Muutke küpsiste eelistusi

E-raamat: Mathematical Methods in the Earth and Environmental Sciences

(University of Georgia)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 18-Apr-2019
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108631266
Teised raamatud teemal:
  • Formaat - EPUB+DRM
  • Hind: 67,91 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Mathematical Methods in the Earth and Environmental SciencesSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 18-Apr-2019
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108631266
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

The Earth and environmental sciences are becoming progressively more quantitative due to the increased use of mathematical models and new data analysis techniques. This accessible introduction presents an overview of the mathematical methods essential for understanding Earth processes, providing an invaluable resource for students and early career researchers who may have missed (or forgotten) the mathematics they need to succeed as scientists. Topics build gently from basic methods such as calculus to more advanced techniques including linear algebra and differential equations. The practical applications of the mathematical methods to a variety of topics are discussed, ranging from atmospheric science and oceanography to biogeochemistry and geophysics. Including over 530 exercises and end-of-chapter problems, as well as additional computer codes in Python and MATLAB®, this book supports readers in applying appropriate analytical or computational methods to solving real research questions.

Muu info

An accessible introduction to the mathematical methods essential for understanding processes in the Earth and environmental sciences.
Preface xi
Acknowledgments xiii
1 Estimation and Dimensional Analysis 1(35)
1.1 Making Estimates on the Back of the Envelope
1(8)
1.2 Scaling
9(3)
1.3 Dimensional Analysis
12(8)
1.4 Dimensionless Ratios and the Pi Theorem
20(9)
1.4.1 Application of the Buckingham Pi Theorem
21(8)
1.5 Dimensional Analysis: Some Remarks
29(1)
1.6 Further Reading
30(1)
Problems
31(5)
2 Derivatives and Integrals 36(93)
2.1 Derivatives, Limits, and Continuity
36(10)
2.2 Rules for Differentiation
46(4)
2.2.1 Product Rule
47(1)
2.2.2 Chain Rule
48(1)
2.2.3 Higher-Order Derivatives
49(1)
2.3 Maxima and Minima
50(3)
2.4 Some Theorems About Derivatives
53(3)
2.5 Taylor's Theorem
56(5)
2.6 L'Hopital's Rule
61(2)
2.7 Using Derivatives
63(4)
2.7.1 Curve Sketching
63(2)
2.7.2 Newton's Method
65(2)
2.8 Partial Derivatives
67(6)
2.9 Using Partial Derivatives
73(5)
2.9.1 Propagating Uncertainty
73(3)
2.9.2 Fitting a Straight Line
76(2)
2.10 Integration
78(7)
2.10.1 Properties of Integrals
82(3)
2.11 Techniques of Integration
85(7)
2.11.1 Partial Fractions
85(2)
2.11.2 Substitution of Variables
87(2)
2.11.3 Integration by Parts
89(1)
2.11.4 Differentiation
90(1)
2.11.5 Other Methods
91(1)
2.12 Proper and Improper Integrals
92(3)
2.13 Mean Value Theorems
95(1)
2.14 Integrals, Areas, and Volumes
96(3)
2.15 Integrating Multivariate Functions
99(13)
2.15.1 Line Integrals
99(7)
2.15.2 Multiple Integrals
106(3)
2.15.3 Green's Theorem
109(3)
2.16 Numerical Evaluation of Integrals
112(8)
2.16.1 Rectangle Rules
112(4)
2.16.2 Trapezium Rule
116(2)
2.16.3 Simpson's Rule
118(2)
2.17 Further Reading
120(1)
Problems
121(8)
3 Series and Summations 129(27)
3.1 Sequences and Series
129(1)
3.2 Arithmetic and Geometric Series
130(4)
3.3 Binomial Theorem and Binomial Series
134(6)
3.4 Power Series
140(2)
3.5 Convergence Criteria
142(8)
3.5.1 Root Test
146(1)
3.5.2 Integral Test
147(2)
3.5.3 Comparison Test
149(1)
3.5.4 Alternating Series
150(1)
3.6 Double Series
150(3)
3.7 Further Reading
153(1)
Problems
153(3)
4 Scalars, Vectors, and Matrices 156(80)
4.1 Scalars and Vectors
156(1)
4.2 Vector Algebra
157(15)
4.2.1 Linear Independence and Basis Vectors
163(2)
4.2.2 Transformations of Vectors
165(4)
4.2.3 Describing Lines and Curves Using Vectors
169(3)
4.3 Multiplying Vectors Together
172(15)
4.3.1 Scalar Product
172(6)
4.3.2 Vector Product
178(7)
4.3.3 Triple Product
185(2)
4.4 Matrices
187(15)
4.4.1 Matrix Arithmetic
189(2)
4.4.2 Linear Transformations and Matrix Multiplication
191(6)
4.4.3 Inverse Matrix
197(1)
4.4.4 Special Matrices
198(4)
4.5 Solving Linear Equations with Matrices
202(15)
4.5.1 Determinants
209(8)
4.6 Kronecker Delta and Levi-Civita Symbol
217(3)
4.7 Eigenvalues and Eigenvectors
220(11)
4.8 Vectors, Matrices, and Data
231(1)
4.9 Further Reading
232(1)
Problems
233(3)
5 Probability 236(53)
5.1 What Is Probabililty?
236(6)
5.2 Random Variables, Expectation, and Variance
242(4)
5.3 Discrete Random Variables
246(10)
5.3.1 Discrete Uniform Distribution
246(3)
5.3.2 Binomial Distribution
249(4)
5.3.3 Poisson Distribution
253(3)
5.4 Continuous Random Variables
256(12)
5.4.1 Normal or Gaussian Distribution
260(8)
5.5 Law of Large Numbers and Central Limit Theorem
268(4)
5.6 Manipulating Random Variables
272(6)
5.6.1 Adding Continuous Random Variables
272(4)
5.6.2 Transforming Random Variables
276(2)
5.7 Monte Carlo Methods
278(5)
5.7.1 Monte Carlo Error Propagation
278(2)
5.7.2 Monte Carlo Integration
280(3)
5.8 Further Reading
283(1)
Problems
284(5)
6 Ordinary Differential Equations 289(117)
6.1 Terminology and Classification
294(1)
6.2 First Order Differential Equations
295(19)
6.2.1 First Order Linear Differential Equations
295(6)
6.2.2 Direction Fields
301(2)
6.2.3 First Order Nonlinear Equations
303(9)
6.2.4 A Question of Uniqueness
312(2)
6.3 Solving Differential Equations in Practice
314(6)
6.4 Second Order Differential Equations
320(17)
6.4.1 Second Order Linear Differential Equations
321(9)
6.4.2 Oscillations and Waves
330(7)
6.5 Series Solutions and Singular Solutions
337(6)
6.6 Higher Order Equations
343(1)
6.7 Differential Equations in Practice
344(3)
6.7.1 Phase Plane
346(1)
6.8 Systems of Linear Differential Equations
347(8)
6.8.1 Real, Distinct Eigenvalues
350(2)
6.8.2 Complex Conjugate Eigenvalues
352(1)
6.8.3 Repeated Roots
353(2)
6.9 Systems of Autonomous Nonlinear Equations
355(3)
6.10 Numerical Solution
358(19)
6.10.1 Euler Method and Its Relations
359(9)
6.10.2 Higher Order Methods: Runge-Kutta
368(5)
6.10.3 Boundary Value Problems
373(3)
6.10.4 Computer Algebra Systems
376(1)
6.11 Dynamical Systems and Chaos
377(9)
6.11.1 Chaos
381(5)
6.12 Boundary Value Problems, Sturm-Liouville Problems, and Green's Functions
386(11)
6.12.1 Green's Functions
394(3)
6.13 Further Reading
397(1)
Problems
398(8)
7 Vectors and Calculus 406(42)
7.1 Differentiating a Vector
406(6)
7.2 Gradient
412(3)
7.3 Divergence and Curl
415(5)
7.3.1 Vector Identities
419(1)
7.4 Curvilinear Coordinate Systems
420(6)
7.5 Integrals and Vectors
426(18)
7.5.1 Divergence Theorem
436(6)
7.5.2 Stokes' Theorem
442(2)
7.6 Further Reading
444(1)
Problems
445(3)
8 Special Functions 448(21)
8.1 Heaviside Function
448(2)
8.2 Delta Function
450(4)
8.3 Gamma and Error Functions
454(3)
8.4 Orthogonal Functions and Orthogonal Polynomials
457(2)
8.5 Legendre Polynomials
459(5)
8.5.1 Associated Legendre Functions and Spherical Harmonics
462(2)
8.6 Bessel Functions
464(2)
8.7 Further Reading
466(1)
Problems
467(2)
9 Fourier Series and Integral Transforms 469(30)
9.1 Fourier Series
469(13)
9.1.1 Complex Fourier Series
477(1)
9.1.2 Even and Odd Functions
477(1)
9.1.3 Dirichlet Conditions
478(2)
9.1.4 Parseval's Theorem
480(2)
9.1.5 Differentiating and Integrating Fourier Series
482(1)
9.2 Fourier Transform
482(10)
9.2.1 Sine and Cosine Transforms
486(1)
9.2.2 Properties of the Fourier Transform
487(3)
9.2.3 Applications of the Fourier Transform
490(2)
9.3 Laplace Transform
492(4)
9.4 Further Reading
496(1)
Problems
496(3)
10 Partial Differential Equations 499(46)
10.1 Introduction
499(2)
10.2 First Order Linear Partial Differential Equations
501(6)
10.3 Classification of Second Order Linear Partial Differential Equations
507(5)
10.3.1 Hyperbolic Equations
509(1)
10.3.2 Parabolic Equations
510(1)
10.3.3 Elliptic Equations
510(1)
10.3.4 Boundary Value Problems
511(1)
10.4 Parabolic Equations: Diffusion and Heat
512(11)
10.4.1 Solving the Diffusion Equation
515(8)
10.5 Hyperbolic Equations: Wave Equation
523(2)
10.6 Elliptic Equations: Laplace's Equation
525(1)
10.7 More Laplace Transforms
526(3)
10.8 Numerical Methods
529(10)
10.8.1 Advection Equation
531(8)
10.9 Further Reading
539(2)
Problems
541(4)
11 Tensors 545(13)
11.1 Covariant and Contravariant Vectors
545(7)
11.2 Metric Tensors
552(1)
11.3 Manipulating Tensors
553(1)
11.4 Derivatives of Tensors
554(2)
11.5 Further Reading
556(1)
Problems
556(2)
Appendix A Units and Dimensions 558(5)
A.1 International System of Units
559(2)
A.2 Converting between Units
561(2)
Appendix B Tables of Useful Formulae 563(5)
B.1 Properties of Basic Functions
563(1)
B.1.1 Trigonometric Functions
563(1)
B.1.2 Logarithms and Exponentials
564(1)
B.1.3 Hyperbolic Functions
564(1)
B.2 Some Important Series
564(1)
B.3 Some Common Derivatives
565(1)
B.4 Some Common Integrals
566(1)
B.5 Fourier and Laplace Transforms
566(1)
B.6 Further Reading
567(1)
Appendix C Complex Numbers 568(5)
C.1 Making Things Complex
568(1)
C.2 Complex Plane
569(1)
C.3 Series
569(1)
C.4 Euler's Formula
570(1)
C.5 De Moivre's Theorem
571(2)
References 573(6)
Index 579
Adrian Burd is an associate professor at the Department of Marine Sciences at the University of Georgia. As a marine scientist, he applies mathematical tools to understand marine systems, including the carbon cycle in the oceans, the health of seagrass and salt marshes, and the fate of oil spills. His work has taken him around the globe, from the heat of Laguna Madre and Florida Bay to the cold climes of Antarctica.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97811086312666e.html
Märksõnad: