ALBERT

Note: Contents 1. Introduction 1.1 Historical Background 1.2 Some Examples of Spectral Methods 1.2.1 A Fourier Galerkin Method for the Wave Equation 1.2.2 A Chebyshev Collocation Method for the Heat Equation 1.2.3 A Legendre Galerkin with Numerical Integration (G-NI) Method for the Advection-Diffusion-Reaction Equation 1.2.4 A Legendre Tau Method for the Poisson Equation 1.2.5 Basic Aspects of Galerkin, Collocation, G-NI and Tau Methods 1.3 Three-Dimensional Applications in Fluids: A Look Ahead 2. Polynomial Approximation 2.1 The Fourier System 2.1.1 The Continuous Fourier Expansion 2.1.2 The Discrete Fourier Expansion 2.1.3 Differentiation 2.1.4 The Gibbs Phenomenon 2.2 Orthogonal Polynomials in (−1, 1) 2.2.1 Sturm-Liouville Problems 2.2.2 Orthogonal Systems of Polynomials 2.2.3 Gauss-Type Quadratures and Discrete Polynomial Transforms 2.3 Legendre Polynomials 2.3.1 Basic Formulas 2.3.2 Differentiation 2.3.3 Orthogonality, Diagonalization and Localization 2.4 Chebyshev Polynomials 2.4.1 Basic Formulas 2.4.2 Differentiation 2.5 Jacobi Polynomials 2.6 Approximation in Unbounded Domains 2.6.1 Laguerre Polynomials and Laguerre Functions 2.6.2 Hermite Polynomials and Hermite Functions 2.7 Mappings for Unbounded Domains 2.7.1 Semi-Infinite Intervals 2.7.2 The Real Line 2.8 Tensor-Product Expansions 2.8.1 Multidimensional Mapping 2.9 Expansions on Triangles and Related Domains 2.9.1 Collapsed Coordinates and Warped Tensor-Product Expansions 2.9.2 Non-Tensor-Product Expansions 2.9.3 Mappings 3. Basic Approaches to Constructing Spectral Methods 3.1 Burgers Equation 3.2 Strong and Weak Formulations of Differential Equations 3.3 Spectral Approximation of the Burgers Equation 3.3.1 Fourier Galerkin 3.3.2 Fourier Collocation 3.3.3 Chebyshev Tau 3.3.4 Chebyshev Collocation 3.3.5 Legendre G-NI 3.4 Convolution Sums 3.4.1 Transform Methods and Pseudospectral Methods 3.4.2 Aliasing Removal by Padding or Truncation 3.4.3 Aliasing Removal by Phase Shifts 3.4.4 Aliasing Removal for Orthogonal Polynomials 3.5 Relation Between Collocation, G-NI and Pseudospectral Methods 3.6 Conservation Forms 3.7 Scalar Hyperbolic Problems 3.7.1 Enforcement of Boundary Conditions 3.7.2 Numerical Examples 3.8 Matrix Construction for Galerkin and G-NI Methods 3.8.1 Matrix Elements 3.8.2 An Example of Algebraic Equivalence between G-NI and Collocation Methods 3.9 Polar Coordinates 3.10 Aliasing Effects 4. Algebraic Systems and Solution Techniques 4.1 Ad-hoc Direct Methods 4.1.1 Fourier Approximations 4.1.2 Chebyshev Tau Approximations 4.1.3 Galerkin Approximations 4.1.4 Schur Decomposition and Matrix Diagonalization 4.2 Direct Methods 4.2.1 Tensor Products of Matrices 4.2.2 Multidimensional Stiffness and Mass Matrices 4.2.3 Gaussian Elimination Techniques 4.3 Eigen-Analysis of Spectral Derivative Matrices 4.3.1 Second-Derivative Matrices 4.3.2 First-Derivative Matrices 4.3.3 Advection-Diffusion Matrices 4.4 Preconditioning 4.4.1 Fundamentals of Iterative Methods for Spectral Discretizations 4.4.2 Low-Order Preconditioning of Model Spectral Operators in One Dimension 4.4.3 Low-Order Preconditioning in Several Dimensions 4.4.4 Spectral Preconditioning 4.5 Descent and Krylov Iterative Methods for Spectral Equations 4.5.1 Multidimensional Matrix-Vector Multiplication 4.5.2 Iterative Methods 4.6 Spectral Multigrid Methods 4.6.1 One-Dimensional Fourier Multigrid Model Problem 4.6.2 General Spectral Multigrid Methods 4.7 Numerical Examples of Direct and Iterative Methods 4.7.1 Fourier Collocation Discretizations 4.7.2 Chebyshev Collocation Discretizations 4.7.3 Legendre G-NI Discretizations 4.7.4 Preconditioners for Legendre G-NI Matrices 4.8 Interlude 5. Polynomial Approximation Theory 5.1 Fourier Approximation 5.1.1 Inverse Inequalities for Trigonometric Polynomials 5.1.2 Estimates for the Truncation and Best Approximation Errors 5.1.3 Estimates for the Interpolation Error 5.2 Sturm-Liouville Expansions 5.2.1 Regular Sturm-Liouville Problems 5.2.2 Singular Sturm-Liouville Problems 5.3 Discrete Norms 5.4 Legendre Approximations 5.4.1 Inverse Inequalities for Algebraic Polynomials 5.4.2 Estimates for the Truncation and Best Approximation Errors 5.4.3 Estimates for the Interpolation Error 5.4.4 Scaled Estimates 5.5 Chebyshev Approximations 5.5.1 Inverse Inequalities for Polynomials 5.5.2 Estimates for the Truncation and Best Approximation Errors 5.5.3 Estimates for the Interpolation Error 5.6 Proofs of Some Approximation Results 5.7 Other Polynomial Approximations 5.7.1 Jacobi Polynomials 5.7.2 Laguerre and Hermite Polynomials 5.8 Approximation in Cartesian-Product Domains 5.8.1 Fourier Approximations 5.8.2 Legendre Approximations 5.8.3 Mapped Operators and Scaled Estimates 5.8.4 Chebyshev and Other Jacobi Approximations 5.8.5 Blended Trigonometric and Algebraic Approximations 5.9 Approximation in Triangles and Related Domains 6. Theory of Stability and Convergence 6.1 Three Elementary Examples Revisited 6.1.1 A Fourier Galerkin Method for the Wave Equation 6.1.2 A Chebyshev Collocation Method for the Heat Equation 6.1.3 A Legendre Tau Method for the Poisson Equation 6.2 Towards a General Theory 6.3 General Formulation of Spectral Approximations to Linear Steady Problems 6.4 Galerkin, Collocation, G-NI and Tau Methods 6.4.1 Galerkin Methods 6.4.2 Collocation Methods 6.4.3 G-NI Methods 6.4.4 Tau Methods 6.5 General Formulation of Spectral Approximations to Linear Evolution Problems 6.5.1 Conditions for Stability and Convergence: The Parabolic Case 6.5.2 Conditions for Stability and Convergence: The Hyperbolic Case 6.6 The Error Equation 7. Analysis of Model Boundary-Value Problems 7.1 The Poisson Equation 7.1.1 Legendre Methods 7.1.2 Chebyshev Methods 7.1.3 Other Boundary-Value Problems 7.2 Singularly Perturbed Elliptic Equations 7.2.1 Stabilization of Spectral Methods 7.3 The Eigenvalues of Some Spectral Operators 7.3.1 The Discrete Eigenvalues for Lu = −uxx 7.3.2 The Discrete Eigenvalues for Lu = −νuxx + βux 7.3.3 The Discrete Eigenvalues for Lu = ux 7.4 The Preconditioning of Spectral Operators 7.5 The Heat Equation 7.6 Linear Hyperbolic Equations 7.6.1 Periodic Boundary Conditions 7.6.2 Nonperiodic Boundary Conditions 7.6.3 The Resolution of the Gibbs Phenomenon 7.6.4 Spectral Accuracy for Non-Smooth Solutions 7.7 Scalar Conservation Laws 7.8 The Steady Burgers Equation Appendix A. Basic Mathematical Concepts A.1 Hilbert and Banach Spaces A.2 The Cauchy-Schwarz Inequality A.3 Linear Operators Between Banach Spaces A.4 The Fr´echet Derivative of an Operator A.5 The Lax-Milgram Theorem A.6 Dense Subspace of a Normed Space A.7 The Spaces Cm(Ω), m ≥ 0 A.8 Functions of Bounded Variation and the Riemann(-Stieltjes) Integral A.9 The Lebesgue Integral and Lp-Spaces A.10 Infinitely Differentiable Functions and Distributions A.11 Sobolev Spaces and Sobolev Norms A.12 The Sobolev Inequality A.13 The Poincar´e Inequality A.14 The Hardy Inequality A.15 The Gronwall Lemma Appendix B. Fast Fourier Transforms Appendix C. Iterative Methods for Linear Systems C.1 A Gentle Approach to Iterative Methods C.2 Descent Methods for Symmetric Problems C.3 Krylov Methods for Nonsymmetric Problems Appendix D. Time Discretizations D.1 Notation and Stability Definitions D.2 Standard ODE Methods D.2.1 Leap Frog Method D.2.2 Adams-Bashforth Methods D.2.3 Adams-Moulton Methods D.2.4 Backwards-Difference Formulas D.2.5 Runge-Kutta Methods D.3 Integrating Factors D.4 Low-Storage Schemes References Index

Note: Contents: 1. Introduction. 2. RC Filter. 3. General linear time invariant systems. 4. The seismometer. 5. The sampling process. 6. Analog-to-digital conversion. 7. From infinitely continuous to finite discrete. 8. The digital anti-alias filter. 9. Inverse and simulation filtering of digital seismograms. 10. The measurement of wavelet parameters from digital seismograms. References. Appendix: Solution to problems.

Note: Zugl.: München,Univ. der Bundeswehr, Diss., 2005

Note: Text. engl. und russ. - Teilw. in kyrill. Schr.

Note: CONTENTS: Preface to the Second Edition. - Preface to the First Edition. - 1 The Atmosphere. - 1.1 History and Evolution of the Earth's Atmosphere. - 1.2 Climate. - 1.3 The Layers of the Atmosphere. - 1.4 Pressure in the Atmosphere. - 1.4.1 Units of Pressure. - 1.4.2 Variation of Pressure with Height in the Atmosphere. - 1.5 Temperature in the Atmosphere. - 1.6 Expressing the Amount of a Substance in the Atmosphere. - 1.7 Spatial and Temporal Scales of Atmospheric Processes. - Problems. - References. - 2 Atmospheric Trace Constituents. - 2.1 Atmospheric Lifetime. - 2.2 Sulfur-Containing Compounds. - 2.2.1 Dimethyl Sulfide (CH3SCH3). - 2.2.2 Carbonyl Sulfide (OCS). - 2.2.3 Sulfur Dioxide (SO2). - 2.3 Nitrogen-Containing Compounds. - 2.3.1 Nitrous Oxide (N2O). - 2.3.2 Nitrogen Oxides (NO* = NO + NO2). - 2.3.3 Reactive Odd Nitrogen (NOy). - 2.3.4 Ammonia (NH3). - 2.4 Carbon-Containing Compounds. - 2.4.1 Classification of Hydrocarbons. - 2.4.2 Methane. - 2.4.3 Volatile Organic Compounds. - 2.4.4 Biogenic Hydrocarbons. - 2.4.5 Carbon Monoxide. - 2.4.6 Carbon Dioxide. - 2.5 Halogen-Containing Compounds. - 2.5.1 Methyl Chloride (CH3C1). - 2.5.2 Methyl Bromide (CH3Br). - 2.6 Atmospheric Ozone. - 2.7 Particulate Matter (Aerosols). - 2.7.1 Stratospheric Aerosol. - 2.7.2 Chemical Components of Tropospheric Aerosol. - 2.7.3 Cloud Condensation Nuclei (CCN). - 2.7.4 Sizes of Atmospheric Particles. - 2.7.5 Sources of Atmospheric Paniculate. - 2.7.6 Carbonaceous Particles. - 2.7.7 Mineral Dust. - 2.8 Emission Inventories. - 2.9 Biomass Burning. - Appendix 2.1 Air Pollution Legislation. - Appendix 2.2 Hazardous Air Pollutants (Air Toxics). - Problems. - References. - 3 Chemical Kinetics. - 3.1 Order of Reaction. - 3.2 Theories of Chemical Kinetics. - 3.2.1 Collision Theory. - 3.2.2 Transition State Theory. - 3.2.3 Potential Energy Surface for a Bimolecular Reaction. - 3.3 The Pseudo-Steady-State Approximation. - 3.4 Reactions of Excited Species. - 3.5 Termolecular Reactions. - 3.6 Chemical Families. - 3.7 Gas-Surface Reactions. - Appendix 3 Free Radicals. - Problems. - References. - 4 Atmospheric Radiation and Photochemistry. - 4.1 Radiation. - 4.1.1 Solar and Terrestrial Radiation. - 4.1.2 Energy Balance for Earth and Atmosphere. - 4.1.3 Solar Variability. - 4.2 Radiative Flux in the Atmosphere. - 4.3 Beer-Lambert Law and Optical Depth. - 4.4 Actinic Flux. - 4.5 Atmospheric Photochemistry. - 4.6 Absorption of Radiation by Atmospheric Gases. - 4.7 Absorption by O2 and O3 122. - 4.8 Photolysis Rate as a Function of Altitude. - 4.9 Photodissociation of O3 to Produce O and O(1D). - 4.10 Photodissociation of NO2. - Problems. - References. - 5 Chemistry of the Stratosphere. - 5.1 Overview of Stratospheric Chemistry. - 5.2 Chapman Mechanism. - 5.3 Nitrogen Oxide Cycles. - 5.3.1 Stratospheric Source of NO* from N2O. - 5.3.2 NO* Cycles. - 5.4 HO* Cycles. - 5.5 Halogen Cycles. - 5.5.1 Chlorine Cycles. - 5.5.2 Bromine Cycles. - 5.6 Reservoir Species and Coupling of the Cycles. - 5.7 Ozone Hole. - 5.7.1 Polar Stratospheric Clouds. - 5.7.2 PSCs and the Ozone Hole. - 5.7.3 Arctic Ozone Hole. - 5.8 Heterogeneous (Nonpolar) Stratospheric Chemistry. - 5.8.1 The Stratospheric Aerosol Layer. - 5.8.2 Heterogeneous Hydrolysis of N2O5. - 5.8.3 Effect of Volcanoes on Stratospheric Ozone. - 5.9 Summary of Stratospheric Ozone Depletion. - 5.10 Transport and Mixing in the Stratosphere. - 5.11 Ozone Depletion Potential. - Problems. - References. - 6 Chemistry of the Troposphere. - 6.1 Production of Hydroxyl Radicals in the Troposphere. - 6.2 Basic Photochemical Cycle of NO2, NO, and O3. - 6.3 Atmospheric Chemistry of Carbon Monoxide. - 6.3.1 Low NO* Limit. - 6.3.2 High NO* Limit. - 6.3.3 Ozone Production Efficiency. - 6.3.4 Theoretical Maximum Yield of Ozone from CO Oxidation. - 6.4 Atmospheric Chemistry of Methane. - 6.5 The NO* and NOy, Families. - 6.5.1 Daytime Behavior. - 6.5.2 Nighttime Behavior. - 6.6 Ozone Budget of the Troposphere and Role of NO*. - 6.6.1 Ozone Budget of the Troposphere. - 6.6.2 Role of NO*. - 6.7 Tropospheric Reservoir Molecules. - 6.7.1 H2O2, CH3OOH, and HONO. - 6.7.2 Peroxyacyl Nitrates (PANs). - 6.8 Relative Roles of VOC and NOx in Ozone Formation. - 6.8.1 Importance of the VOC/NOx Ratio. - 6.8.2 Ozone Isopleth Plot. - 6.9 Simplified Organic/NOx Chemistry. - 6.10 Chemistry of Nonmethane Organic Compounds in the Troposphere. - 6.10.1 Alkanes. - 6.10.2 Alkenes. - 6.10.3 Aromatics. - 6.10.4 Aldehydes. - 6.10.5 Ketones. - 6.10.6 α, β-Unsaturated Carbonyls. - 6.10.7 Ethers. - 6.10.8 Alcohols. - 6.11 Atmospheric Chemistry of Biogenic Hydrocarbons. - 6.12 Atmospheric Chemistry of Reduced Nitrogen Compounds. - 6.12.1 Amines. - 6.12.2 Nitriles. - 6.12.3 Nitrites. - 6.13 Atmospheric Chemistry (Gas Phase) of Sulfur Compounds. - 6.13.1 Sulfur Oxides. - 6.13.2 Reduced Sulfur Compounds (Dimethyl Sulfide). - 6.14 Tropospheric Chemistry of Halogen Compounds. - 6.14.1 Chemical Cycles of Halogen Species. - 6.14.2 Tropospheric Chemistry of CFC Replacements: Hydrofluorocarbons (HFCs) and Hydrochlorofluorocarbons (HCFCs). - Problems. - References. - 7 Chemistry of the Atmospheric Aqueous Phase. - 7.1 Liquid Water in the Atmosphere. - 7.2 Absorption Equilibria and Henry's Law. - 7.3 Aqueous-Phase Chemical Equilibria. - 7.3.1 Water. - 7.3.2 Carbon Dioxide-Water Equilibrium. - 7.3.3 Sulfur Dioxide-Water Equilibrium. - 7.3.4 Ammonia-Water Equilibrium. - 7.3.5 Nitric Acid-Water Equilibrium. - 7.3.6 Equilibria of Other Important Atmospheric Gases. - 7.4 Aqueous-Phase Reaction Rates. - 7.5 S(IV)-S(VI) Transformation and Sulfur Chemistry. - 7.5.1 Oxidation of S(IV) by Dissolved O3. - 7.5.2 Oxidation of S(IV) by Hydrogen Peroxide. - 7.5.3 Oxidation of S(IV) by Organic Peroxides. - 7.5.4 Uncatalyzed Oxidation of S(IV) by O2. - 7.5.5 Oxidation of S(IV) by O2 Catalyzed by Iron and Manganese. - 7.5.6 Comparison of Aqueous-Phase S(IV) Oxidation Paths. - 7.6 Dynamic Behavior of Solutions with Aqueous-Phase Chemical Reactions. - 7.6.1 Closed System. - 7.6.2 Calculation of Concentration Changes in a Droplet with Aqueous-Phase Reactions. - Appendix 7.1 Thermodynamic and Kinetic Data. - Appendix 7.2 Additional Aqueous-Phase Sulfur Chemistry. - 7.A.1 S(IV) Oxidation by the OH Radical. - 7.A.2 Oxidation of S(IV) by Oxides of Nitrogen. - 7.A.3 Reaction of Dissolved SO2 with HCHO. - Appendix 7.3 Aqueous-Phase Nitrite and Nitrate Chemistry. - 7.A.4 NOx Oxidation. - 7.A.5 Nitrogen Radicals. - Appendix 7.4 Aqueous-Phase Organic Chemistry. - Appendix 7.5 Oxygen and Hydrogen Chemistry. - Problems. - References. - 8 Properties of the Atmospheric Aerosol. - 8.1 The Size Distribution Function. - 8.1.1 The Number Distribution nN(Dp). - 8.1.2 The Surface Area, Volume, and Mass Distributions. - 8.1.3 Distributions Based on In Dp and log Dp. - 8.1.4 Relating Size Distributions Based on Different Independent Variables. - 8.1.5 Properties of Size Distributions. - 8.1.6 The Lognormal Distribution. - 8.1.7 Plotting the Lognormal Distribution. - 8.1.8 Properties of the Lognormal Distribution. - 8.2 Ambient Aerosol Size Distributions. - 8.2.1 Urban Aerosols. - 8.2.2 Marine Aerosols. - 8.2.3 Rural Continental Aerosols. - 8.2.4 Remote Continental Aerosols. - 8.2.5 Free Tropospheric Aerosols. - 8.2.6 Polar Aerosols. - 8.2.7 Desert Aerosols. - 8.3 Aerosol Chemical Composition. - 8.4 Spatial and Temporal Variation. - 8.5 Vertical Variation. - Problems. - References. - 9 Dynamics of Single Aerosol Particles. - 9.1 Continuum and Noncontinuum Dynamics: The Mean Free Path. - 9.2 The Drag on a Single Particle: Stokes' Law. - 9.2.1 Corrections to Stokes' Law: The Drag Coefficient. - 9.2.2 Stokes' Law and Noncontinuum Effects: Slip Correction Factor. - 9.3 Gravitational Settling of an Aerosol Particle. - 9.4 Motion of an Aerosol Particle in an External Force Field. - 9.5 Brownian Motion of Aerosol Particles. - 9.5.1 Particle Diffusion. - 9.5.2 Aerosol Mobility and Drift Velocity. - 9.5.3 Mean Free Path of an Aerosol Particle. - 9.6 Aer

Note: Contents Preface Part I Anatomy of a cyclone 1 Anatomy of a cyclone 1.1 A 'typical' extra-tropical cyclone 1.2 Describing the atmosphere 1.3 Air masses and fronts 1.4 The structure of a typical extra-tropical cyclone Review questions 2 Mathematical methods in fluid dynamics 2.1 Scalars and vectors 2.2 The algebra of vectors 2.3 Scalar and vector fields 2.4 Coordinate systems on the Earth 2.5 Gradients of vectors 2.6 Line and surface integrals 2.7 Eulerian and Lagrangian frames of reference 2.8 Advection Review questions 3 Properties of fluids 3.1 Solids, liquids, and gases 3.2 Thermodynamic properties of air 3.3 Composition of the atmosphere 3.4 Static stability 3.5 The continuum hypothesis 3.6 Practical assumptions 3.7 Continuity equation Review questions 4 Fundamental forces 4.1 Newton's second law: F=ma 4.2 Body, surface, and line forces 4.3 Forces in an inertial reference frame 4.4 Forces in a rotating reference frame 4.5 The Navier-Stokes equations Review questions 5 Scale analysis 5.1 Dimensional homogeneity 5.2 Scales 5.3 Non-dimensional parameters 5.4 Scale analysis 5.5 The geostrophic approximation Review questions 6 Simple steady motion 6.1 Natural coordinate system 6.2 Balanced flow 6.3 The Boussinesq approximation 6.4 The thermal wind 6.5 Departures from balance Review questions 7 Circulation and vorticity 7.1 Circulation 7.2 Vorticity 7.3 Conservation of potential vorticity 7.4 An introduction to the vorticity equation Review questions 8 Simple wave motions 8.1 Properties of waves 8.2 Perturbation analysis 8.3 Planetary waves Review questions 9 Extra-tropical weather systems 9.1 Fronts 9.2 Frontal cyclones 9.3 Baroclinic instability Review questions Part II Atmospheric phenomena 10 Boundary layers 10.1 Turbulence 10.2 Reynolds decomposition 10.3 Generation of turbulence 10.4 Closure assumptions Review questions 11 Clouds and severe weather 11.1 Moist processes in the atmosphere 11.2 Air mass thunderstorms 11.3 Multi-cell thunderstorms 11.4 Supercell thunderstorms and tornadoes 11.5 Mesoscale convective systems Review questions 12 Tropical weather 12.1 Scales of motion 12.2 Atmospheric oscillations 12.3 Tropical cyclones Review questions 13 Mountain weather 13.1 Internal gravity waves 13.2 Flow over mountains 13.3 Downslope windstorms Review questions 14 Polar weather 14.1 Katabatic winds 14.2 Barrier winds 14.3 Polar lows Review questions 15 Epilogue: the general circulation 15.1 Fueled by the Sun 15.2 Radiative-convective equilibrium 15.3 The zonal mean circulation 15.4 The angular momentum budget 15.5 The energy cycle Appendix A - symbols Appendix Β - constants and units Bibliography Index

Note: Zugl.: Greifswald, Univ., Diss., 2005

Note: Contents Acknowledgments Chapter 1. Introduction 1.1 Discovery 1.2 General Introduction 1.3 Just for Fun — An Isotope Biography of Mr. Polychaete Chapter 2. Isotope Notation and Measurement Overview 2.1 The Necessary Minimum for Ecologists 2.2 Why Use the 5 Notation? 2.3 Why Is 8 a Good Substitute for % Heavy Isotope? 2.4 8 and the Ratio-of-Ratios 2.5 Chapter Summary Chapter 3. Using Stable Isotope Tracers Overview 3.1 Isotope Circulation in the Biosphere 3.2 Landscape Ecology and Isotope Maps 3.3 Community Ecology and Invasive Species in Food Webs 3.4 Life History Ecology and Animal Migrations 3.5 Plants, Microbes, and Scaling Up 3.6 Chapter Summary Chapter 4. Isotope Chi ("I Chi") Overview 4.1 Chocolate Isotopes 4.2 Oxygen in the Sea 4.3 Equations for Isotope Chi ("I Chi") 4.4 Building an I Chi Gain-Loss Model, Step by Step 4.5 Errors in I Chi Models 4.6 Exact Equations for I Chi Models 4.7 Cows in a Pasture 4.8 Chapter Summary Chapter 5. Mixing Overview 5.1 Isotope Mixing in Food Webs 5.2 Isotope Sourcery 5.3 Mixing Mechanics 5.4 Advanced Mixing Mechanics 5.5 Mixing Assumptions and Errors or the Art and Wisdom of Using Isotope Mixing Models 5.6 River Sulfate and Mass-Weighted Mixing 5.7 A Special Muddy Case and Mixing Through Time 5.8 The Qualquan Chronicles and Mixing Across Landscapes 5.9 Dietary Mixing, Turnover, and a Stable Isotope Clock 5.10 Chapter Summary Chapter 6. Isotope Additions Overview 6.1 Addition Addiction 6.2 The Golden Spike Award for Isotopes 6.3 Chapter Summary Chapter 7. Fractionation Overview 7.1 Fractionation Fundamentals 7.2 Isotopium and Fractionation in Closed Systems 7.3 A Strange and Routine Case 7.4 A Genuine Puzzle — Fractionation or Mixing? 7.5 Cracking the Closed Systems 7.6 Equilibrium Fractionation, Subtle Drama in the Cold 7.7 A Supply/Demand Model for Open System Fractionation 7.8 Open System Fractionation and Evolution of the Earth's Sulfur Cycle 7.9 Open System Legacies 7.10 Conducting Fractionation Experiments 7.11 Chapter Summary Chapter 8. Scanning the Future Overview 8.1 The Isotope Scanner 8.2 Mangrove Maude 8.3 The Beginner's Advantage—Imagine! 8.4 Chapter Summary Appendix. Important Isotope Equations and Useful Conversions Index Supplemental Electronic Materials on the Accompanying CD A. Chapter 1 Color Figures and Cartoon Problems B. Chapter 2 Color Figures and Cartoon Problems Technical Supplement 2A: Measuring Spiked Samples Technical Supplement 2B: Ion Corrections Technical Supplement 2C: The Ratio Notation and The Power of 1 C. Chapter 3 Color Figures and Cartoons Problems D. Chapter 4 Color Figures and Cartoons Problems I Chi Spreadsheets E. Chapters 5 Color Figures and Cartoons Problems I Chi Spreadsheets F. Chapter 6 Color Figure and Cartoon Problems I Chi Spreadsheet Technical Supplement 6A: How Much Isotope Should I Add? Technical Supplement 6B: Noisy Data and Data Analysis with Enriched Samples G. Chapter 7 Color Figures and Cartoons Problems I Chi Spreadsheets Technical Supplement 7A: A Chemist's View of Isotope Effects Technical Supplement 7B: Derivations of Closed System Isotope Equations H. Chapter 8 Color Figures and Cartoons Problems I. All Problems for Chapters 1-8 J. All Answers to Problems for Chapters 1-8 K. All Figures and Cartoons L. All I Chi Spreadsheets M. A Reading List

Note: Contents: 1 Introduction: The Transitory Century ; 2 Urbanization in a global context ; 2.1 Current urbanization dynamics ; 2.2 Understanding the city ; 2.3 Cities and environmental change ; 2.4 The city as a habitat ; 2.5 Urban governance: actors, structures, processes ; 2.6 Global urbanization reports: problem descriptions, solution approaches and actors ; 2.7 Challenges and needs for action ; 3 The Normative Compass ; 3.1 The Great transformation and cities ; 3.2 An extended normative concept for the transformation towards sustainability ; 3.3 Sustaining the natural life-support systems ; 3.4 Inclusion ; 3.5 Eigenart ; 3.6 Dynamics between the three dimensions of the normative compass ; 4 Exemplary transformative action fields ; 4.1 Transformative action fields: concep ; 4.2 Internationally discussed fields ; 4.3 Transformative action field: ‘urban land use ; 4.4 Transformative action field: ‘materials and material flows' ; 4.5 Transformative action field: ‘urban health' ; 4.6 Transformative action fields: conclusions ; 5 Cities in the global transformation process ; 5.1 Introduction ; 5.2 Mumbai: transformation of a colonial metropolis into a globally networked megacity ; 5.3 Cairo: metropolis between an authoritarian state and weak governance ; 5.4 Copenhagen: a people-oriented pioneer of sustainable urban planning ; 5.5 Guangzhou: Open Door policy, globalization and migration-driven urbanization in the ‘world’s workshop’ ; 5.6 The Ruhr area: the post-industrial metropolis – polycentric and sustainable ; 5.7 Kigali: post-conflict city in Sub-Saharan Africa ; 5.8 São Paulo: the fragmented metropolis ; 5.9 Novi Beograd: 20th century socialist planned city district ; 5.10 Synopsis ; 6 Urban designers: actors of the urban transformation ; 6.1 Introduction. ; 6.2 Transformative urban networks ; 6.3 Inclusive urban planning ; 6.4 Social inclusion and cohesion ; 6.5 Participation in urban development ; 6.6 Small-scale green transformations as part of the Great Transformation ; 6.7 Preventive healthcare ; 6.8 Innovative investment instruments for the urban transformation ; 6.9 Science as a catalyst of urban development ; 6.10 Conclusions ; 7 Urban patterns ; 7.1 From phenomenology to designing cities: forces, forms, values ; 7.2 Newly planned cities and city districts ; 7.3 Informal settlements ; 7.4 Mature cities and city districts ; 7.5 Urbanization surge up to 2050 – six development risks of global change ; 8 Transformative urban governance: empowering cities ; 8.1 Challenges for transformative urban governance ; 8.2 Empowering local governments for the transformation ; 8.3 Strengthen civil society: involve residents, act collaboratively ; 8.4 Shape global governance structures in a way that meets present-day needs ; 8.5 Build a polycentric responsibility architecture ; 9 Recommendations for action ; 9.1 Challenges ; 9.2 Elements of a social contract for the urban transformation ; 9.3 Transformative action fields in cities ; 9.4 Governance ; 9.5 Financing ; 9.6 Synopsis ; 10 Research on sustainable urbanization ; 10.1 Cities and the Great Transformation: important lines of research ; 10.2 Programmes and institutions: where does urban sustainability research stand? ; 10.3 Towards a new urban research agenda ; References ; Glossary

Note: Zugl.: Helsinki, Univ., Diss., 2006

Note: Text englisch mit englischer und deutscher Zusammenfassung

Note: Contents: 1 Introduction ; I Background ; 2 Vector Spaces ; 3 Linear Algebra and Matrices ; 4 Foundations of Probability ; 5 Modeling Dependence ; 6 Asymptotics ; 7 Further Topics in Probability ; II Foundations of Statistics ; 8 Estimators ; 9 Properties of Estimators ; 10 Confidence Intervals and Tests ; III Econometric Models ; 11 Regression ; 12 Ordinary Least Squares ; 13 Large Samples and Dependence ; 14 Regularization ; IV Appendix

Note: Contents ; Introduction and Overview ; PART I CORPORATE GOVERNANCE IN EUROPE ; 1. An Evolutionary Overview of the Ownership, Governance and Strategy of Mediobanca: From the Kingmaker of Italian Capitalism to a Large Financial Conglomerate ; 2. The Co-Operative Bank – What Went Wrong? ; 3. Remuneration-Based Incentives in a Global Bank before and after Lehman - The Case of Deutsche Bank ; PART II CORPORATE GOVERNANCE IN THE USA AND SOUTH AMERICA , 4. CEO Compensation in US Financial Institutions ; 5. Regulation, Ownership and Corporate Governance in Brazilian Banks ; PART III CORPORATE GOVERNANCE IN THE ASIA PACIFIC ; 6. Corporate Governance of Japanese Banks ; 7. Corporate Governance of China’s City Commercial Banks ; 8. Failure in Corporate Governance - Financial Planning and Greed ; PART IV CORPORATE GOVERNANCE: ADDITIONAL DIMENSIONS ; 9. Determinants of Corporate Governance in Russian Banks ; 10. Corporate Governance Practices in the Nigerian Banking Industry ; 11. Corporate Governance in Islamic Financial Institutions: What Have we Learnt? ; Index

Note: Text englisch, Zusammenfassung englisch und deutsch

Note: Contents: Structure and function of contemporary food webs on Arctic shelves: an introduction / P. Wassmann. - Past glacial and interglacial conditions in the Arctic Ocean and marginal seas - a review / D. A. Darby, L. Polyak and H. A. Bauch. - Climate variability and physical forcing of the food webs and the carbon budget on panarctic shelves / E. Carmack, D. Barber, J. Christensen, R. Macdonald, B. Rudels and E. Sakshaug. - Physical and biological characteristics of the pelagic system across Fram Strait to Kongsfjorden / H. Hop, S. Falk-Petersen, H. Svendsen, S. Kwasniewski, V. Pavlov, O. Pavlova and J. E. Søreide. - Food webs and carbon flux in the Barents Sea / P. Wassmann, M. Reigstad, T. Haug, B. Rudels, M. L. Carroll, H. Hop, G. W. Gabrielsen, S. Falk-Petersen, S. G. Denisenko, E. Arashkevich, D. Slagstad and O. Pavlova.

Note: Solar terrestrial physics: the evolution of a disciplineThe upper atmosphere and ionosphere -- Physics of magnetized plasmas -- The Sun and its atmosphere -- The solar wind and heliosphere -- Collisionless shocks -- Solar wind interaction with magnetized obstacles -- Plasma interactions with unmagnetized bodies -- Solar wind magnetosphere coupling -- The terrestrial magnetosphere -- The aurora -- Planetary magnetospheres -- Plasma waves..

Note: Zusammenfassungen in deutscher und englischer Sprache

Note: Contents: Chapter 1: Preparing the Work Environment -- Chapter 2: The Geocaching App -- Chapter 3: Combining Multiple Data Sources -- Chapter 4: Improving the App Search Capabilities -- Chapter 5: Making Maps

Note: Contents: Section 1: The Facts of Economic Growth and Economic Fluctuation ; Chapter 1: RBC Methodology and the Development of Aggregate Economic Theory ; Chapter 2: The Facts of Economic Growth ; Chapter 3: Macroeconomic Shocks and Their Propagation ; Chapter 4: Macroeconomic Regimes and Regime Shifts ; Chapter 5: The Macroeconomics of Time Allocation ; Chapter 6: "Who Bears the Cost of Recessions? The Role of House Prices and Household Debt" ; Chapter 7: "Allocative and Remitted Wages: New Facts and Challenges for Keynesian Models" ; Chapter 8: Financial and Fiscal Crises ; Section 2: The Methodology of Macroeconomics ; Chapter 9: Factor Models and Structural Vector Autoregressions in Macroeconomics ; Chapter 10: Solution and Estimation Methods for DSGE Models ; Chapter 11: Recursive Contracts and Endogenously Incomplete Markets ; Chapter 12: Macroeconomics and Household Heterogeneity ; Chapter 13: Natural Experiments in Macroeconomics ; Chapter 14: Accounting for Business Cycles ; Chapter 15: "Incomplete Information in Macroeconomics: Accommodating Frictions in Coordination" ; Chapter 16: New Methods for Macro-Financial Model Comparison and Policy Analysis

Note: Knowledge as a public good (2009)Open access, markets, and missions (2010) -- Open access overview (2004) -- Removing the barriers to research : an introduction to open access for librarians (2003) -- The taxpayer argument for open access (2003) -- It's the authors, stupid! (2004) -- Six things that researchers need to know about open access (2006) -- Trends favoring open access (2007) -- Gratis and libre open access (2008) -- The scaling argument (2004) -- Problems and opportunities (blizzards and beauty) (2007) -- Open access and the self-correction of knowledge (2008) -- Open access and the last-mile problem for knowledge (2008) -- The case for OAI in the age of Google (2004) -- Good facts, bad predictions (2006) -- No-fee open-access journals (2006) -- Balancing author and publisher rights (2007) -- Flipping journal to open access (2007) -- Society publishers with open access journals (2007) -- Ten challenges for open-access journals (2009) -- The final version of the NIH public-access policy (2005) -- Another OA mandate : the Federal Research Public Access Act of 2006 (2006) -- Twelve reminders about FRPAA (2007) -- An open access mandate for the NIH (2008) -- The open access mandate at Harvard (2008) -- A bill to overturn the NIH policy (2008) -- Open access policy options for funding agencies and universities (2009) -- Open access and quality (2006) -- Thinking about prestige, quality, and open access (2008) -- Not napster for science (2003) -- Two distractions (2004) -- Praising progress, preserving precision (2004) -- Who should control access to research literature? (2004) -- Four analogies to clean energy (2010) -- Promoting open access in the humanities (2005) -- Helping scholars and helping libraries (2005) -- Unbinding knowledge : a proposal for providing open access to past research articles, staring with the most important (2006) -- Open access to electronic theses and dissertations (2006) -- Open access for digitization projects (2009) -- Analogies and precendents for the FOS revolution (2002) -- Thoughts on the first and second-order scholarly judgments (2002) -- Saving the oodlehood and shebangity of the internet (2003) -- What's the ullage of your library? (2004) -- Can search tame the wild Web? : can open access help? (2005) -- Glossary..

Note: Contents: Section 3: Financial-Real Connections ; Chapter 17: "Wholesale Banking and Bank Runs in Macroeconomic Modelling of Financial Crises" ; Chapter 18: "Housing and Credit Markets: Bubbles and Crashes" ; Chapter 19: Macro, Money and Finance: A Continuous-Time Approach ; Chapter 20: Housing and Macroeconomics ; Chapter 21: Term Structure of Uncertainty in the Macroeconomy ; Chapter 22: Quantitative Models of Sovereign Debt Crises ; Section 4: Models of Economic Growth and Fluctuations ; Chapter 23: Families in Macroeconomics ; Chapter 24: Environmental Macroeconomics ; Chapter 25: The Staying Power of Staggered Wage and Price Setting Models in Macroeconomics ; Chapter 26: Neoclassical Models in Macroeconomics ; Chapter 27: Macroeconomics of Persistent Slumps ; Chapter 28: Macroeconomics and the Labor Market ; Section 5: Macroeconomic Policy ; Chapter 29: Challenges for Central Banks' Macro Models ; Chapter 30: Liquidity requirements, liquidity choice and financial stability ; Chapter 31: "Understanding Inflation as a Joint Monetary-Fiscal Phenomenon" ; Chapter 32: "Fiscal Multipliers: Liquidity Traps and Currency Unions" ; Chapter 33: What is a Sustainable Public Debt? ; Chapter 34: The Political Economy of Government Debt

Note: Contents: 1 Introduction 1.1 The idea of the Representative Agent and his or her lifetime ; 2 Basic Real Business Cycle Model (RBC) ; 3 Basic New-Keynesian model (NK) ; 4 New-Keynesian model with sticky wages ; 5 New-Keynesian model with habit formation and non-ricardian agents ; 6 The New-Keynesian model with investment adjustment costs and variable capital utilization ; 7 New-Keynesian model with government ; References ; Appendices ; A Mathematical tools ; B Basic ideas about DSGE

Note: Zusammenfassungen in deutscher und englischer Sprache

Note: Contents: Foreword to the Encyclopedia ; Foreword to Volume 1 ; Introduction to Volume 1 ; PART I GENERAL THEMES The Goals of Climate Policy ; 1. The Science of Climate Change: A Legal Perspective on the IPCC ; 2. The Precautionary Principle and Climate Change ; 3. Setting the Social Cost of Carbon ; 4. Human Rights and Climate Change: Building Synergies for a Common Future ; Approaches to Addressing Climate Change ; 5. Climate Policy Instrument Choices ; 6. Corporate Social Responsibility and Climate Change ; 7. Local Authorities and Climate Change ; 8. Individual Behaviour, The Social Sciences and Climate Change ; 9. Criminal Law and Climate Change ; 10. Research and Scholarship on Climate Change Law in Developing Countries ; PART II INTERNATIONAL LAW PERSPECTIVE General Issues ; 11. The Climate as a Global Common ; 12. CBDR and Climate Change ; 13. The Potential Roles of the ICJ in Climate Change-related Claims ; 14. Unilateralism, Extraterritoriality and Climate Change ; 15. Climate Engineering and International Law ; 16. Carbon Capture and Storage as a Bridging Technology ; Treaties Related to Climate Change ; The UN Negotiation Process ; 17. The United Nations Framework Convention on Climate Change: A Framework Approach to Climate Change ; 18. The UNFCCC: Legal Scholarship in Four Key Areas ; 19. The Kyoto Protocol, With a Special Focus on the Flexible Mechanisms ; 20. The Kyoto Protocol’s Compliance Mechanism ; 21. REDD+ as a Climate Change Mitigation Mechanism ; 22. International Treaty Fragmentation and Climate Change ; Alternative International Approaches ; 23. ICAO and IMO: International Sectoral Approaches to Greenhouse Gas Reductions in Transport ; 24. Interlinkages Between Climate Change, Ozone Depletion and Air Pollution: The International Legal Framework ; 25. The WTO and Climate Change ; 26. Climate Change and International Investment Treaties ; PART III NATIONAL AND REGIONAL PERSPECTIVES ON REDUCING GREENHOUSE GASES General Issues ; 27. Polycentrism and Climate Change ; 28. Climate Change Federalism ; 29. Environmental Impact Assessments and Climate Change ; 30. The Role of the National Courts in GHG Emissions Reductions ; Regional and National Mitigation Approaches ; Emissions Trading ; 31. Greenhouse Gas Emissions Trading in the EU ; 32. North American Greenhouse Gas Emission Trading Systems ; 33. Emissions Trading in China ; Other Regulatory Approaches to Reduce Greenhouse Gases ; 34. Traditional Regulation’s Role in Greenhouse Gas Abatement ; 35. Carbon Taxes ; 36. Transportation as a Climate Wedge and Challenge under United States Law ; 37. Biofuel ; 38. Renewable Energy: Support Mechanisms ; 39. Renewable Energy: Public Acceptance and Citizens’ Financial Participation ; 40. Energy Efficiency and Conservation ; Mitigation Strategies in Developing Countries ; 41. India’s Climate Change Mitigation Strategy ; 42. Green Growth Policy in Korea ; PART IV ADAPTATION Specific Impacts and Sectors ; 43. Integrated Water Law and Climate Change: An EU Perspective ; 44. Water Availability and Allocation ; 45. Managing Ecosystem Effects in an Era of Rapid Climate Change ; 46.Ocean Adaptation ; 47. Coastal Issues ; 48. Adaptation and the Energy Sector ; Cross-cutting Issues and Adaptation Techniques ; 49. Adaptation Justice ; 50. Loss and Damage in the UN Climate Regime ; 51. Indigenous Peoples and Climate Change ; 52. Human Mobility and Climate Change ; 53. Urban Planning and Climate Change ; 54. Insurance ; 55. Disaster Law and Climate Change ; PART V CONCLUSIONS 56. The Emergence of Global Climate Law

Note: Contents: 1 Computing with Formulas. - 1.1 The First Programming Encounter: a Formula. - 1.1.1 Using a Program as a Calculator. - 1.1.2 About Programs and Programming. - 1.1.3 Tools for Writing Programs. - 1.1.4 Writing and Running Your First Python Program. - 1.1.5 Warning About Typing Program Text. - 1.1.6 Verifying the Result. - 1.1.7 Using Variables. - 1.1.8 Names of Variables. - 1.1.9 Reserved Words in Python. - 1.1.10 Comments. - 1.1.11 Formatting Text and Numbers. - 1.2 Computer Science Glossary. - 1.3 Another Formula: Celsius-Fahrenheit Conversion. - 1.3.1 Potential Error: Integer Division. - 1.3.2 Objects in Python. - 1.3.3 Avoiding Integer Division. - 1.3.4 Arithmetic Operators and Precedence. - 1.4 Evaluating Standard Mathematical Functions. - 1.4.1 Example: Using the Square Root Function. - 1.4.2 Example: Computing with sinh x. - 1.4.3 A First Glimpse of Rounding Errors. - 1.5 Interactive Computing. - 1.5.1 Using the Python Shell. - 1.5.2 Type Conversion. - 1.5.3 IPython. - 1.6 Complex Numbers. - 1.6.1 Complex Arithmetics in Python. - 1.6.2 Complex Functions in Python. - 1.6.3 Unified Treatment of Complex and Real Functions. - 1.7 Symbolic Computing. - 1.7.1 Basic Differentiation and Integration. - 1.7.2 Equation Solving. - 1.7.3 Taylor Series and More. - 1.8 Summary. - 1.8.1 Chapter Topics. - 1.8.2 Example: Trajectory of a Ball. - 1.8.3 About Typesetting Conventions in This Book. - 1.9 Exercises. - 2 Loops and Lists. - 2.1 While Loops. - 2.1.1 A Naive Solution. - 2.1.2 While Loops. - 2.1.3 Boolean Expressions. - 2.1.4 Loop Implementation of a Sum. - 2.2 Lists. - 2.2.1 Basic List Operations. - 2.2.2 For Loops. - 2.3 Alternative Implementations with Lists and Loops. - 2.3.1 While Loop Implementation of a for Loop. - 2.3.2 The Range Construction. - 2.3.3 For Loops with List Indices. - 2.3.4 Changing List Elements. - 2.3.5 List Comprehension. - 2.3.6 Traversing Multiple Lists Simultaneously. - 2.4 Nested Lists. - 2.4.1 A table as a List of Rows or Columns. - 2.4.2 Printing Objects. - 2.4.3 Extracting Sublists. - 2.4.4 Traversing Nested Lists. - 2.5 Tuples. - 2.6 Summary. - 2.6.1 Chapter Topics. - 2.6.2 Example: Analyzing List Data. - 2.6.3 How to Find More Python Information. - 2.7 Exercises. - 3 Functions and Branching. - 3.1 Functions. - 3.1.1 Mathematical Functions as Python Functions. - 3.1.2 Understanding the Program Flow. - 3.1.3 Local and Global Variables. - 3.1.4 Multiple Arguments. - 3.1.5 Function Argument or Global Variable?. - 3.1.6 Beyond Mathematical Functions. - 3.1.7 Multiple Return Values. - 3.1.8 Computing Sums. - 3.1.9 Functions with No Return Values. - 3.1.10 Keyword Arguments. - 3.1.11 Doc Strings. - 3.1.12 Functions as Arguments to Functions. - 3.1.13 The Main Program. - 3.1.14 Lambda Functions. - 3.2 Branching. - 3.2.1 If-else Blocks. - 3.2.2 Inline if Tests. - 3.3 Mixing Loops, Branching, and Functions in Bioinformatics Examples. - 3.3.1 Counting Letters in DNA Strings. - 3.3.2 Efficiency Assessment. - 3.3.3 Verifying the Implementations. - 3.4 Summary. - 3.4.1 Chapter Topics. - 3.4.2 Example: Numerical Integration. - 3.5 Exercises. - 4 User Input and Error Handling. - 4.1 Asking Questions and Reading Answers. - 4.1.1 Reading Keyboard Input. - 4.2 Reading from the Command Line. - 4.2.1 Providing Input on the Command Line. - 4.2.2 A Variable Number of Command-Line Arguments. - 4.2.3 More on Command-Line Arguments. - 4.3 Turning User Text into Live Objects. - 4.3.1 The Magic Eval Function. - 4.3.2 The Magic Exec Function. - 4.3.3 Turning String Expressions into Functions. - 4.4 Option-Value Pairs on the Command Line. - 4.4.1 Basic Usage of the Argparse Module. - 4.4.2 Mathematical Expressions as Values. - 4.5 Reading Data from File. - 4.5.1 Reading a File Line by Line. - 4.5.2 Alternative Ways of Reading a File. - 4.5.3 Reading a Mixture of Text and Numbers. - 4.6 Writing Data to File. - 4.6.1 Example: Writing a Table to File. - 4.6.2 Standard Input and Output as File Objects. - 4.6.3 What is a File, Really?. - 4.7 Handling Errors. - 4.7.1 Exception Handling. - 4.7.2 Raising Exceptions. - 4.8 A Glimpse of Graphical User Interfaces. - 4.9 Making Modules. - 4.9.1 Example: Interest on Bank Deposits. - 4.9.2 Collecting Functions in a Module File. - 4.9.3 Test Block. - 4.9.4 Verification of the Module Code. - 4.9.5 Getting Input Data. - 4.9.6 Doc Strings in Modules. - 4.9.7 Using Modules. - 4.9.8 Distributing Modules. - 4.9.9 Making Software Available on the Internet. - 4.10 Making Code for Python 2 and 3. - 4.10.1 Basic Differences Between Python 2 and 3. - 4.10.2 Turning Python 2 Code into Python 3 Code. - 4.11 Summary. - 4.11.1 Chapter Topics. - 4.11.2 Example: Bisection Root Finding. - 4.12 Exercises. - 5 Array Computing and Curve Plotting. - 5.1 Vectors. - 5.1.1 The Vector Concept. - 5.1.2 Mathematical Operations on Vectors. - 5.1.3 Vector Arithmetics and Vector Functions. - 5.2 Arrays in Python Programs. - 5.2.1 Using Lists for Collecting Function Data. - 5.2.2 Basics of Numerical Python Arrays. - 5.2.3 Computing Coordinates and Function Values. - 5.2.4 Vectorization. - 5.3 Curve Plotting. - 5.3.1 MATLAB-Style Plotting with Matplotlib. - 5.3.2 Matplotlib; Pyplot Prefix. - 5.3.3 SciTools and Easyviz. - 5.3.4 Making Animations. - 5.3.5 Making Videos. - 5.3.6 Curve Plots in Pure Text. - 5.4 Plotting Difficulties. - 5.4.1 Piecewisely Defined Functions. - 5.4.2 Rapidly Varying Functions. - 5.5 More Advanced Vectorization of Functions. - 5.5.1 Vectorization of StringFunction Objects. - 5.5.2 Vectorization of the Heaviside Function. - 5.5.3 Vectorization of a Hat Function. - 5.6 More on Numerical Python Arrays. - 5.6.1 Copying Arrays. - 5.6.2 In-Place Arithmetics. - 5.6.3 Allocating Arrays. - 5.6.4 Generalized Indexing. - 5.6.5 Testing for the Array Type. - 5.6.6 Compact Syntax for Array Generation. - 5.6.7 Shape Manipulation. - 5.7 High-Performance Computing with Arrays. - 5.7.1 Scalar Implementation. - 5.7.2 Vectorized Implementation. - 5.7.3 Memory-Saving Implementation. - 5.7.4 Analysis of Memory Usage. - 5.7.5 Analysis of the CPU Time. - 5.8 Higher-Dimensional Arrays. - 5.8.1 Matrices and Arrays. - 5.8.2 Two-Dimensional Numerical Python Arrays. - 5.8.3 Array Computing. - 5.8.4 Matrix Objects. - 5.9 Some Common Linear Algebra Operations. - 5.9.1 Inverse, Determinant, and Eigenvalues. - 5.9.2 Products. - 5.9.3 Norms. - 5.9.4 Sum and Extreme Values. - 5.9.5 Indexing. - 5.9.6 Transpose and Upper/Lower Triangular Parts. - 5.9.7 Solving Linear Systems. - 5.9.8 Matrix Row and Column Operations. - 5.9.9 Computing the Rank of a Matrix. - 5.9.10 Symbolic Linear Algebra. - 5.10 Plotting of Scalar and Vector Fields. - 5.10.1 Installation. - 5.10.2 Surface Plots. - 5.10.3 Parameterized Curve. - 5.10.4 Contour Lines. - 5.10.5 The Gradient Vector Field. - 5.11 Matplotlib. - 5.11.1 Surface Plots. - 5.11.2 Contour Plots. - 5.11.3 Vector Field Plots. - 5.12 Mayavi. - 5.12.1 Surface Plots. - 5.12.2 Contour Plots. - 5.12.3 Vector Field Plots. - 5.12.4 A 3D Scalar Field and Its Gradient Field. - 5.12.5 Animations. - 5.13 Summary. - 5.13.1 Chapter Topics. - 5.13.2 Example: Animating a Function. - 5.14 Exercises. - 6 Dictionaries and Strings. - 6.1 Dictionaries. - 6.1.1 Making Dictionaries. - 6.1.2 Dictionary Operations. - 6.1.3 Example: Polynomials as Dictionaries. - 6.1.4 Dictionaries with Default Values and Ordering. - 6.1.5 Example: Storing File Data in Dictionaries. - 6.1.6 Example: Storing File Data in Nested Dictionaries. - 6.1.7 Example: Reading and Plotting Data Recorded at Specific Dates. - 6.2 Strings. - 6.2.1 Common Operations on Strings. - 6.2.2 Example: Reading Pairs of Numbers. - 6.2.3 Example: Reading Coordinates. - 6.3 Reading Data fromWeb Pages. - 6.3.1 About Web Pages. - 6.3.2 How to Access Web Pages