamatud teemal:
Teised raamatud sellest sooduspakkumisest: Kevadine sooduspakkumine - kuni 31. maini üle miljoni raamatu kuni 25% soodsamalt
Püsilink: https://www.kriso.ee/db/9780198766803.html
Märksõnad:
An innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum mechanics: Part I is an introduction to analytical mechanics, suitable for a graduate or advanced undergraduate course. Part II presents material designed principally for graduate students. The appendices in Part III summarize the mathematical methods used in the text. The book integrates relativity into the teaching of classical mechanics. Part II introduces special relativity and covariant mechanics. It develops extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics, including an extended definition of canonical transformation that both simplifies the theory and no longer excludes the Lorentz transformation.

The book assists students who study classical mechanics as a preparation for quantum mechanics. Analytical mechanics is presented using methods - such as linear vector operators and dyadics - that familiarize the student with similar operator techniques in quantum theory and the dyadic Dirac notation. Comparisons to quantum mechanics appear throughout the text. For example, the chapter on Hamilton-Jacobi theory includes discussions of the closely related Bohm hidden variable model and Feynman path integral method. The chapter on angle-action variables concludes with a section on the old quantum theory. Several of the fundamental problems in physics - the development of quantum information technology, and the problem of quantizing the gravitational field, to name two - require a rethinking of the quantum-classical connection. Graduate students preparing for research careers will find a graduate mechanics course based on this book to be an essential bridge between their undergraduate training and advanced study in analytical mechanics, relativity, and quantum mechanics.

New to the Second Edition: Part I contains new chapters on Central Force Motion (Chapter 11) and Scattering (Chapter 12), and new material on time-independent canonical transformations. Part II contains a new chapter (Chapter 22) on Angle-Action Variables. These additions allow a more flexible use of the text. Part I is now a self-contained, introductory analytical mechanics course. The instructor can then select a range of topics from Part II appropriate to the interests of more advanced students.

Arvustused

Review from previous edition The author deserves to be congratulated on the production of what soon will establish itself as a well-respected and useful book which I am pleased to have on my shelf. In short, it would be difficult to conceive of any initial course of instruction and study on the subject which would not benefit from use of this well-planned and conceived and refreshing presentation. * Current Engineering Practice * An excellent book on analytical mechanics, which offers both graduate and undergradute students a stimulating read. * Contemporary Physics *

Dedication v
Prefaces vii
Acknowledgments xi
Part I Introduction: The Traditional Theory
1 Basic Dynamics of Point Particles and Collections
3(21)
1.1 Newton's Space and Time
3(2)
1.2 Single Point Particle
5(1)
1.3 Collective Variables
6(1)
1.4 The Law of Momentum for Collections
7(1)
1.5 The Law of Angular Momentum for Collections
8(1)
1.6 "Derivations" of the Axioms
9(1)
1.7 The Work-Energy Theorem for Collections
10(1)
1.8 Potential and Total Energy for Collections
10(1)
1.9 The Center of Mass
11(2)
1.10 Center of Mass and Momentum
13(1)
1.11 Center of Mass and Angular Momentum
13(1)
1.12 Center of Mass and Torque
14(1)
1.13 Change of Angular Momentum
14(1)
1.14 Center of Mass and the Work-Energy Theorems
15(1)
1.15 Center of Mass as a Point Particle
16(1)
1.16 Special Results for Rigid Bodies
17(1)
1.17 Exercises
18(6)
2 Introduction to Lagrangian Mechanics
24(22)
2.1 Configuration Space
24(2)
2.2 Newton's Second Law in Lagrangian Form
26(1)
2.3 A Simple Example
27(1)
2.4 Arbitrary Generalized Coordinates
27(1)
2.5 Generalized Velocities in the q-System
28(1)
2.6 Generalized Forces in the q-System
29(1)
2.7 The Lagrangian Expressed in the q-System
30(1)
2.8 Two Important Identities
31(1)
2.9 Invariance of the Lagrange Equations
31(2)
2.10 Relation Between Any Two Systems
33(1)
2.11 More of the Simple Example
34(1)
2.12 Generalized Momenta in the q-System
34(1)
2.13 Ignorable Coordinates
35(1)
2.14 Some Remarks About Units
35(1)
2.15 The Generalized Energy Function
36(1)
2.16 The Generalized Energy and the Total Energy
37(1)
2.17 Velocity Dependent Potentials
38(3)
2.18 Exercises
41(5)
3 Lagrangian Theory of Constraints
46(24)
3.1 Constraints Defined
46(2)
3.2 Virtual Displacement
t47
3.3 Virtual Work
48(1)
3.4 Form of the Forces of Constraint
49(3)
3.5 General Lagrange Equations with Constraints
52(1)
3.6 An Alternate Notation for Holonomic Constraints
53(1)
3.7 Example of the General Method
53(1)
3.8 Reduction of Degrees of Freedom
54(2)
3.9 Example of a Reduction
56(2)
3.10 Example of a Simpler Reduction Method
58(1)
3.11 Recovery of the Forces of Constraint
59(1)
3.12 Example of a Recovery
60(1)
3.13 Generalized Energy Theorem with Constraints
61(1)
3.14 Tractable Non-Holonomic Constraints
62(2)
3.15 Exercises
64(6)
4 Introduction to Hamiltonian Mechanics
70(22)
4.1 Phase Space
70(3)
4.2 Hamilton Equations
73(2)
4.3 An Example of the Hamilton Equations
75(1)
4.4 Non-Potential and Constraint Forces
76(1)
4.5 Reduced Hamiltonian
76(2)
4.6 Poisson Brackets
78(2)
4.7 From Lagrangian to Hamiltonian Mechanics
80(1)
4.8 Canonical Transformations
80(2)
4.9 Generating Functions
82(2)
4.10 The Schroedinger Equation
84(1)
4.11 The Ehrenfest Theorem
85(1)
4.12 The Virial Theorem
86(1)
4.13 Exercises
87(5)
5 The Calculus of Variations
92(27)
5.1 Paths in an N -Dimensional Space
93(1)
5.2 Variations of Coordinates
94(1)
5.3 Variations of Functions
95(1)
5.4 Variation of a Line Integral
96(2)
5.5 Finding Extremum Paths
98(1)
5.6 Example of an Extremum Path Calculation
99(2)
5.7 Invariance and Homogeneity
101(3)
5.8 The Brachistochrone Problem
104(1)
5.9 Calculus of Variations with Constraints
105(3)
5.10 An Example with Constraints
108(1)
5.11 Reduction of Degrees of Freedom
109(1)
5.12 Example of a Reduction
110(1)
5.13 Example of a Better Reduction
111(1)
5.14 The Coordinate Parametric Method
111(3)
5.15 Comparison of the Methods
114(1)
5.16 Exercises
115(4)
6 Hamilton's Principle
119(6)
6.1 Hamilton's Principle in Lagrangian Form
119(1)
6.2 Hamilton's Principle with Constraints
120(1)
6.3 Comments on Hamilton's Principle
121(1)
6.4 Phase-Space Hamilton's Principle
122(2)
6.5 Exercises
124(1)
7 Linear Operators and Dyadics
125(27)
7.1 Definition of Operators
125(2)
7.2 Operators and Matrices
127(2)
7.3 Addition and Multiplication
129(1)
7.4 Determinant, Trace, and Inverse
129(2)
7.5 Special Operators
131(1)
7.6 Dyadics
132(2)
7.7 Resolution of Unity
134(1)
7.8 Operators, Components, Matrices, and Dyadics
135(1)
7.9 Complex Vectors and Operators
136(1)
7.10 Real and Complex Inner Products
137(1)
7.11 Eigenvectors and Eigenvalues
138(1)
7.12 Eigenvectors of Real Symmetric Operator
139(1)
7.13 Eigenvectors of Real Anti-Symmetric Operator
139(2)
7.14 Normal Operators
141(1)
7.15 Determinant and Trace of Normal Operator
142(1)
7.16 Eigen-Dyadic Expansion of Normal Operator
143(1)
7.17 Functions of Normal Operators
144(2)
7.18 The Exponential Function
146(1)
7.19 The Dirac Notation
147(1)
7.20 Exercises
148(4)
8 Kinematics of Rotation
152(48)
8.1 Characterization of Rigid Bodies
152(1)
8.2 The Center of Mass of a Rigid Body
153(2)
8.3 General Definition of Rotation Operator
155(2)
8.4 Rotation Matrices
157(1)
8.5 Some Properties of Rotation Operators
157(1)
8.6 Proper and Improper Rotation Operators
158(1)
8.7 The Rotation Group
159(2)
8.8 Kinematics of a Rigid Body
161(1)
8.9 Rotation Operators and Rigid Bodies
162(1)
8.10 Differentiation of a Rotation Operator
163(3)
8.11 Meaning of the Angular Velocity Vector
166(1)
8.12 Velocities of the Masses of a Rigid Body
167(1)
8.13 Savio's Theorem
168(1)
8.14 Infinitesimal Rotation
169(1)
8.15 Addition of Angular Velocities
170(1)
8.16 Fundamental Generators of Rotations
171(2)
8.17 Rotation with a Fixed Axis
173(1)
8.18 Expansion of Fixed-Axis Rotation
174(3)
8.19 Eigenvectors of the Fixed-Axis Rotation Operator
177(1)
8.20 The Euler Theorem
177(3)
8.21 Rotation of Operators
180(1)
8.22 Rotation of the Fundamental Generators
180(1)
8.23 Rotation of a Fixed-Axis Rotation
181(1)
8.24 Parameterization of Rotation Operators
182(1)
8.25 Differentiation of Parameterized Operator
182(2)
8.26 Euler Angles
184(2)
8.27 Fixed-Axis Rotation from Euler Angles
186(1)
8.28 Time Derivative of a Product
187(1)
8.29 Angular Velocity from Euler Angles
188(1)
8.30 Active and Passive Rotations
189(1)
8.31 Passive Transformation of Vector Components
190(1)
8.32 Passive Transformation of Matrix Elements
191(1)
8.33 The Body Derivative
192(1)
8.34 Passive Rotations and Rigid Bodies
193(1)
8.35 Passive Use of Euler Angles
194(2)
8.36 Exercises
196(4)
9 Rotational Dynamics
200(42)
9.1 Basic Facts of Rigid-Body Motion
200(1)
9.2 The Inertia Operator and the Spin
201(1)
9.3 The Inertia Dyadic
202(1)
9.4 Kinetic Energy of a Rigid Body
203(1)
9.5 Meaning of the Inertia Operator
203(1)
9.6 Principal Axes
204(2)
9.7 Guessing the Principal Axes
206(2)
9.8 Time Evolution of the Spin
208(1)
9.9 Torque-Free Motion of a Symmetric Body
209(4)
9.10 Euler Angles of the Torque-Free Motion
213(1)
9.11 Body with One Point Fixed
214(3)
9.12 Preserving the Principal Axes
217(1)
9.13 Time Evolution with One Point Fixed
218(1)
9.14 Body with One Point Fixed, Alternate Derivation
218(1)
9.15 Work-Energy Theorems
219(1)
9.16 Rotation with a Fixed Axis
220(2)
9.17 The Symmetric Top with One Point Fixed
222(4)
9.18 The Initially Clamped Symmetric Top
226(1)
9.19 Approximate Treatment of the Symmetric Top
227(1)
9.20 Inertial Forces
228(3)
9.21 Laboratory on the Surface of the Earth
231(2)
9.22 Coriolis Force Calculations
233(1)
9.23 The Magnetic - Coriolis Analogy
234(1)
9.24 Exercises
235(7)
10 Small Vibrations About Equilibrium
242(18)
10.1 Equilibrium Defined
242(1)
10.2 Finding Equilibrium Points
243(1)
10.3 Small Coordinates
244(1)
10.4 Normal Modes
245(1)
10.5 Generalized Eigenvalue Problem
246(1)
10.6 Stability
247(1)
10.7 Initial Conditions
248(1)
10.8 The Energy of Small Vibrations
249(1)
10.9 Single Mode Excitations
249(1)
10.10 A Simple Example
250(5)
10.11 Zero-Frequency Modes
255(1)
10.12 Exercises
256(4)
11 Central Force Motion
260(21)
11.1 Formulation of the Problem
260(2)
11.2 Kepler's Law of Areas
262(1)
11.3 Orbital Motion
263(1)
11.4 Inverse Square Force: the Kepler Problem
264(2)
11.5 General Features of the Motion
266(1)
11.6 Details of the Kepler Orbits
267(4)
11.7 Kepler's Third Law
271(1)
11.8 The Eccentricity Vector
272(3)
11.9 Periodic Orbits
275(1)
11.10 The Isotropic Harmonic Oscillator
276(3)
11.11 Exercises
279(2)
12 Scattering
281(10)
12.1 Cross Sections
281(1)
12.2 Differential Cross Sections
282(2)
12.3 Scattering by Hard Spheres
284(1)
12.4 Scattering by an Inverse-Square Central Force
285(2)
12.5 Scattering by General Central Forces
287(1)
12.6 Exercises
287(4)
Part II Mechanics With Time As A Coordinate
13 Lagrangian Mechanics with Time as a Coordinate
291(17)
13.1 Time as a Coordinate
291(1)
13.2 A Change of Notation
292(1)
13.3 Extended Lagrangian
293(1)
13.4 Extended Momenta
294(1)
13.5 Extended Lagrange Equations
295(2)
13.6 A Simple Example
297(1)
13.7 Invariance Under Change of Parameter
298(1)
13.8 Change of Generalized Coordinates
299(2)
13.9 Redundancy of the Extended Lagrange Equations
301(1)
13.10 Forces of Constraint
301(3)
13.11 Reduced Lagrangians with Time as a Coordinate
304(2)
13.12 Exercises
306(2)
14 Hamiltonian Mechanics with Time as a Coordinate
308(19)
14.1 Extended Phase Space
308(1)
14.2 Dependency Relation
308(1)
14.3 Only One Dependency Relation
309(2)
14.4 From Traditional to Extended Hamiltonian Mechanics
311(2)
14.5 Equivalence to Traditional Hamilton Equations
313(1)
14.6 Example of Extended Hamilton Equations
314(1)
14.7 Equivalent Extended Hamiltonians
314(1)
14.8 Alternate Hamiltonians
315(2)
14.9 Alternate Traditional Hamiltonians
317(1)
14.10 Not a Legendre Transformation
318(1)
14.11 Dirac's Theory of Phase-Space Constraints
319(2)
14.12 Poisson Brackets with Time as a Coordinate
321(2)
14.13 Poisson Brackets and Quantum Commutators
323(1)
14.14 Exercises
324(3)
15 Hamilton's Principle and Noether's Theorem
327(8)
15.1 Extended Hamilton's Principle
327(2)
15.2 Noether's Theorem
329(1)
15.3 Examples of Noether's Theorem
330(2)
15.4 Hamilton's Principle in an Extended Phase Space
332(1)
15.5 Exercises
333(2)
16 Relativity and Spacetime
335(29)
16.1 Galilean Relativity
335(2)
16.2 Conflict with the Aether
337(1)
16.3 Einsteinian Relativity
338(1)
16.4 What Is a Coordinate System?
339(1)
16.5 A Survey of Spacetime
340(12)
16.6 The Lorentz Transformation
352(6)
16.7 The Principle of Relativity
358(1)
16.8 Lorentzian Relativity
359(1)
16.9 Mechanism and Relativity
360(2)
16.10 Exercises
362(2)
17 Fourvectors and Operators
364(31)
17.1 Fourvectors
364(2)
17.2 Inner Product
366(2)
17.3 Choice of Metric
368(1)
17.4 Relativistic Interval
368(1)
17.5 Spacetime Diagram
369(2)
17.6 General Fourvectors
371(1)
17.7 Construction of New Fourvectors
372(1)
17.8 Covariant and Contravariant Components
373(2)
17.9 General Lorentz Transformations
375(2)
17.10 Transformation of Components
377(1)
17.11 Examples of Lorentz Transformations
378(3)
17.12 Gradient Fourvector
381(1)
17.13 Manifest Covariance
382(1)
17.14 Formal Covariance
382(1)
17.15 The Lorentz Group
383(1)
17.16 Proper Lorentz Transformations and the Little Group
384(1)
17.17 Parameterization
385(1)
17.18 Fourvector Operators
386(1)
17.19 Fourvector Dyadics
387(1)
17.20 Wedge Products
388(1)
17.21 Scalar, Fourvector, and Operator Fields
389(1)
17.22 Manifestly Covariant Form of Maxwell's Equations
390(3)
17.23 Exercises
393(2)
18 Relativistic Mechanics
395(34)
18.1 Modification of Newton's Laws
395(1)
18.2 The Momentum Fourvector
396(1)
18.3 Fourvector Form of Newton's Second Law
397(1)
18.4 Conservation of Fourvector Momentum
398(1)
18.5 Particles of Zero Mass
399(1)
18.6 Traditional Lagrangian
400(1)
18.7 Traditional Hamiltonian
401(1)
18.8 Invariant Lagrangian
402(1)
18.9 Manifestly Covariant Lagrange Equations
403(1)
18.10 Momentum Fourvectors and Canonical Momenta
404(1)
18.11 Extended Hamiltonian
405(1)
18.12 Invariant Hamiltonian
405(1)
18.13 Manifestly Covariant Hamilton Equations
406(1)
18.14 The Klein-Gordon Equation
407(2)
18.15 The Dirac Equation
409(1)
18.16 The Manifestly Covariant N-Body Problem
410(7)
18.17 Covariant Serret-Frenet Theory
417(2)
18.18 Fermi-Walker Transport
419(2)
18.19 Example of Fermi-Walker Transport
421(2)
18.20 Exercises
423(6)
19 Canonical Transformations
429(22)
19.1 Definition of Canonical Transformations
429(1)
19.2 Example of a Canonical Transformation
430(1)
19.3 Symplectic Coordinates
431(3)
19.4 Symplectic Matrix
434(1)
19.5 Standard Equations in Symplectic Form
435(1)
19.6 Poisson Bracket Condition
436(1)
19.7 Inversion of Canonical Transformations
437(1)
19.8 Direct Condition
438(1)
19.9 Lagrange Bracket Condition
439(1)
19.10 The Canonical Group
440(2)
19.11 Form Invariance of Poisson Brackets
442(1)
19.12 Form Invariance of the Hamilton Equations
443(2)
19.13 Traditional Canonical Transformations
445(3)
19.14 Exercises
448(3)
20 Generating Functions
451(26)
20.1 Proto-Generating Functions
451(2)
20.2 Generating Functions of the F1 Type
453(1)
20.3 Generating Functions of the F2 Type
454(2)
20.4 Examples of Generating Functions
456(1)
20.5 Other Simple Generating Functions
457(1)
20.6 Mixed Generating Functions
458(3)
20.7 Example of a Mixed Generating Function
461(1)
20.8 Finding Simple Generating Functions
461(2)
20.9 Finding Mixed Generating Functions
463(1)
20.10 Finding Mixed Generating Functions-An Example
464(1)
20.11 Traditional Generating Functions
465(2)
20.12 Standard Form of Extended Hamiltonian Recovered
467(1)
20.13 Differential Canonical Transformations
468(1)
20.14 Active Canonical Transformations
469(1)
20.15 Phase-Space Analog of Noether Theorem
470(1)
20.16 Liouville Theorem
471(1)
20.17 Exercises
472(5)
21 Hamilton-Jacobi Theory
477(32)
21.1 Definition of the Action
477(1)
21.2 Momenta from the S1 Action Function
478(2)
21.3 The S2 Action Function
480(1)
21.4 Example of S1 and S2 Action Functions
481(1)
21.5 The Hamilton-Jacobi Equation
482(1)
21.6 Hamilton's Characteristic Equations
483(3)
21.7 Complete Integrals
486(1)
21.8 Complete Integrals and System Motion
487(3)
21.9 Additive Separation of Variables
490(1)
21.10 General Integrals
491(5)
21.11 Time Independent Hamiltonian
496(2)
21.12 Mono-Energetic Complete Integrals
498(1)
21.13 The Optical Analogy
498(2)
21.14 The Relativistic Hamilton-Jacobi Equation
500(1)
21.15 Schroedinger and Hamilton-Jacobi Equations
500(1)
21.16 The Quantum Cauchy Problem
501(1)
21.17 The Bohm Hidden Variable Model
502(2)
21.18 Feynman Path-Integral Technique
504(1)
21.19 Quantum and Classical Mechanics
505(1)
21.20 Exercises
506(3)
22 Angle-Action Variables
509(20)
22.1 Definition of the Action Variables
509(1)
22.2 Canonical Transformation to Angle-Action Variables
510(2)
22.3 Multiply Periodic Motion
512(2)
22.4 Harmonic Oscillator
514(2)
22.5 Central Force Motion
516(1)
22.6 The Plane Kepler System
517(2)
22.7 Transforming to Plane Delaunay Variables
519(1)
22.8 The Bohr Model
520(2)
22.9 The Old Quantum Theory
522(1)
22.10 Inclined Orbits
523(2)
22.11 Old and New Quantum Theories
525(1)
22.12 Exercises
526(3)
Part III Mathematical Appendices
A Vector Fundamentals
529(14)
A.1 Properties of Vectors
529(1)
A.2 Dot Product
529(1)
A.3 Cross Product
530(1)
A.4 Linearity
530(1)
A.5 Cartesian Basis
531(1)
A.6 The Position Vector
532(1)
A.7 Fields
533(1)
A.8 Polar Coordinates
533(2)
A.9 The Algebra of Sums
535(2)
A.10 Miscellaneous Vector Formulae
537(1)
A.11 Gradient Vector Operator
538(1)
A.12 The Serret-Frenet Formulae
539(4)
B Matrices and Determinants
543(25)
B.1 Definition of Matrices
543(1)
B.2 Transposed Matrix
543(1)
B.3 Column Matrices and Column Vectors
543(1)
B.4 Square, Symmetric, and Hermitian Matrices
544(1)
B.5 Algebra of Matrices: Addition
545(1)
B.6 Algebra of Matrices: Multiplication
546(1)
B.7 Diagonal and Unit Matrices
547(1)
B.8 Trace of a Square Matrix
548(1)
B.9 Differentiation of Matrices
548(1)
B.10 Determinants of Square Matrices
548(1)
B.11 Properties of Determinants
549(1)
B.12 Cofactors
550(1)
B.13 Expansion of a Determinant by Cofactors
550(1)
B.14 Inverses of Nonsingular Matrices
551(1)
B.15 Partitioned Matrices
552(1)
B.16 Cramer's Rule
553(1)
B.17 Minors and Rank
554(1)
B.18 Linear Independence
554(1)
B.19 Homogeneous Linear Equations
555(1)
B.20 Inner Products of Column Vectors
556(1)
B.21 Complex Inner Products
557(1)
B.22 Orthogonal and Unitary Matrices
557(1)
B.23 Eigenvalues and Eigenvectors of Matrices
558(1)
B.24 Eigenvectors of Real Symmetric Matrix
559(3)
B.25 Eigenvectors of Complex Hermitian Matrix
562(1)
B.26 Normal Matrices
562(1)
B.27 Properties of Normal Matrices
563(3)
B.28 Functions of Normal Matrices
566(2)
C Eigenvalue Problem with General Metric
568(6)
C.1 Positive-Definite Matrices
568(1)
C.2 Generalization of the Real Inner Product
569(1)
C.3 The Generalized Eigenvalue Problem
570(1)
C.4 Finding Eigenvectors in the Generalized Problem
571(1)
C.5 Uses of the Generalized Eigenvectors
572(2)
D The Calculus of Many Variables
574(33)
D.1 Basic Properties of Functions
574(1)
D.2 Regions of Definition of Functions
574(1)
D.3 Continuity of Functions
574(1)
D.4 Compound Functions
575(1)
D.5 The Same Function in Different Coordinates
575(1)
D.6 Partial Derivatives
576(1)
D.7 Continuously Differentiable Functions
577(1)
D.8 Order of Differentiation
577(1)
D.9 Chain Rule
577(1)
D.10 Mean Values
577(1)
D.11 Orders of Smallness
578(1)
D.12 Differentials
578(1)
D.13 Differential of a Function of Several Variables
579(1)
D.14 Differentials and the Chain Rule
580(1)
D.15 Differentials of Second and Higher Orders
580(1)
D.16 Taylor Series
581(1)
D.17 Higher-Order Differential as a Difference
581(1)
D.18 Differential Expressions
582(1)
D.19 Line Integral of a Differential Expression
583(1)
D.20 Perfect Differentials
584(2)
D.21 Perfect Differential and Path Independence
586(1)
D.22 Jacobians
587(2)
D.23 Global Inverse Function Theorem
589(3)
D.24 Local Inverse Function Theorem
592(1)
D.25 Derivatives of the Inverse Functions
593(1)
D.26 Implicit Function Theorem
594(1)
D.27 Derivatives of Implicit Functions
594(1)
D.28 Functional Independence
595(1)
D.29 Dependency Relations
596(1)
D.30 Legendre Transformations
596(1)
D.31 Homogeneous Functions
597(1)
D.32 Derivatives of Homogeneous Functions
598(1)
D.33 Stationary Points
599(1)
D.34 Lagrange Multipliers
599(2)
D.35 Geometry of the Lagrange Multiplier Theorem
601(1)
D.36 Coupled Differential Equations
602(3)
D.37 Surfaces and Envelopes
605(2)
E Geometry of Phase Space
607(12)
E.1 Abstract Vector Space
607(2)
E.2 Subspaces
609(1)
E.3 Linear Operators
610(1)
E.4 Vectors in Phase Space
611(1)
E.5 Canonical Transformations in Phase Space
612(1)
E.6 Orthogonal Subspaces
613(1)
E.7 A Special Canonical Transformation
614(1)
E.8 Special Self-Orthogonal Subspaces
615(1)
E.9 Arnold's Theorem
616(1)
E.10 Existence of a Mixed Generating Function
617(2)
References 619(3)
Index 622
Oliver Davis Johns is Professor of Physics Emeritus at San Francisco State University.