Mathematical Modeling : Branching Beyond Calculus

Description

Mathematical Modeling: Branching Beyond Calculus reveals the versatility of mathematical modeling. The authors present the subject in an attractive manner and flexibley manner. Students will discover that the topic not only focuses on math, but biology, engineering, and both social and physical sciences. The book is written in a way to meet the needs of any modeling course. Each chapter includes examples, exercises, and projects offering opportunities for more in-depth investigations into the world of mathematical models. The authors encourage students to approach the models from various angles while creating a more complete understanding. The assortment of disciplines covered within the book and its flexible structure produce an intriguing and promising foundation for any mathematical modeling course or for self-study. Content: Cover Half title Textbooks in mathematics Title Copyrights Contents Preface Chapter 1 Modeling Concepts, Visualization, and Interpretation 1.1 Modeling and Representation 1.2 Articulation and Interpretation Using Calculus 1.3 Transformations of Functions 1.4 Sensitivity Chapter Synthesis Chapter 2 Modeling with Calculus 2.1 Using Derivatives and Rates of Change 2.2 Optimization 2.3 Accumulation 2.4 Volumes 2.5 Sequences and Series Chapter Synthesis Chapter 3 Modeling with Linear Algebra 3.1 Systems of Linear Equations 3.2 Discrete Stochastic Processes 3.3 Optimization 3.4 Linear Techniques for Data Analysis -- Least Squares Regression3.5 Linear Techniques for Data Analysis -- Seriation 3.6 Linear Techniques for Data Analysis -- Singular Value Decompo- sition Chapter Synthesis Chapter 4 Modeling with Differential Equations 4.1 Introduction and Terminology 4.2 First Order Differential Equations 4.3 Systems of First Order Differential Equations 4.4 Second Order Differential Equations Chapter Synthesis Chapter 5 Additional Topics in Modeling 5.1 Monte Carlo Simulation 5.2 Equation-Based Models versus Agent-Based Models 5.3 Modeling Using Game Theory 5.4 Optimization with Voronoi DiagramsChapter Synthesis Bibliography Solutions Index