College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory

Learning mathematical modeling need not be difficult. Unlike other books, this book not only lists the equations one-by-one, but explains in detail how they are each derived, used, and finally assembled into a computer program for model simulations. This book shows how mathematics is applied in agriculture, in particular to modeling the growth and yield of a generic crop. Topics covered are agriculture meteorology, solar radiation interception and absorption, evapotranspiration, energy and soil water balance, soil water flow, photosynthesis, respiration, and crop growth development. Rather than covering many modeling approaches but in superficial detail, this book selects one or two widely-used modeling approaches and discusses about them in depth. Principles learned from this book equips readers when they encounter other modeling approaches or when they develop their own crop models.

In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers. A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites. This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models.

Noted for its crystal clear explanations, this book is considered the most comprehensive introductory text to structural equation modeling (SEM). Noted for its thorough review of basic concepts and a wide variety of models, this book better prepares readers to apply SEM to a variety of research questions. Programming details and the use of algebra are kept to a minimum to help readers easily grasp the concepts so they can conduct their own analysis and critique related research. Featuring a greater emphasis on statistical power and model validation than other texts, each chapter features key concepts, examples from various disciplines, tables and figures, a summary, and exercises. Highlights of the extensively revised 4th edition include: -Uses different SEM software (not just Lisrel) including Amos, EQS, LISREL, Mplus, and R to demonstrate applications. -Detailed introduction to the statistical methods related to SEM including correlation, regression, and factor analysis to maximize understanding (Chs. 1 – 6). -The 5 step approach to modeling data (specification, identification, estimation, testing, and modification) is now covered in more detail and prior to the modeling chapters to provide a more coherent view of how to create models and interpret results (ch. 7). -More discussion of hypothesis testing, power, sampling, effect sizes, and model fit, critical topics for beginning modelers (ch. 7). - Each model chapter now focuses on one technique to enhance understanding by providing more description, assumptions, and interpretation of results, and an exercise related to analysis and output (Chs. 8 -15). -The use of SPSS AMOS diagrams to describe the theoretical models. -The key features of each of the software packages (Ch. 1). -Guidelines for reporting SEM research (Ch. 16). -www.routledge.com/9781138811935 which provides access to data sets that can be used with any program, links to other SEM examples, related readings, and journal articles, and more. Reorganized, the new edition begins with a more detailed introduction to SEM including the various software packages available, followed by chapters on data entry and editing, and correlation which is critical to understanding how missing data, non-normality, measurement, and restriction of range in scores affects SEM analysis. Multiple regression, path, and factor models are then reviewed and exploratory and confirmatory factor analysis is introduced. These chapters demonstrate how observed variables share variance in defining a latent variables and introduce how measurement error can be removed from observed variables. Chapter 7 details the 5 SEM modeling steps including model specification, identification, estimation, testing, and modification along with a discussion of hypothesis testing and the related issues of power, and sample and effect sizes.Chapters 8 to 15 provide comprehensive introductions to different SEM models including Multiple Group, Second-Order CFA, Dynamic Factor, Multiple-Indicator Multiple-Cause, Mixed Variable and Mixture, Multi-Level, Latent Growth, and SEM Interaction Models. Each of the 5 SEM modeling steps is explained for each model along with an application. Chapter exercises provide practice with and enhance understanding of the analysis of each model. The book concludes with a review of SEM guidelines for reporting research. Designed for introductory graduate courses in structural equation modeling, factor analysis, advanced, multivariate, or applied statistics, quantitative techniques, or statistics II taught in psychology, education, business, and the social and healthcare sciences, this practical book also appeals to researchers in these disciplines. Prerequisites include an introduction to intermediate statistics that covers correlation and regression principles.

This book shows readers how to write small, well-understood procedures in successive versions within well-defined modules with separate test drivers. With a focus on language-independent design, this book instructs readers in designing programs from specifications, and to work first with descriptions, then prototypes, through program revision. The book brings a mathematical viewpoint to concrete problems, and utilizes Modula-2 for programming examples. Each new set of concepts is accompanied by diagrams, words, and equations, in addition to question-answer dialogues that reflect the most common reader difficulties.

Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, giving students hands-on experience developing and sharpening their skills in the modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem-solving process to enhance students' problem-solving capabilities -- whatever their level. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible -- beginning with short projects -- the book facilitates their progressive development and confidence in mathematics and modeling. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

This book explains a procedure for constructing realistic stochastic differential equation models for randomly varying systems in biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation.