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9780387342276

Introduction to Applied Mathematics for Environmental Science

by
  • ISBN13:

    9780387342276

  • ISBN10:

    0387342273

  • Format: Hardcover
  • Copyright: 2006-07-01
  • Publisher: Springer Nature
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Supplemental Materials

What is included with this book?

Summary

"Introduction to Applied Mathematics for Environmental Science evolved from the author's 30 years' experience teaching mathematics to graduate and advanced undergraduate students in the environmental sciences. Its basic purpose is to teach various types of mathematical structures and how they can be applied in a broad range of environmental science subfields. Derivatives and integrals, ordinary and partial differential equations, and linear and non-linear algebraic equations are the basic kinds of structures (types of mathematical models) discussed." "This text assumes that its readers will already have been introduced to the basic ideas of differential and integral calculus, so it is not an introduction to calculus. It does, however, include three early chapters to review basic algebra, derivatives, and integrals."--BOOK JACKET.

Table of Contents

Preface v
Contents vii
Introduction
1(18)
On Translating Ideas to Mathematics
1(3)
Pre-Calculus Math Review
4(1)
Trigonometry
5(1)
Units, Dimensions, and Conversion Factors
5(2)
Ratios and Percentages
7(1)
Analysis versus Numerical Analysis
8(2)
Notes on Significant Digits
10(3)
Exercises
13(5)
Questions and Answers
18(1)
Derivatives and Differentiation
19(33)
What Is a Derivative?
19(1)
Usefulness in Environmental Science
20(7)
Taylor Series; a Basis for Numerical Analysis
27(5)
Numerical Differentiation
32(4)
Checking Analytic Derivatives
36(1)
Exercises
37(9)
Questions and Answers
46(6)
Integration
52(30)
What is Integration?
52(1)
Usefulness in Environmental Science
53(4)
Analytic Integration
57(3)
Numerical Integration
60(5)
Differentiation-Integration Contrasts
65(3)
Exercises
68(9)
Questions and Answers
77(5)
Ordinary Differential Equations
82(41)
How ODEs Arise
82(7)
Solution of Simple First-Order ODEs
89(5)
Checking Solutions of ODEs
94(4)
Notes on Differential Equations
98(4)
Analytic Solution of First-Order ODEs
102(4)
Table of Solutions of Selected ODEs
106(3)
Analytic Solution with MATLAB
109(1)
Exercises
110(9)
Questions and Answers
119(4)
Further Topics in ODEs
123(14)
Asymptotic Behavior
123(3)
Integrating Factors
126(5)
Table of Integrals
131(1)
Exercises
132(3)
Questions and Answers
135(2)
ODE Systems
137(10)
ODEs for Multiple Response Variables
137(4)
Exercises
141(6)
Numerical Solution of ODEs
147(19)
Euler's Method
147(4)
Runge-Kutta
151(8)
Solving ODEs Numerically with MATLAB
159(1)
Exercises
160(3)
Questions and Answers
163(3)
Second-Order ODEs
166(27)
Cartesian Coordinate Systems
167(8)
Generalizations
175(1)
Heat Conduction
176(2)
Curved Geometry
178(4)
MATLAB and Second-Order ODEs
182(1)
Exercises
183(7)
Questions and Answers
190(3)
Linear Algebra
193(36)
Linear Algebraic Equations
193(1)
How Linear Systems Arise
194(3)
Solution Methods
197(11)
System Conditioning
208(4)
Matrix Population Modelling
212(3)
Other Applications
215(1)
Exercises
216(6)
Questions and Answers
222(7)
Non-Linear Equations
229(21)
Roots
230(9)
Repeated Roots
239(2)
Exercises
241(6)
Questions and Answers
247(3)
Partial Differential Equations
250(35)
Partial Derivatives
250(3)
Mass and Heat Transfer
253(6)
Schmidt's Method
259(3)
Three-Dimensional Diffusion
262(10)
Exercises
272(11)
Questions and Answers
283(2)
Pre-Calculus Math Review 285(7)
Solutions to Odd-Numbered Exercises 292(15)
List of Applications 307(3)
Bibliography 310(3)
Index 313

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