Introduction to Mathematical Methods for Environmental Engineers and Scientists E-Book
Charles Prochaska
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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
The authors' aim is to offer the reader the fundamentals of numerous mathematical methods with accompanying practical environmental applications. The material in this book addresses mathematical calculations common to both the environmental science and engineering professionals. It provides the reader with nearly 100 solved illustrative examples and the interrelationship between both theory and applications is emphasized in nearly all of the 35 chapters. One key feature of this book is that the solutions to the problems are presented in a stand-alone manner. Throughout the book, the illustrative examples are laid out in such a way as to develop the reader's technical understanding of the subject in question, with more difficult examples located at or near the end of each set. In presenting the text material, the authors have stressed the pragmatic approach in the application of mathematical tools to assist the reader in grasping the role of mathematical skills in environmental problem-solving situations. The book is divided up into 5 parts: * Introduction; Analytical Analysis; Numerical Analysis; Statistical Analysis; and Optimization. * The analytical analysis includes graphical, trial-and-error, search, etc. methods. * The numerical analysis includes integration, differentiation, differential equation, Monte Carlo, etc. * The statistical analysis includes probability, probability distribution, decision trees, regression analysis, etc. * Optimization includes both traditional approaches and linear programming.
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Veröffentlichungsjahr: 2018
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Contents
Cover
Title page
Copyright page
Dedication
Preface
Part I: Introductory Principles
Chapter 1: Fundamentals and Principles of Numbers
1.1 Interpolation and Extrapolation
1.2 Significant Figures and Approximate Numbers [1]
1.3 Errors
1.4 Propagation of Errors
Chapter 2: Series Analysis
2.1 Other Infinite Series
2.2 Tests for Convergence and Divergence [2]
2.3 Infinite Series Equations
References
Chapter 3: Graphical Analysis
3.1 Rectangular Coordinates
3.2 Logarithmic-Logarithmic (Log-Log) Coordinates
3.3 Semilogarithmic (Semi-Log) Coordinates
3.4 Other Graphical Coordinates
3.5 Methods of Plotting Data
References
Chapter 4: Flow Diagrams
4.1 Process Schematics
4.2 Flow Chart Symbols
4.3 Preparing Flow Diagrams
4.4 Simplified Flow Diagrams
4.5 Hazard Risk Assessment Flow Chart
References
Chapter 5: Dimensional Analysis
5.1 The Metric System [1]
5.2 The SI System
5.3 Conversion of Units
5.4 Select Common Abbreviations [1]
5.5 Dimensionless Numbers
5.6 Buckingham Pi (π) Theorem
References
Chapter 6: Economics
6.1 Definitions
6.2 The Need for an Economic Analysis [1]
6.3 Capital Investment and Risk
6.4 Applications
References
Chapter 7: Problem Solving
7.1 Sources of Information [1]
7.2 Generic Problem-Solving Techniques [6]
7.3 An Approach
7.4 Some General Concerns
Part II: Analytical Analysis
Chapter 8: Analytical Geometry
8.1 Rectangular Coordinates
8.2 Cylindrical Coordinates
8.3 Spherical Coordinates
8.4 Key Physical Equations
8.5 Applications
Chapter 9: Differentiation
9.1 Graphical Methods
9.2 Finite Differences
Chapter 10: Integration
10.1 Graphical Integration
10.2 The Rectangle Method [5]
10.3 The Method of Rectangles
10.4 The Method of Trapezoids
10.5 Rayleigh Equation for Simple Batch (Differential) Distillation
References
Chapter 11: Differential Calculus
11.1 Differential Operations
11.2 Ordinary Differential Equations
11.3 Partial Differential Equations
11.4 Maxima and Minima
References
Chapter 12: Integral Calculus
12.1 Analytical integration
12.2 Indefinite Integrals
12.3 Definite Integrals
12.4 Integration Applications
References
Chapter 13: Matrix Algebra [1]
13.1 Definitions
13.2 Rules for Determinants and Matricies
13.3 Rank and Solution of Linear Equations
13.4 Linear Equations
References
Chapter 14: Laplace Transforms
14.1 Laplace Transform Theorems
14.2 Laplace Transforms of Specific Functions
14.3 Splitting Proper Rational Fractions into Partial Fractions
14.4 Converting An Ordinary Differential Equation (ODE) Into An Algebraic Equation
14.5 Converting a Partial Differential Equation (PDE) into an Ordinary Differential Equation (ODE)
References
Part III: Numerical Analysis
Chapter 15: Trial-and-Error Solutions
15.1 Square Root Calculations
15.2 Quadratic and Cubic Equations
15.3 Two or More Simultaneous Non-Linear Equations
15.4 Higher Order Algebraic Equations
15.5 Other Approaches
References
Chapter 16: Nonlinear Algebraic Equations
16.1 The Reguli-Falsi (False Position) Method
16.2 Newton-Raphson Method
16.3 Newton’s Second Order Method
References
Chapter 17: Simultaneous Linear Algebraic Equations
17.1 Notation For Solving Simultaneous Linear Algebraic Equations
17.2 Gauss Elimination Method
17.3 Gauss-Jordan Reduction Method
17.4 Gauss-Seidel Method
References
Chapter 18: Differentiation
18.1 Employing Two and Three Point Formulas
18.2 Employing Five Point Formulas
18.3 Method of Least Squares
References
Chapter 19: Integration
19.1 Trapezoidal Rule
19.2 Simpson’s Rule
19.3 Comparing the Trapezoidal and Simpson’s Rules
References
Chapter 20: Ordinary Differential Equations
20.1 Finite Difference/Lumped Parameter Method
20.2 Runge-Kutta Method
20.3 Runge-Kutta-Gill Method
20.4 Several Ordinary Differential Equations
20.5 Higher Order Ordinary Differential Equations
Chapter 21: Partial Differential Equations
21.1 Partial Differential Equation (PDE) Classification
21.2 Parabolic Partial Differential Equations
21.3 Parabolic PDE with Three Independent Variables
21.4 Elliptical Partial Differential Equations
References
Part IV: Statistical Analysis
Chapter 22: Basic Probability Concepts
22.1 Probability Definitions
22.2 Permutations and Combinations
22.3 Series and Parallel Systems
References
Chapter 23: Estimation of Mean and Variance
23.1 Estimation of the Mean
23.2 Estimation of the Variance
23.3 Interpretation of Mean and Variance
Reference
Chapter 24: Discrete Probability Distributions
24.1 The Binomial Distribution
24.2 Hypergeometric Distribution
24.3 Poisson Distribution
Chapter 25: Continuous Probability Distributions
25.1 Exponential Distribution
25.2 Weibull Distribution
25.3 Normal Distribution
25.5 Log-Normal Distribution
Reference
Chapter 26: Fault Tree and Event Tree Analysis [1]
26.1 Fault Trees
26.2 Event Trees
References
Chapter 27: Monte Carlo Simulation
27.1 Exponential Distribution Applications
27.2 Normal Distribution Applications
27.3 Heat Conduction Applications
References
Chapter 28: Regression Analysis [1, 2]
28.1 Scatter Diagrams
28.2 Method of Least Squares
28.3 The Correlation Coefficient
References
Part V: Optimization
Chapter 29: Introduction to Optimization
29.1 The History of Optimization
29.2 The Computer Age
29.3 The Scope Of Optimization
References
Chapter 30: Perturbation Techniques
30.1 One Independent Variable
30.2 Two Independent Variables
30.3 Three Independent Variables
30.4 The Heat Exchange Network Dilemma
References
Chapter 31: Search Methods
31.1 Interval Halving
31.2 Golden Section
31.4 Steepest Ascent/Descent
References
Chapter 32: Graphical Approaches
32.1 Rectangular Coordinates
32.2 Logarithmic-Logarithmic (Log-Log) Coordinates
32.3 Semilogarithmic (Semi-Log) Coordinates
32.4 Methods of Plotting Data
32.5 Optimization Illustrative Examples
References
Chapter 33: Analytical Approaches
33.1 Breakeven Considerations
33.2 One Independent Variable
33.3 General Analytical Formulation of the Optimum
33.4 Two Independent Variables
33.5 Three Independent Variables
References
Chapter 34: Introduction to Linear Programming
34.1 Definitions
34.2 Basic Concepts of Optimization
34.3 Applied Mathematics Concepts on Linear Programming
34.4 Applied Engineering Concepts in Linear Programming
34.5 Applied Engineering Concepts in Linear Programming
References
Chapter 35: Linear Programming Applications
References
Index
End User License Agreement
Guide
Cover
Copyright
Contents
Begin Reading
List of Tables
Chapter 1
Table 1.1
Reservoir height vs. time in days.
Table 1.2
Information for Illustrative Example 1.1.
Table 1.3
Investment data.
Table 1.4
Rotary dryer experiment data.
Chapter 3
Table 3.1
Log data.
Table 3.2
Log data.
Table 3.3
Procedures for plotting equations.
Chapter 5
Table 5.1
Conversion constants.
Table 5.2
Selected common abbreviations.
Table 5.3
Dimensionless numbers [2].
Chapter 6
Table 6.1
Costs results for two different sized pipes.
Chapter 11
Table 11.1
Differential operations.
Chapter 12
Table 12.1
Indefinite integrals.
Table 12.2
Definite integrals.
Chapter 14
Table 14.1
Special Laplace Transforms.
Chapter 15
Table 15.1
Calculated results for Illustrative Example 15.3.
Chapter 18
Table 18.1
Concentration-Time data.
Chapter 19
Table 19.1
Trapezoid rule for various step sizes.
Table 19.2
Values of
I
vs
x
; Illustrative Example 19.3.
Chapter 20
Table 20.1
Concentration profile via three methods.
Chapter 22
Table 22.1
Subsets of permutations and combinations.
Table 22.2
Describing equations for permutations and combinations.
Chapter 23
Table 23.1
SO
2
calculations.
Chapter 23
Table 24.1
Binomial and Poisson Comparison.
Chapter 24
Table 25.1
Standard normal cumulative probability; right-hand tail.
Table 25.2
Estuary BOD data.
Table 25.3
BOD calculations.
Chapter 27
Table 27.1
Simulated time to failure.
Table 27.2
Simulated values of
Z
Table 27.3
Minimum simulated values.
Table 27.4
Thermometer data.
Table 27.5
Thermometer random numbers.
Table 27.6
Lifetime of thermometer A (
T
A
).
Table 27.7
Lifetime of thermometer B (
T
B
).
Table 27.8
Lifetime of thermometer C (
T
C
).
Table 27.9
Thermometer system lifetime.
Table 27.10
Thermometer standard deviation calculation.
Chapter 28
Table 28.1
Temperature – biological yield data.
Table 28.2
Reaction rate data.
Table 28.3
Transistor resistance – failure time data.
Table 28.4
Benzene / toluene equilibrium data.
Chapter 30
Table 30.1
Calculations for Illustrative Example 30.1.
Table 30.2
Illustrative Example 30.2 calculation.
Table 30.3
Streams to be heated.
Table 30.4
Streams to be cooled.
Chapter 31
Table 31.1
Results of Illustrative Example 31.4.
Chapter 32
Table 32.1
Plotting procedure.
Table 32.2
Optimal
T
and
P
results
Chapter 35
Table 35.1
Catcracker information
Table 35.2
Drug laboratory production time expenditure (hours); Illustrative Example 35.7.
Table 35.3
Process data for butadiene plant; Illustrative Example 35.8.
Table 35.4
Profit function table; Illustrative Example 35.8.
Table 35.5
Establish maximum profit.
Table 35.6
Problem solution; Illustrative Example 35.8.
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Scrivener Publishing 100 Cummings Center, Suite 541J Beverly, MA 01915-6106
Publishers at Scrivener Martin Scrivener ([email protected]) Phillip Carmical ([email protected])
Introduction to Mathematical Methods for Environmental Engineers and Scientists
Charles Prochaska
Louis Theodore
This edition first published 2018 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA © 2018 Scrivener Publishing LLC For more information about Scrivener publications please visit www.scrivenerpublishing.com.
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Library of Congress Cataloging-in-Publication Data
ISBN 978-1-119-36349-1
To
my parents who have provided immeasurable support in every aspect of my life (CP)
and
Arthur Lovely, a truly great guy and the world’s greatest sports historian… ever (LT)
Preface
It is no secret that in recent years the number of people entering the environmental field has increased at a near exponential rate. Some are beginning college students and others had earlier chosen a non-technical major/career path. A large number of these individuals are today seeking technical degrees in environmental engineering or in the environmental sciences. These prospective students will require an understanding and appreciation of the numerous mathematical methods that are routinely employed in practice. This technical steppingstone to a successful career is rarely provided at institutions that award technical degrees. This introductory text on mathematical methods attempts to supplement existing environmental curricula with a sorely needed tool to eliminate this void.
The question often arises as to the educational background required for meaningful analysis capabilities since technology has changed the emphasis that is placed on certain mathematical subjects. Before computer usage became popular, instruction in environmental analysis was (and still is in many places) restricted to simple systems and most of the effort was devoted to solving a few derived elementary equations. These cases were mostly of academic interest, and because of their simplicity, were of little practical value. To this end, a considerable amount of time is now required to acquire skills in mathematics, especially in numerical methods, statistics, and optimization. In fact, most environmental engineers and scientists are given courses in classical mathematics, but experience shows that very little of this knowledge is retained after graduation for the simple reason that these mathematical methods are not adequate for solving most systems of equations encountered in industry. In addition, advanced mathematical skills are either not provided in courses or are forgotten through sheer disuse.
As noted in the above paragraph, the material in this book was prepared primarily for beginning environmental engineering and science students and, to a lesser extent, for environmental professionals who wish to obtain a better understanding of the various mathematical methods that can be employed in solving technical problems. The content is such that it is suitable both for classroom use and for individual study. In presenting the text material, the authors have stressed the pragmatic approach in the application of mathematical tools to assist the reader in grasping the role of mathematical skills in environmental problem solving situations.
In effect, this book serves two purposes. It may be used as a textbook for beginning environmental students or as a “reference” book for practicing engineers, scientists, and technicians involved with the environment. The authors have assumed that the reader has already taken basic courses in physics and chemistry, and should have a minimum background in mathematics through elementary calculus. The authors’ aim is to offer the reader the fundamentals of numerous mathematical methods with accompanying practical environmental applications. The reader is encouraged through references to continue his or her own development beyond the scope of the presented material.
As is usually the case in preparing any text, the question of what to include and what to omit has been particularly difficult. The material in this book attempts to address mathematical calculations common to both the environmental engineering and science professionals. The book provides the reader with nearly 100 solved illustrative examples. The interrelationship between both theory and applications is emphasized in nearly all of the chapters. One key feature of this book is that the solutions to the problems are presented in a stand-alone manner. Throughout the book, the illustrative examples are laid out in such a way as to develop the reader’s technical understanding of the subject in question, with more difficult examples located at or near the end of each set.
The book is divided up into five (V) parts (see also the Table of Contents):
I. Introduction
II. Analytical Analysis
III. Numerical Analysis
IV. Statistical Analysis
V. Optimization
Most chapters contain a short introduction to the mathematical method in question, which is followed by developmental material, which in turn, is followed by one or more illustrative examples. Thus, this book offers material not only to individuals with limited technical background but also to those with extensive environmental industrial experience. As noted above, this book may be used as a text in either a general introductory environmental engineering/ science course and (perhaps) as a training tool in industry for challenged environmental professionals.
Hopefully, the text is simple, clear, to the point, and imparts a basic understanding of the theory and application of many of the mathematical methods employed in environmental practice. It should also assist the reader in helping master the difficult task of explaining what was once a very complicated subject matter in a way that is easily understood. The authors feel that this delineates this text from the numerous others in this field.
It should also be noted that the authors have long advocated that basic science courses – particularly those concerned with mathematics – should be taught to engineers and applied scientists by an engineer or applied scientist. Also, the books adopted for use in these courses should be written by an engineer or an applied scientist. For example, a mathematician will lecture on differentiation – say dx/dy – not realizing that in a real-world application involving an estuary y could refer to concentration while x could refer to time. The reader of this book will not encounter this problem.
The reader should also note that parts of the material in the book were drawn from one of the author’s notes of yesteryear. In a few instances, the original source was not available for referencing purposes. Any oversight will be corrected in a later printing/edition.
The authors wish to express appreciation to those who have contributed suggestions for material covered in this book. Their comments have been very helpful in the selection and presentation of the subject matter. Special appreciation is extended to Megan Menzel for her technical contributions and review, Dan McCloskey for preparing some of the first draft material in Parts II and III, and Christopher Testa for his contributions to Chapters 13 and 14. Thanks are also due to Rita D’Aquino, Mary K. Theodore, and Ronnie Zaglin.
Finally, the authors are especially interested in learning the opinions of those who read this book concerning its utility and serviceability in meeting the needs for which it was written. Corrections, improvements and suggestions will be considered for inclusion in later editions.
Chuck ProchaskaLou Theodore April 2018
Part IINTRODUCTORY PRINCIPLES
Webster defines introduction as … “the preliminary section of a book, usually explaining or defining the subject matter …” And indeed, that is exactly what this Part I of the book is all about. The chapters contain material that one might view as a pre-requisite for the specific mathematical methods that are addressed in Parts II–V.
There are seven chapters in Part I. The chapter numbers and accompanying titles are listed below.
Chapter 1: Fundamentals and Principles of Numbers
Chapter 2: Series Analysis
Chapter 3: Graphical Analysis
Chapter 4: Flow Diagrams
Chapter 5: Dimensional Analysis
Chapter 6: Economics
Chapter 7: Problem Solving
