Mathematical modeling and applied calculus
This textbook is rich with real-life data sets, uses RStudio to streamline computations, builds "big picture" conceptual understandings, and applies them in diverse settings. Mathematical Modeling and Applied Calculus will develop the insights and skills needed to describe and model many d...
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| Main Authors | , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Oxford
Oxford University Press
2018
Oxford University Press, Incorporated |
| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9780198824725 0198824726 0198824734 9780198824732 |
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| Abstract | This textbook is rich with real-life data sets, uses RStudio to streamline computations, builds "big picture" conceptual understandings, and applies them in diverse settings. Mathematical Modeling and Applied Calculus will develop the insights and skills needed to describe and model many different aspects of our world. This textbook provides an excellent introduction to the process of mathematical modeling, the method of least squares, and both differentialand integral calculus, perfectly meeting the needs of today's students. Mathematical Modeling and Applied Calculus provides a modern outline of the ideas of Calculus and is aimed at those who do not intend to enter the traditional calculus sequence. Topics that are not traditionally taught in a one-semester Calculus course, such as dimensional analysis and the method of least squares, are woven together with the ideas of mathematical modeling and the ideas of calculus to provide a rich experience and a large toolbox of mathematical techniques for futurestudies. Additionally, multivariable functions are interspersed throughout the text, presented alongside their single-variable counterparts. This text provides a fresh take on these ideas that is ideal for the modern student. |
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| AbstractList | This textbook is rich with real-life data sets, uses RStudio to streamline computations, builds "big picture" conceptual understandings, and applies them in diverse settings. Mathematical Modeling and Applied Calculus will develop the insights and skills needed to describe and model many different aspects of our world. This textbook provides an excellent introduction to the process of mathematical modeling, the method of least squares, and both differentialand integral calculus, perfectly meeting the needs of today's students. Mathematical Modeling and Applied Calculus provides a modern outline of the ideas of Calculus and is aimed at those who do not intend to enter the traditional calculus sequence. Topics that are not traditionally taught in a one-semester Calculus course, such as dimensional analysis and the method of least squares, are woven together with the ideas of mathematical modeling and the ideas of calculus to provide a rich experience and a large toolbox of mathematical techniques for futurestudies. Additionally, multivariable functions are interspersed throughout the text, presented alongside their single-variable counterparts. This text provides a fresh take on these ideas that is ideal for the modern student. Mathematical Modeling and Applied Calculus is a modern take on modeling and calculus aimed at students who need some experience with these ideas. |
| Author | McAllister, Alex M. Kilty, Joel |
| Author_xml | – sequence: 1 fullname: Kilty, Joel – sequence: 2 fullname: McAllister, Alex M. |
| BackLink | https://cir.nii.ac.jp/crid/1130000795207588992$$DView record in CiNii |
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| ISBN | 9780198824725 0198824726 0198824734 9780198824732 |
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| Notes | Includes index |
| OCLC | 1119640075 |
| PQID | EBC5891965 |
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| PublicationDate | 2018 2018-09-13 |
| PublicationDateYYYYMMDD | 2018-01-01 2018-09-13 |
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| PublicationPlace | Oxford |
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| Publisher | Oxford University Press Oxford University Press, Incorporated |
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| Snippet | Mathematical Modeling and Applied Calculus is a modern take on modeling and calculus aimed at students who need some experience with these ideas. This textbook is rich with real-life data sets, uses RStudio to streamline computations, builds "big picture" conceptual understandings, and applies them in... |
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| SubjectTerms | Calculus Mathematical models |
| TableOfContents | Cover -- Mathematical Modeling and Applied Calculus -- Copyright -- Dedication -- Contents -- Preface -- Overview of the Book -- Pedagogical Features -- Course Designs -- Acknowledgments -- Chapter 1. Functions for Modeling Data -- 1.1 Functions -- Tabular Functions and Nonfunctions -- Graphical Functions and Nonfunctions -- Analytic Presentations of Functions -- Piecewise Functions -- Exercises -- 1.2 Multivariable Functions -- Exercises -- 1.3 Linear Functions -- Parameters of Linear Functions -- Monotonicity -- Exercises -- 1.4 Exponential Functions -- Recognizing Exponential Functions Graphically -- Parameters of Exponential Functions -- Concavity -- Algebra of Exponents -- Exercises -- 1.5 Inverse Functions -- Tabular Inverses -- Graphical Inverses -- Existence of Inverses -- Monotonicity and Inverses -- Finding Inverses Algebraically -- Exercises -- 1.6 Logarithmic Functions -- Logarithms as Parametrized Families of Functions -- Algebra of Logarithms -- Logarithms and Exponential Models -- Semi-log Plots and Log-Log Plots -- Exercises -- 1.7 Trigonometric Functions -- Measuring Angles -- Right Triangle Definitions of Trigonometric Functions -- The Unit Circle Definitions of Trigonometric Functions -- Graphs of Trigonometric Functions -- Trigonometric Identities -- Exercises -- Chapter 2. Mathematical Modeling -- 2.1 Modeling with Linear Functions -- Numerically Identifying Linear Data Sets -- Conjecturing Linear Models -- Best Possible Linear Models -- Exercises -- 2.2 Modeling with Exponential Functions -- Numerically Identifying Exponential Data Sets -- Conjecturing Exponential Models -- Best Possible Exponential Models -- Exercises -- 2.3 Modeling with Power Functions -- Graphically Identifying Power Functional Data Sets -- Numerically Identifying Power Functional Data Sets -- Conjecturing Power Function Models Starting Values and Ending Criteria -- Determining Points of Intersection -- Optimization Using Newton's Method -- Understanding Newton's Method -- Newton's Method and Dimensions -- Exercises -- 5.5 Multivariable Optimization -- Contour Plots and Extreme Values -- Critical Points -- Multivariable Second Derivative Test -- Global Extreme Values -- Exercises -- 5.6 Constrained Optimization -- The Gradient -- Properties of the Gradient -- Constrained Optimization -- Understanding the Lagrange Multiplier -- Method of Lagrange Multipliers -- Understanding the Method of Lagrange Multipliers -- Exercises -- Chapter 6. Accumulation and Integration -- 6.1 Accumulation -- Left and Right Approximations -- Midpoint Rule -- Obtaining More Accurate Approximations -- Riemann Sums -- Exercises -- 6.2 The Definite Integral -- Net Accumulation and Geometry -- Dimensions and Units of Definite Integrals -- Properties of the Definite Integral -- Understanding the Algebraic Properties of Integrals -- Exercises -- 6.3 First Fundamental Theorem -- The Net Accumulation Function -- The First Fundamental Theorem of Calculus -- Antiderivatives of Modeling Functions -- Exercises -- 6.4 Second Fundamental Theorem -- Using the Second Fundamental Theorem -- Area Between Curves -- Understanding the Fundamental Theorems -- A Partial Proof of the Fundamental Theorems -- Exercises -- 6.5 The Method of Substitution -- The Chain Rule -- Antiderivatives via Substitution -- Substitution with Intermediate Algebra -- The Method of Substitution and Definite Integrals -- Understanding Di↵erentials -- Exercises -- 6.6 Integration by Parts -- Method of Integration by Parts -- Choosing f(x) and g'(x) -- Integration by Parts and Definite Integrals -- Understanding Integration by Parts -- Exercises -- Appendix A. Answer to Questions -- Section 1.1 Questions -- Section 1.2 Questions Best Possible Power Function Models -- Logarithmic Scale Plots -- Exercises -- 2.4 Modeling with Sine Functions -- The Sine Function -- Parameters of Sine Functions -- Conjecturing Sine Models -- Best Possible Sine Models -- Exercises -- 2.5 Modeling with Sigmoidal Functions -- Parameters of Sigmoidal Functions -- Conjecturing Sigmoidal Models -- Best Possible Sigmoidal Models -- Exercises -- 2.6 Single-Variable Modeling -- Graphically Identifying Reasonable Models -- Context and Choosing Models -- Refining Models Using More Data -- A Limitation of Mathematical Models -- Exercises -- 2.7 Dimensional Analysis -- Fundamental and Derived Dimensions -- Arithmetic with Dimensions and Units -- Solving for Unknown Dimensions -- Generalized Products -- Dimensional Analysis -- Exercises -- Chapter 3. The Method of Least Squares -- 3.1 Vectors and Vector Operations -- Three Vector Operations -- A Geometric Interpretation of Scalar Multiplication -- A Geometric Interpretation of Vector Addition -- An Introduction to Vector Fields -- Exercises -- 3.2 Linear Combinations of Vectors -- Finding Desired Linear Combinations -- Vector Equations as Matrix Equations -- Matrix-Vector Multiplication -- Solving Matrix Equations -- Exercises -- 3.3 Existence of Linear Combinations -- Linear Combinations of Two Vectors -- Linear Combinations of Three or More Vectors -- Linear Combinations and Data Sets -- Exercises -- 3.4 Vector Projection -- The Dot Product -- Geometry of the Dot Product -- Residual Vectors -- Vector Projection -- Understanding Vector Projection -- Exercises -- 3.5 The Method of Least Squares -- Applying the Method of Least Squares -- The Residual Vector of Minimal Length -- Understanding the Method of Least Squares -- Exercises -- Chapter 4. Derivatives -- 4.1 Rates of Change -- Average Rate of Change -- Instantaneous Rate of Change Appendix C. Getting Started with RStudio Section 1.3 Questions -- Section 1.4 Questions -- Section 1.5 Questions -- Section 1.6 Questions -- Section 1.7 Questions -- Section 2.1 Questions -- Section 2.2 Questions -- Section 2.3 Questions -- Section 2.4 Questions -- Section 2.5 Questions -- Section 2.6 Questions -- Section 2.7 Questions -- Section 3.1 Questions -- Section 3.2 Questions -- Section 3.3 Questions -- Section 3.4 Questions -- Section 3.5 Questions -- Section 4.1 Questions -- Section 4.2 Questions -- Section 4.3 Questions -- Section 4.4 Questions -- Section 4.5 Questions -- Section 4.6 Questions -- Section 4.7 Questions -- Section 5.1 Questions -- Section 5.2 Questions -- Section 5.3 Questions -- Section 5.4 Questions -- Section 5.5 Questions -- Section 5.6 Questions -- Section 6.1 Questions -- Section 6.2 Questions -- Section 6.3 Questions -- Section 6.4 Questions -- Section 6.5 Questions -- Section 6.6 Questions -- Appendix B. Answers to Odd-Numbered Exercises -- Section 1.1 Exercises -- Section 1.2 Exercises -- Section 1.3 Exercises -- Section 1.4 Exercises -- Section 1.5 Exercises -- Section 1.6 Exercises -- Section 1.7 Exercises -- Section 2.1 Exercises -- Section 2.2 Exercises -- Section 2.3 Exercises -- Section 2.4 Exercises -- Section 2.5 Exercises -- Section 2.6 Exercises -- Section 2.7 Exercises -- Section 3.1 Exercises -- Section 3.2 Exercises -- Section 3.3 Exercises -- Section 3.4 Exercises -- Section 3.5 Exercises -- Section 4.1 Exercises -- Section 4.2 Exercises -- Section 4.3 Exercises -- Section 4.4 Exercises -- Section 4.6 Exercises -- Section 4.7 Exercises -- Section 5.1 Exercises -- Section 5.2 Exercises -- Section 5.3 Exercises -- Section 5.4 Exercises -- Section 5.5 Exercises -- Section 5.6 Exercises -- Section 6.1 Exercises -- Section 6.2 Exercises -- Section 6.3 Exercises -- Section 6.4 Exercises -- Section 6.5 Exercises -- Section 6.6 Exercises Tangent Line Question and Fermat's Solution -- Exercises -- 4.2 The Derivative as a Function -- Existence of Derivatives -- Dimensions and Derivatives -- Higher-Order Derivatives -- Monotonicity of Functions -- Exercises -- 4.3 Derivatives of Modeling Functions -- Derivatives of Linear Functions -- The Power Rule -- Di↵erentiation and Basic Arithmetic -- Di↵erentiating Other Modeling Functions -- Evidence for Di↵erentiation Rules -- Tangent Lines and Linear Approximations -- Exercises -- 4.4 Product and Quotient Rules -- The Product Rule -- The Quotient Rule -- More Trigonometric Derivatives -- Differentiating with Multiple Rules -- Tabular Functions -- Exercises -- 4.5 The Chain Rule -- Composition of Functions -- The Chain Rule -- Di↵erentiating with Multiple Rules -- Tabular Functions -- Revisiting Extended Di↵erentiation Rules -- Evidence for the Chain Rule -- Exercises -- 4.6 Partial Derivatives -- Approximating Partial Derivatives -- Differentiation Rules and Partial Derivatives -- Higher-Order Partial Derivatives -- Linear Approximation -- Exercises -- 4.7 Limits and the Derivative -- Continuous Functions -- Evaluating Limits at Discontinuities -- Reprise: The Definition of the Derivative -- Exercises -- Chapter 5. Optimization -- 5.1 Global Extreme Values -- Extreme Value Theorem -- Critical Numbers -- Determining Critical Numbers from the Derivative -- Locating Global Extreme Values -- Exercises -- 5.2 Local Extreme Values -- Critical Numbers -- Critical Numbers and Monotonicity -- First Derivative Test -- Revisiting Global Extreme Values -- Exercises -- 5.3 Concavity and Extreme Values -- Concavity and Points of Inflection -- Determining Concavity Graphically -- Determining Concavity from the Second Derivative -- Second Derivative Test -- Exercises -- 5.4 Newton's Method and Optimization -- Applying Newton's Method |
| Title | Mathematical modeling and applied calculus |
| URI | https://cir.nii.ac.jp/crid/1130000795207588992 https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=5891965 https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9780192558138 |
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