Muutke küpsiste eelistusi

Applied Analysis: Mathematics For Science, Technology, Engineering (Third Edition) [Kõva köide]

(Osaka Univ, Japan)
  • Formaat: Hardback, 688 pages
  • Ilmumisaeg: 14-Jun-2022
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811257353
  • ISBN-13: 9789811257353
Teised raamatud teemal:
Applied Analysis: Mathematics For Science, Technology, Engineering (Third Edition)Suurem pilt
  • Formaat: Hardback, 688 pages
  • Ilmumisaeg: 14-Jun-2022
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811257353
  • ISBN-13: 9789811257353
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9789811257353.html
Märksõnad:
"Provides a general introduction to applied analysis. Discusses developments in nonlinear science using fundamental ideas of applied mathematics, and describes tools in linear PDE theory"--

Updating his textbook on applied analysis after more than 10 years, Suzuki has added several fundamental materials of applied and theoretical sciences that scientists and engineers now need to know, as well as recent developments in pure and applied mathematics. The book is based on graduate and undergraduate courses and seminars that Suzuki has taught at several universities. His topics include mathematical modeling, the language of modern geometry, calculus of variations, infinite-dimension analysis, the random motion of particles, and real analysis in partial differential equations. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)

This Book Is To Be A New Edition Of Applied Analysis. Several Fundamental Materials Of Applied And Theoretical Sciences Are Added, Which Are Needed By The Current Society, As Well As Recent Developments In Pure And Applied Mathematics. New Materials In The Basic Level Are The Mathematical Modelling Using Odes In Applied Sciences, Elements In Riemann Geometry In Accordance With Tensor Analysis Used In Continuum Mechanics, Combining Engineering And Modern Mathematics, Detailed Description Of Optimization, And Real Analysis Used In The Recent Study Of Pdes. Those In The Advance Level Are The Integration Of Odes, Inverse Strum Liouville Problems, Interface Vanishing Of The Maxwell System, Method Of Gradient Inequality, Diffusion Geometry, Mathematical Oncology. Several Descriptions On The Analysis Of Smoluchowski-Poisson Equation In Two Space Dimension Are Corrected And Extended, To Ensure Quantized Blowup Mechanism Of This Model, Particularly, The Residual Vanishing Both In Blowup Solution In Finite Time With Possible Collision Of Sub-Collapses And Blowup Solutions In Infinite Time Without It.

Preface to the Third Edition v
Preface to the Second Edition vii
Preface to the First Edition ix
Chapter 1 Mathematical Modeling
1(50)
1.1 Mathematics for Modeling
1(11)
1.1.1 Differentiation
1(3)
1.1.2 Linear and Nonlinear Equations
4(4)
1.1.3 Exponential Function of Matrices
8(2)
1.1.4 Unique Solvability
10(2)
1.2 Models in Chemistry
12(10)
1.2.1 Self-Resolution
12(1)
1.2.2 Mass Action
13(3)
1.2.3 Michaelis Menten Reduction
16(2)
1.2.4 Polymerization
18(1)
1.2.5 Reaction Network
19(3)
1.3 Systems of Differential Equations
22(10)
1.3.1 Dynamical Systems
22(5)
1.3.2 Gradient Systems
27(3)
1.3.3 Hamilton Systems
30(2)
1.4 Models in Ecology
32(9)
1.4.1 Population
32(1)
1.4.2 Prey Predator Systems
33(3)
1.4.3 Competitive Systems
36(2)
1.4.4 Hamilton Structure of Ecological Models
38(3)
1.5 Models in Cell Biology
41(5)
1.5.1 Infection
41(2)
1.5.2 Invasion
43(2)
1.5.3 Immunity
45(1)
1.6 Models in Physiology
46(5)
1.6.1 Heart Beating
46(2)
1.6.2 Nerve Impulse Transmission
48(3)
Chapter 2 Field Formation
51(40)
2.1 Classical Mechanics
51(9)
2.1.1 Outer Product
51(3)
2.1.2 Particle Motion
54(6)
2.2 Basic Notions of Vector Analysis
60(17)
2.2.1 Gradient
60(5)
2.2.2 Divergence
65(6)
2.2.3 Rotation
71(4)
2.2.4 Material Derivatives
75(2)
2.3 Continuum Mechanics
77(14)
2.3.1 Fluid Motion
77(5)
2.3.2 Tensors
82(4)
2.3.3 Solid Deformation
86(2)
2.3.4 Viscous Fluids
88(3)
Chapter 3 Objects and Coordinates
91(34)
3.1 Curvature
91(14)
3.1.1 Surfaces
91(4)
3.1.2 Curves
95(5)
3.1.3 Curves on Surfaces
100(5)
3.2 Integral Formulae
105(20)
3.2.1 Integrations
105(2)
3.2.2 Integration on Surfaces
107(4)
3.2.3 Circulations
111(1)
3.3 Transformation of Coordinates
112(1)
3.3.1 Orthogonal Coordinates
112(5)
3.3.2 Curved Coordinates
117(2)
3.3.3 Co-variant Derivatives
119(6)
Chapter 4 Languages of Modern Geometry
125(38)
4.1 Differential Forms
125(11)
4.1.1 Differential Forms in R3
125(5)
4.1.2 Differential Forms in Rn
130(4)
4.1.3 Minkowski Spaces
134(2)
4.2 Notions of Metric
136(17)
4.2.1 Differential Forms on Surfaces
136(4)
4.2.2 Tangent and Co-tangent Spaces
140(3)
4.2.3 Ortho-normal Frames
143(4)
4.2.4 Connections
147(3)
4.2.5 Riemann Surfaces
150(3)
4.3 Riemann Manifolds
153(10)
4.3.1 Manifolds
153(4)
4.3.2 Vector Fields on Manifolds
157(2)
4.3.3 Riemann Metrics
159(4)
Chapter 5 Optimizations
163(58)
5.1 Extremals
163(17)
5.1.1 Local Maxima and Minima
163(2)
5.1.2 Gradient Method
165(1)
5.1.3 Newton Method
166(6)
5.1.4 Adjoint Gradient Method
172(4)
5.1.5 Optimization with Constraints
176(4)
5.2 Linear Programmings
180(13)
5.2.1 Method of Simplices
180(5)
5.2.2 Duality Theorem
185(4)
5.2.3 Matrix Games
189(4)
5.3 Convex Analysis
193(13)
5.3.1 Convex Functions
193(6)
5.3.2 Kuhn Tucker Duality
199(4)
5.3.3 Duality Theorem Revisited
203(3)
5.4 Notion of Graphs
206(5)
5.4.1 Graphs
206(2)
5.4.2 Connected Graphs
208(3)
5.5 Statistical Inferences
211(10)
5.5.1 Statistical Optimizations
211(2)
5.5.2 Statistical Optimization with Constraints
213(3)
5.5.3 Classifications of the Data
216(5)
Chapter 6 Calculus of Variation
221(42)
6.1 Isoperimetric Inequalities
221(8)
6.1.1 Analytic Proof
221(4)
6.1.2 Geometric Proof
225(4)
6.2 Indirect Methods
229(14)
6.2.1 Euler Equations
229(3)
6.2.2 Minimal Surfaces
232(3)
6.2.3 Analytic Mechanics
235(2)
6.2.4 Quantum Mechanics
237(6)
6.3 Direct Methods
243(11)
6.3.1 Vibrating Strings
243(2)
6.3.2 Minimizing Sequences
245(2)
6.3.3 Sobolev Spaces
247(3)
6.3.4 Lower Semi-Continuity
250(4)
6.4 Numerical Schemes
254(9)
6.4.1 Finite Difference Methods
254(1)
6.4.2 Finite Element Methods
255(2)
6.4.3 Error Analysis
257(6)
Chapter 7 Infinite-Dimensional Analysis
263(78)
7.1 Hilbert Spaces
263(8)
7.1.1 Bounded Linear Operators
263(2)
7.1.2 Representation Theorem of Riesz
265(4)
7.1.3 Complete Orthonormal Systems
269(2)
7.2 Fourier Analysis
271(19)
7.2.1 Historical Notes
271(3)
7.2.2 Completeness
274(5)
7.2.3 Uniform Convergences
279(3)
7.2.4 Pointwise Convergences
282(3)
7.2.5 Fourier Transformations
285(5)
7.3 Eigenvalue Problems
290(24)
7.3.1 Vibrating Membranes
290(6)
7.3.2 Gel'fand Triples
296(4)
7.3.3 Self-Adjoint Operators
300(2)
7.3.4 Symmetric Forms
302(3)
7.3.5 Compact Operators
305(2)
7.3.6 Eigenfunction Expansions
307(3)
7.3.7 Minimax Principles
310(2)
7.3.8 Hilbert Schmidt Operators
312(2)
7.4 Distributions
314(27)
7.4.1 Delta Functions
314(3)
7.4.2 Locally Convex Spaces
317(2)
7.4.3 Frechet Spaces
319(2)
7.4.4 Inductive Limits
321(3)
7.4.5 Bounded Sets
324(1)
7.4.6 Definitions and Examples
325(3)
7.4.7 Fundamental Properties
328(4)
7.4.8 Supports
332(2)
7.4.9 Convergences
334(2)
7.4.10 Fourier Transformations Revisited
336(5)
Chapter 8 Scattering
341(46)
8.1 Direct Theory
341(23)
8.1.1 Jost Solution
341(11)
8.1.2 5-Matrix
352(7)
8.1.3 GLM Equation
359(5)
8.2 Reverse Theory
364(23)
8.2.1 GLM Equation Continued
364(8)
8.2.2 Reconstruction
372(7)
8.2.3 Consistency
379(8)
Chapter 9 Random Motion of Particles
387(34)
9.1 Mean Field Limits
387(17)
9.1.1 Master Equation
387(5)
9.1.2 Einstein's Formula
392(3)
9.1.3 Local Information Model
395(2)
9.1.4 Smoluchowski Equation
397(6)
9.1.5 Multiscale Models
403(1)
9.2 Kinetic Models
404(17)
9.2.1 Transport Equation
404(3)
9.2.2 Boltzmann Equation
407(4)
9.2.3 Semiconductor Device Equation
411(4)
9.2.4 Drift Diffusion Model
415(6)
Chapter 10 Linear PDE
421(52)
10.1 Well-Posedness
421(6)
10.1.1 Heat Equations
421(2)
10.1.2 Uniqueness
423(2)
10.1.3 Existence
425(2)
10.2 Fundamental Solutions
427(10)
10.2.1 Cauchy Problems
427(3)
10.2.2 Gaussian Kernel
430(3)
10.2.3 Semigroups
433(4)
10.3 Laplace Equations
437(14)
10.3.1 Harmonic Functions
437(2)
10.3.2 Poisson Integrals
439(5)
10.3.3 Perron Solutions
444(3)
10.3.4 Boundary Regularities
447(2)
10.3.5 Green's Function
449(2)
10.4 Potentials
451(22)
10.4.1 Newton Potentials
451(6)
10.4.2 Layer Potentials
457(6)
10.4.3 Fredholm Theories
463(1)
10.4.4 Poisson Equations
464(2)
10.4.5 Schauder Estimates
466(7)
Chapter 11 Real Analysis in PDE
473(32)
11.1 Holder Regularities
473(14)
11.1.1 Dirichlet Principles
473(3)
11.1.2 Moser's Iteration Schemes
476(4)
11.1.3 Local Minimum Principles
480(7)
11.2 Hardy Spaces and BMO
487(18)
11.2.1 John Nirenberg Inequality
487(9)
11.2.2 Maximal Functions
496(3)
11.2.3 Div Rot Lemma
499(2)
11.2.4 Estimates of the Jacobian
501(2)
11.2.5 A Harmonic Map
503(2)
Chapter 12 Nonlinear PDE
505(86)
12.1 Perturbations
505(13)
12.1.1 Duhamel Principles
505(2)
12.1.2 Semilinear Heat Equations
507(4)
12.1.3 Global Existence
511(4)
12.1.4 Blowup of the Solution
515(3)
12.2 Energies
518(23)
12.2.1 Lyapunov Functions
518(5)
12.2.2 Global-in-Time Solutions
523(7)
12.2.3 Unbounded Solutions
530(7)
12.2.4 Stable and Unstable Sets
537(4)
12.3 Rescaling
541(19)
12.3.1 ODE Parts
541(4)
12.3.2 Variational Structure
545(3)
12.3.3 Scaling Invariance
548(5)
12.3.4 Forward Self-Similar Transformations
553(4)
12.3.5 Backward Self-Similar Transformations
557(3)
12.4 Chemotaxis
560(31)
12.4.1 Cellular Slime Molds
560(1)
12.4.2 Symplified Systems
561(2)
12.4.3 Free Energy
563(4)
12.4.4 Smoluchowski Poisson Equation
567(5)
12.4.5 Quantized Blowup Mechanism
572(5)
12.4.6 Mass Quantization
577(10)
12.4.7 Recursive Hierarchy
587(4)
Appendix A Catalogue of Mathematical Analysis
591(22)
A.1 Basic Analysis
591(4)
A.2 Topological Spaces
595(3)
A.3 Complex Analysis
598(5)
A.4 Real Analysis
603(6)
A.5 Abstract Analysis
609(4)
Appendix B An Elliptic-Parabolic System
613(20)
B.1 The System
613(2)
B.2 Linearized System
615(7)
B.3 The Mapping T
622(9)
B.4 Unique Solvability
631(2)
Appendix C Commentaries
633(18)
C.1 Systems of ODEs
633(3)
C.2 Sturm Liouville Problems
636(3)
C.3 Elliptic Equations
639(2)
C.4 Parabolic Equations
641(1)
C.5 Diffusion Geometry
642(3)
C.6 Self-Interacting Particles
645(1)
C.7 Models in Theoretical Biology
646(5)
C.8 Maxwell Systems
651(1)
Bibliography 651(10)
Index 661