Download PDF CALCULUS EARLY TRANSCENDENTALS 9TH Edition by HOWARD ANTON

Sinopsis

One of the important themes in calculus is the analysis of relationships between physical or mathematical quantities. Such relationships can be described in terms of graphs, formulas, numerical data, or words. In this chapter we will develop the concept of a “function,” which is the basic idea that underlies almost all mathematical and physical relationships, regardless of the form in which they are expressed. We will study properties of some of the most basic functions that occur in calculus, including polynomials, trigonometric functions, inverse trigonometric functions, exponential functions, and logarithmic functions.

Many scientific laws and engineering principles describe how one quantity depends on another. This idea was formalized in 1673 by Gottfried Wilhelm Leibniz (see p. xx) who coined the term function to indicate the dependence of one quantity on another, as described in the following definition.

In the mid-eighteenth century the Swiss mathematician Leonhard Euler (pronounced “oiler”) conceived the idea of denoting functions by letters of the alphabet, thereby making it possible to refer to functions without stating specific formulas, graphs, or tables. To understand Euler’s idea, think of a function as a computer program that takes an input x, operates on it in some way, and produces exactly one output y. The computer program is an object in its own right, so we can give it a name, say f . Thus, the function f (the computer program) associates a unique output y with each input x (Figure 0.1.2). This suggests the following definition.

Content

1. BEFORE CALCULUS
2. LIMITS AND CONTINUITY
3. THE DERIVATIVE
4. TOPICS IN DIFFERENTIATION
5. THE DERIVATIVE IN GRAPHING AND APPLICATIONS
6. INTEGRATION
7. APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING
8. PRINCIPLES OF INTEGRAL EVALUATION
9. MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
10. INFINITE SERIES
11. PARAMETRIC AND POLAR CURVES; CONIC SECTIONS
12. THREE-DIMENSIONAL SPACE; VECTORS
13. VECTOR-VALUED FUNCTIONS
14. PARTIAL DERIVATIVES
15. MULTIPLE INTEGRALS
16. TOPICS IN VECTOR CALCULUS

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Download PDF Calculus For The Practical Man by D. Van Nostrand

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Download PDF Applied Statistics Using SPSS, STATISTICA, MATLAB and R by Joaquim P. Marques de Sá

Sinopsis

This book is intended as a reference book for students, professionals and research workers who need to apply statistical analysis to a large variety of practical problems using STATISTICA, SPSS and MATLAB. The book chapters provide a comprehensive coverage of the main statistical analysis topics (data description, statistical inference, classification and regression, factor analysis, survival data, directional statistics) that one faces in practical problems, discussing their solutions with the mentioned software packages.

The only prerequisite to use the book is an undergraduate knowledge level of mathematics. While it is expected that most readers employing the book will have already some knowledge of elementary statistics, no previous course in probability or statistics is needed in order to study and use the book. The first two chapters introduce the basic needed notions on probability and statistics. In addition, the first two Appendices provide a short survey on Probability Theory and Distributions for the reader needing further clarification on the theoretical foundations of the statistical methods described.

The book is partly based on tutorial notes and materials used in data analysis disciplines taught at the Faculty of Engineering, Porto University. One of these management. The students in this course have a variety of educational backgrounds and professional interests, which generated and brought about datasets and analysis objectives which are quite challenging concerning the methods to be applied and the interpretation of the results. The datasets used in the book examples and exercises were collected from these courses as well as from research. They are included in the book CD and cover a broad spectrum of areas: engineering, medicine, biology, psychology, economy, geology, and astronomy.

Every chapter explains the relevant notions and methods concisely, and is illustrated with practical examples using real data, presented with the distinct intention of clarifying sensible practical issues. The solutions presented in the examples are obtained with one of the software packages STATISTICA, SPSS or MATLAB; therefore, the reader has the opportunity to closely follow what is being done. The book is not intended as a substitute for the STATISTICA, SPSS and MATLAB user manuals. It does, however, provide the necessary guidance for applying the methods taught without having to delve into the manuals. This includes, for each topic explained in the book, a clear indication of which

STATISTICA, SPSS or MATLAB tools to be applied. These indications appear in use the tools, whenever necessary. In this way, a comparative perspective of the specific “Commands” frames together with a complementary description on how tocapabilities of those software packages is also provided, which can be quite useful for practical purposes.

STATISTICA, SPSS or MATLAB do not provide specific tools for some of the statistical topics described in the book. These range from such basic issues as the choice of the optimal number of histogram bins to more advanced topics such as directional statistics. The book CD provides these tools, including a set of MATLAB functions for directional statistics.

Content

1. Introduction
2. Presenting and Summarising the Data
3. Estimating Data Parameters
4. Parametric Tests of Hypotheses
5. Non-Parametric Tests of Hypotheses
6. Statistical Classification
7. Data Regression
8. Data Structure Analysis
9. Survival Analysis
10. Directional Data

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Download PDF Computational Statistics Handbook with MATLAB® by Wendy L. Martinez

Sinopsis

Obviously, computational statistics relates to the traditional discipline of statistics. So, before we define computational statistics proper, we need to get a handle on what we mean by the field of statistics. At a most basic level, statistics is concerned with the transformation of raw data into knowledge [Wegman, 1988]. 

Statistics is concerned with the science of uncertainty and can help the scientist deal with these questions. Many classical methods (regression, hypothesis testing, parameter estimation, confidence intervals, etc.) of statistics developed over the last century are familiar to scientists and are widely used in many disciplines [Efron and Tibshirani, 1991].
 

Now, what do we mean by computational statistics? Here we again follow the definition given in Wegman [1988]. Wegman defines computational statistics as a collection of techniques that have a strong “focus on the exploitation of computing in the creation of new statistical methodology.

Content

1. Introduction
2. Probability Concepts
3. Sampling Concepts
4. Generating Random Variables
5. Exploratory Data Analysis
6. Monte Carlo Methods for Inferential Statistics
7. Data Partitioning
8. Probability Density Estimation
9. Statistical Pattern Recognition
10. Nonparametric Regression
11. Markov Chain Monte Carlo Methods
12. Spatial Statistics

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Download PDF SCHAUM’S Easy OUTLINES PROBABILITY AND STATISTICS by MIKE LEVAN

Sinopsis

In many cases the number of sample points in a sample space is not very large, and so direct enumeration or counting of sample points needed to obtain probabilities is not difficult. However, problems arise where direct counting becomes a practical impossibility. In such cases use is made of combinatorial analysis, which could also be called a sophisticated way of counting.

Content

1. Basic Probability
2. Descriptive Statistics
3. Discrete Random Variables
4. Continuous Random Variables
5. Examples of Random Variables
6. Sampling Theory
7. Estimation Theory
8. Test of Hypothesis and Significance
9. Curve Fitting, Regression, and Correlation
10. Other Probability Distributions
11. Mathematical Topics
12. Areas under the Standard Normal Curve from 0 to z

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Download PDF STATISTICS IN PSYCHOLOGY AND EDUCATION BY HENRY E. GARRETT

Sinopsis

In the measurement of mental and social traits or capacities most of the facts with which we deal fall into what are known as continuous series. A continuous series may be defined simply as a series which is theoretically capable of any degree of subdivision. JQ's, for example, are generally thought of as increasing by increments of 1 on a scale which extends from the idiot to the genius; however, there is actually no real reason at least theoretically why with more refined methods of measurement we should not be able to get IQ's of 100.8 or even 100.83. Nearly all capacities measured by mental and educational tests and scales, as well as such attributes as height, weight, cephalic index, etc., have been found to be continuous, so that within the range of the scale used, any measure integral or fractional may exist and have meaning. Whenever gaps occur in a truly continuous series, therefore, these are usually to be attributed to our failure to measure enough cases, or to the relative crudity of our measuring instruments, or to some other fact of the same sort, rather than to the fact that no measures exist within the gaps.

There are, however, measures which do not fall into continuous series. Thus a salary scale in a department store may run from $10 per week to $20 per week in units of 50 cents or $1.00; no one receives, let us say, $17.53 per week. Or, to take another example, the average family in a certain locality may work out mathematically to be 4.57 children, although there is obviously a real gap between four and five children. Series like these, which contain real gaps, are called discrete or discontinuous. It is probably fortunate—at least from the standpoint of the beginner in statistics—that nearly all of the measures which we make in psychology are continuous or can be treated as continuous. This considerably simplifies the problem, inasmuch as we may concern ourselves (for the present at least) almost entirely with methods of handling continuous data, postponing the discussion of discrete series to a later page.

Content

1. The Tabulation of Measures into a Frequency Distribution
2. Measures of Central Tendency
3. Measures of Variability
4. The Short Method of Finding the Average, AD, and SD(a)
5. The Comparison of Groups
6. The Calculation of the Percentiles in a Frequency Distribution
7. When to Use the Different Measures of Central Tendency and Variability
8. Summary of Formulas for Finding the Measures of Central Tendency and Variability

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Download PDF Linear Algebra with Applications Eighth Edition by Steven J. Leon

Sinopsis

Probably the most important problem in mathematics is that of solving a system of linear equations. Well over 75 percent of all mathematical problems encountered in scientific or industrial applications involve solving a linear system at some stage. By using the methods of modern mathematics, it is often possible to take a sophisticated problem and reduce it to a single system of linear equations. Linear systems arise in applications to such areas as business, economics, sociology, ecology, demography, genetics, electronics, engineering, and physics. Therefore, it seems appropriate to begin this book with a section on linear systems.

Content

1. Matrices and Systems of Equations
2. Systems of Linear Equations
3. Row Echelon Form
4. Matrix Arithmetic
5. Matrix Algebra
6. Elementary Matrices
7. Partitioned Matrices
8. Determinants
9. The Determinant of a Matrix
10. Properties of Determinants
11. Additional Topics and Applications
12. Vector Spaces
13. Definition and Examples
14. Subspaces
15. Linear Independence
16. Basis and Dimension
17. Change of Basis
18. Row Space and Column Space
19. Linear Transformations
20. Definition and Examples
21. Matrix Representations of Linear Transformations
22. Similarity
23. Orthogonality
24. The Scalar Product in Rn
25. Orthogonal Subspaces
26. Least Squares Problems
27. Inner Product Spaces
28. Orthonormal Sets
29. The Gram–Schmidt Orthogonalization Process
30. Orthogonal Polynomials
31. Eigenvalues
32. Eigenvalues and Eigenvectors
33. Diagonalization
34. Hermitian Matrices
35. The Singular Value Decomposition
36. Quadratic Forms
37. Positive Definite Matrices
38. Nonnegative Matrices
39. Numerical Linear Algebra
40. Floating-Point Numbers
41. Gaussian Elimination
42. Pivoting Strategies
43. Matrix Norms and Condition Numbers
44. Orthogonal Transformations
45. The Eigenvalue Problem
46. Least Squares Problems
47. Iterative Methods

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Download PDF Statistics for Business and Economics EIGHTH EDITION by Paul Newbold

Sinopsis

Statistics are used to predict or forecast sales of a new product, construction costs, customer-satisfaction levels, the weather, election results, university enrollment figures, grade point averages, interest rates, currencyexchange rates, and many other variables that affect our daily lives. We need to absorb and interpret substantial amounts of data. Governments, businesses, and scientific researchers spend billions of dollars collecting data. But once data are collected, what do we do with them? How do data impact decision making?

In our study of statistics we learn many tools to help us process, summarize, analyze, and interpret data for the purpose of making better decisions in an uncertain environment. Basically, an understanding of statistics will permit us to make sense of all the data.

In this chapter we introduce tables and graphs that help us gain a better understanding of data and that provide visual support for improved decision making. Reports are enhanced by the inclusion of appropriate tables and graphs, such as frequency distributions, bar charts, pie charts, Pareto diagrams, line charts, histograms, stem-and-leaf displays, or ogives. Visualization of data is important. We should always ask the following questions: What does the graph suggest about the data? What is it that we see?

Content

1. CHAPTER 1 Describing Data: Graphical 
2. CHAPTER 2 Describing Data: Numerical 
3. CHAPTER 3 Probability 
4. CHAPTER 4 Discrete Random Variables and Probability Distributions 
5. CHAPTER 5 Continuous Random Variables and Probability Distributions 
6. CHAPTER 6 Sampling and Sampling Distributions 
7. CHAPTER 7 Estimation: Single Population 
8. CHAPTER 8 Estimation: Additional Topics 
9. CHAPTER 9 Hypothesis Testing: Single Population 
10. CHAPTER 10 Hypothesis Testing: Additional Topics 
11. CHAPTER 11 Simple Regression 
12. CHAPTER 12 Multiple Regression 
13. CHAPTER 13 Additional Topics in Regression Analysis
14. CHAPTER 14 Analysis of Categorical Data 
15. CHAPTER 15 Analysis of Variance 
16. CHAPTER 16 Time-Series Analysis and Forecasting 
17. CHAPTER 17 Additional Topics in Sampling

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Download PDF TIME AND CHANCE by DAVID Z ALBERT

Sinopsis

What I want to talk about here is a certain tension between fundamental microscopic physical theory and everyday macroscopic human experience, a tension that comes up (more particularly) in connection with the question of precisely how the past is different from the future.

And the fundamental theory in which it will work best to start that talk out, the fundamental theory (that is) in which this tension is at its purest and most straightforward, is the mechanics of Newton. Never mind (for the moment) that the mechanics of Newton turns out not to be the mechanics of the actual world.1 We’ll talk about that later.

▲▲▲ According to Newtonian mechanics, or at any rate according to the particularly clean and simple version of it that I want to start off with here, the physical furniture of the universe consists entirely of point particles. The only dynamical variables of such particles—the only physical attributes of such particles that can change with time—are (on this theory) their positions; and (consequently) a list of what particles exist, and of what sorts of particles they are,2 and of what their positions are at all times, is a list of absolutely everything there is to say about the physical history of the world.3

Content

1. Time-Reversal Invariance
2. Thermodynamics
3. Statistical Mechanics
4. The Reversibility Objections and the Past-Hypothesis 
5. The Scope of Thermodynamics
6. The Asymmetries of Knowledge and Intervention
7. Quantum Mechanics

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Download PD Tracking Control of Linear System by Lyubomir T. Gruyitch

Sinopsis

Time is not only the basic constituent of the existence, but it is also the crucial physical variable for every process, every motion, for the work of every dynamic system, hence for every control system. The behavior of every plant, of its controller and of its control system occurs in time. The physical reality, the human experience with it, the human understanding, the accumulated human knowledge lead to the following de…nition of time.

Content

1. Introduction
2. Control Systems
3. System Regimes
4. Transfer function matrix G(s)
5. Problem statement
6. Nondegenerate matrices
7. Full transfer function matrix F(s)
8. Tracking theory
9. Trackability theory
10. Linear tracking control (LITC)
11. Lyapunov Tracking Control (LTC)
12. Natural Tracking Control (NTC)
13. NTC versus LTC

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Download PDF Applied Speech and Audio Processing: With MATLAB Examples by Ian McLoughlin

Sinopsis

Audio and speech processing systems have steadily risen in importance in the everyday lives of most people in developed countries. From ‘Hi-Fi’ music systems, through radio to portable music players, audio processing is firmly entrenched in providing entertainment to consumers. Digital audio techniques in particular have now achieved a domination in audio delivery, with CD players, Internet radio, MP3 players and iPods being the systems of choice in many cases. Even within television and film studios, and in mixing desks for ‘live’ events, digital processing now predominates. Music and sound effects are even becoming more prominent within computer games.

Speech processing has equally seen an upward worldwide trend, with the rise of cellular communications, particularly the European GSM (Global System for Mobile communications) standard. GSM is now virtually ubiquitous worldwide, and has seen tremendous adoption even in the world’s poorest regions.

Of course, speech has been conveyed digitally over long distance, especially satellite communications links, for many years, but even the legacy telephone network (named POTS for ‘Plain Old Telephone Services’) is now succumbing to digitisation in many countries. The last mile, the several hundred metres of twisted pair copper wire running to a customer’s home, was never designed or deployed with digital technology in mind, and has resisted many attempts over the years to be replaced with optical fibre, Ethernet or wireless links. However with DSL (digital subscriber line – normally asymmetric so it is faster in one direction than the other, hence ADSL), even this analogue twisted pair will convey reasonably high-speed digital signals. ADSL is fast enough to have allowed the rapid growth of Internet telephony services such as Skype which, of course, convey 

digitised speech.

Content

1. Introduction
2. Basic audio processing
3. Speech
4. Hearing
5. Speech communications
6. Audio analysis
7. Advanced topics

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Download PDF Numerical Analysis NINTH EDITION by Richard L. Burden

Sinopsis

This book was written for a sequence of courses on the theory and application of numerical approximation techniques. It is designed primarily for junior-level mathematics, science, and engineering majors who have completed at least the standard college calculus sequence. Familiarity with the fundamentals of linear algebra and differential equations is useful, but there is sufficient introductory material on these topics so that courses in these subjects are not needed as prerequisites.

The book contains sufficient material for at least a full year of study, but we expect many people to use it for only a single-term course. In such a single-term course, students learn to identify the types of problems that require numerical techniques for their solution and see examples of the error propagation that can occur when numerical methods are applied. They accurately approximate the solution of problems that cannot be solved exactly and learn typical techniques for estimating error bounds for the approximations. The remainder of the text then serves as a reference for methods not considered in the course. Either the full-year or single-course treatment is consistent with the philosophy of the text.

Virtually every concept in the text is illustrated by example, and this edition contains more than 2600 class-tested exercises ranging from elementary applications of methods and algorithms to generalizations and extensions of the theory. In addition, the exercise sets include numerous applied problems from diverse areas of engineering as well as from the physical, computer, biological, economic, and social sciences. The chosen applications clearly and concisely demonstrate how numerical techniques can be, and often must be, applied in real-life situations.

Content

1. Mathematical Preliminaries and Error Analysis
2. Solutions of Equations in One Variable
3. Interpolation and Polynomial Approximation
4. Numerical Differentiation and Integration
5. Initial-Value Problems for Ordinary Differential Equations
6. Direct Methods for Solving Linear Systems
7. IterativeTechniques in Matrix Algebra
8. ApproximationTheory
9. Approximating Eigenvalues
10. Numerical Solutions of Nonlinear Systems of Equations
11. Boundary-Value Problems for Ordinary Differential Equations
12. Numerical Solutions to Partial Differential Equations

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Download PDF CALCULUS SEVENTH EDITION by JAMES STEWART

Sinopsis

Calculus is fundamentally different from the mathematics that you have studied previously: calculus is less static and more dynamic. It is concerned with change and motion; it deals with quantities that approach other quantities. For that reason it may be useful to have an overview of the subject before beginning its intensive study. Here we give a glimpse of some of the main ideas of calculus by showing how the concept of a limit arises when we attempt to solve a variety of problems.

Content

1. Functions and Limits
2. Derivatives
3. Applications of Differentiation
4. Integrals
5. Applications of Integration
6. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
7. Techniques of Integration
8. Further Applications of Integration
9. Differential Equations
10. Parametric Equations and Polar Coordinates
11. Infinite Sequences and Series
12. Vectors and the Geometry of Space
13. Vector Functions
14. Partial Derivatives
15. Multiple Integrals
16. Vector Calculus
17. Second-Order Differential Equations

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COLLEGE ALGEBRA For First Year and Pre-Degree Student by Kulkarni

Content

1 Sets 

2 Real Numbers 

3 Complex Numbers

4 Indices ( Exponents ) .

5 Logarithms 

6 Surds

7 Quadratic Equations 

8 Method of Induction 

9 Progressions 

10 Summation of Series 

11 Permutations and Combinations 

12 Binomial Theorem 

13 Determinants

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Download PDF DIAGNOSTIC AND STATISTICAL MANUAL OF MENTAL DISORDERS FOURTH EDITION TEXT REVISION

Content

1. Introduction
2. Cautionary Statement 
3. Use of the Manual
4. DSM-IV-TR Classification
5. Multiaxial Assessment
6. Disorders Usually First Diagnosed in  Infancy, Childhood, or Adolescence
7. Delirium, Dementia, and Amnestic and  Other Cognitive Disorders
8. Mental Disorders Due to a General Medical Condition
9. Substance-Related Disorders
10. Schizophrenia and  Other Psychotic Disorders
11. Mood Disorders
12. Anxiety Disorders
13. Somatoform Disorders
14. Factitious Disorders
15. Dissociative Disorders
16. Sexual and Gender Identity Disorders
17. Eating Disorders
18. Sleep Disorders
19. Impulse-Control Disorders Not Elsewhere Classified
20. Adjustment Disorders
21. Personality Disorders
22. Other Conditions That May Be a Focus of Clinical Attention
23. Additional Codes
    
    
    

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Downlod PDF DSP for MATLAB and LabVIEW Volume III: Digital Filter Design

Content

1. Principles of FIR Design
2. FIR Design Techniques
3. Classical IIR Design
4. Software for Use with this Book
5. Vector/Matrix Operations in M-Code
6. FIR Frequency Sampling Design Formulas

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Download PDF CALCULUS III Paul Dawkins

Sinopsis

In this chapter we will start taking a more detailed look at three dimensional space (3-D space or ¡3 ). This is a very important topic in Calculus III since a good portion of Calculus III is done in three (or higher) dimensional space.

We will be looking at the equations of graphs in 3-D space as well as vector valued functions and how we do calculus with them. We will also be taking a look at a couple of new coordinate systems for 3-D space.

This is the only chapter that exists in two places in my notes. When I originally wrote these notes all of these topics were covered in Calculus II however, we have since moved several of them into Calculus III. So, rather than split the chapter up I have kept it in the Calculus II notes and also put a copy in the Calculus III notes. Many of the sections not covered in Calculus III will be used on occasion there anyway and so they serve as a quick reference for when we need them.

Content

1. Three Dimensional Space
2. Partial Derivatives
3. Applications of Partial Derivatives
4. Multiple Integrals
5. Line Integrals
6. Surface Integrals

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Download PDF Applied Statistics and Probability for Engineers Third Edition by Douglas C. Montgomery

Sinopsis

ENGINEERING METHOD AND STATISTICAL THINKING An engineer is someone who solves problems of interest to society by the efficient application of scientific principles. Engineers accomplish this by either refining an existing product or process or by designing a new product or process that meets customers’ needs. The engineering, or scientific, method is the approach to formulating and solving these problems. The steps in the engineering method are as follows:

1. Develop a clear and concise description of the problem.
2. Identify, at least tentatively, the important factors that affect this problem or that may play a role in its solution.
3. Propose a model for the problem, using scientific or engineering knowledge of the phenomenon being studied. State any limitations or assumptions of the model.
4. Conduct appropriate experiments and collect data to test or validate the tentative model or conclusions made in steps 2 and 3.
5. Refine the model on the basis of the observed data.
6. Manipulate the model to assist in developing a solution to the problem.
7. Conduct an appropriate experiment to confirm that the proposed solution to the problem is both effective and efficient.
8. Draw conclusions or make recommendations based on the problem solution.

The steps in the engineering method are shown in Fig. 1-1. Notice that the engineering method features a strong interplay between the problem, the factors that may influence its solution, a model of the phenomenon, and experimentation to verify the adequacy of the model and the proposed solution to the problem. Steps 2–4 in Fig. 1-1 are enclosed in a box, indicating that several cycles or iterations of these steps may be required to obtain the final solution. Consequently, engineers must know how to efficiently plan experiments, collect data, analyze and interpret the data, and understand how the observed data are related to the model they have proposed for the problem under study.

The field of statistics deals with the collection, presentation, analysis, and use of data to make decisions, solve problems, and design products and processes. Because many aspects of engineering practice involve working with data, obviously some knowledge of statistics is important to any engineer. Specifically, statistical techniques can be a powerful aid in designing new products and systems, improving existing designs, and designing, developing, and improving production processes.

Content

1. The Role of Statistics in Engineering
2. Probability
3. Discrete Random Variables and Probability Distributions 
4. Continuous Random Variables and Probability Distributions
5. Joint Probability Distributions
6. Random Sampling and Data Description
7. Point Estimation of Parameters
8. Statistical Intervals for a Single Sample
9. Tests of Hypotheses for a Single Sample
10. Statistical Inference for Two Samples
11. Simple Linear Regression and Correlation
12. Design and Analysis of Single-Factor Experiments: The Analysis of Variance
13. Design of Experiments with Several Factors
14. Nonparametric Statistics
15. Statistical Quality Control

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Download PDF Engineering Statistics Fifth Edition by Douglas C. Montgomery

Sinopsis

Engineering is about bridging the gaps between problems and solutions, and that process requires an approach called the scientific method.

In 2009 Eileen Huffman, an undergraduate student in civil engineering at Virginia Tech, applied the scientific method to her study of an antique bridge. The Ironto Wayside Footbridge was built in 1878 and is the oldest standing metal bridge in Virginia. Although it has now been restored as a footbridge, in its former life it routinely carried heavy wagonloads, three tons or more, of goods and materials. Ms. Huffman conducted a historical survey of the bridge and found that a load-bearing analysis had never been done. Her problem was to conduct the first known load-bearing analysis of the bridge.

After gathering the available structural data on the bridge, she created a computer model stress analysis based on typical loads that it would have carried. After analyzing her results, she tested them on the bridge itself to verify her model. She set up dial gauges under the center of each truss. She then had a 3.5-ton truck, typical of the load weight the bridge would have carried, drive over the bridge.

The results from this test will be contributed to the Adaptive Bridge Use Project based at the University of Massachusetts Amherst and supported by the National Science Foundation (www.ecs.umass.edu/adaptive_bridge_use/). Her results and conclusions will be helpful in maintaining the bridge and in helping others to restore and study historic bridges. Her adviser Cris Moen points out that her computer model can be used to create structural models to test other bridges.

Ms. Huffman’s study reflects careful use of the scientific method in the context of an engineering project. It is an excellent example of using sample data to verify an engineering model.

Content

1. The Role of Statistics in Engineering
2. Data Summary and Presentation
3. Random Variables and Probability Distributions
4. Decision Making for a Single Sample
5. Decision Making for Two Samples
6. Building Empirical Models
7. Design of Engineering Experiments
8. Statistical Process Control

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Download PDF Essential Medical Statistics Second Editon by Betty R Kirkwood

Sinopsis

Statistics is the science of collecting, summarizing, presenting and interpreting data, and of using them to estimate the magnitude of associations and test hypotheses. It has a central role in medical investigations. Not only does it provide a way of organizing information on a wider and more formal basis than relying on the exchange of anecdotes and personal experience, it takes into account the intrinsic variation inherent in most biological processes. For example, not only does blood pressure differ from person to person, but in the same person it also varies from day to day and from hour to hour. It is the interpretation of data in the presence of such variability that lies at the heart of statistics. Thus, in investigating morbidity associated with a particular stressful occupation, statistical methods would be needed to assess whether an observed average blood pressure above that of the general population could simply be due to chance variations or whether it represents a real indication of an occupational health risk.

Variability can also arise unpredictably (randomly) within a population. Individuals do not all react in the same way to a given stimulus. Thus, although smoking and heavy drinking are in general bad for the health, we may hear of a heavy smoker and drinker living to healthy old age, whereas a non-smoking teetotaller may die young. As another example, consider the evaluation of a new vaccine. Individuals vary both in their responsiveness to vaccines and in their susceptibility and exposure to disease. Not only will some people who are unvaccinated escape infection, but also a number of those who are vaccinated may contract the disease. What can be concluded if the proportion of people free from the disease is greater among the vaccinated group than among the unvaccinated? How effective is the vaccine? Could the apparent effect just be due to chance? Or, was there some bias in the way people were selected for vaccination, for example were they of different ages or social class, such that their baseline risk of contracting the disease was already lower than those selected into the non-vaccinated group? The methods of statistical analysis are used to address the first two of these questions, while the choice of an appropriate design should exclude the third. This example illustrates that the usefulness of statistics is not confined to the analysis of results. It also has a role to play in the design and conduct of a study.

In this first part of the book we cover the basics needed to understand data and commence formal statistical analysis. In Chapter 1 we describe how to use the book to locate the statistical methods needed in different situations, and to progress from basic techniques and concepts to more sophisticated analyses.

Content

1. Basics
2. Analysis of numerical outcomes
3. Analysis of binary outcomes
4. Longitudinal studies: Analysis of rates and survival times
5. Statistical modelling
6. Study design, analysis and interpretation

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