Calculus
Edition: 1
Copyright: 2021
Pages: 1028
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$99.54
The book presents the essential calculus material using a traditional approach and organization of the canonical collection of concepts. The writing style is clear and concise, oriented toward students’ understanding, and augmented by numerous figures, drawings, animations (movies), and lecture videos.
A major feature of the book is the abundance of new examples and exercises, both traditional and computational, which can be blended into the calculus sequence according to the instructor’s preferences.
Features of the Book
- Can be bundled with a detailed and elaborate electronic Solutions Manuals (SMs) for the odd-numbered exercises in Chapters 1–14. The SMs, written by the authors, contain all the steps in the progression toward the answer and many comments on the underlying algebra (and calculus). NOTE: These SMs are titled Calculus Single Variable Solutions Manual and Calculus Multivariable Solutions Manual and may be purchased separately.
- Includes unique sections: An Alternative to Trig Substitutions, A New Class of Arc Length Problems, A New Class of Surface Area Problems, An Overlooked Class of Solids of Revolution, and A Simplified, Rigorous Approach to the Theorems of Stokes, Green, and Gauss.
- Contains thoughtfully designed exercise sets, with exercises ranging from basic to hard, both computational and theoretical
Preface
Chapter 1 Limits
1.1 Limits: An Informal View
1.2 Limit Tools: The Graphical Method
1.3 Limit Tools: The Numerical Method
1.4 Limit Tools: The Algebraic Method
1.5 Limit Laws
1.6 One-Sided Limits
1.7 Continuous Functions
1.8 Limits Involving Infinity
1.9 The Definition of a Limit
Chapter 2 Derivatives
2.1 The Tangent Line Problem
2.2 The Derivative Function
2.3 Derivatives of Power Functions
2.4 Velocity
2.5 Differentials and Higher Derivatives
2.6 The Product and Quotient Rules
2.7 Derivatives of Trig Functions
2.8 The Chain Rule
2.9 Derivatives of Exponential and Logarithmic Functions
2.10 Implicit Differentiation
2.11 Derivatives of Inverse Functions
2.12 Hyperbolic Functions
2.13 Related Rates
Chapter 3 Applications of Derivatives
3.1 Curve Sketching: 1st Derivatives
3.2 Curve Sketching: 2nd Derivatives
3.3 Maximum and Minimum Values
3.4 Optimization
3.5 The Mean Value Theorem
3.6 L’ Hospital’s Rule
3.7 Antiderivatives and Integrals
Chapter 4 Integrals
4.1 Areas and Sums
4.2 Riemann Sums
4.3 Definite Integrals
4.4 The Fundamental Theorem of Calculus
4.5 The Substitution Method
Chapter 5 Applications of Integrals
5.1 Areas of Planar Regions
5.2 Solids with Known Sectional Area
5.3 Solids of Revolutions–Disk Method
5.4 The Washer and Shell Methods
5.5 Lengths of Curves
5.6 Surface Area of Solids of Revolutions
5.7 Force and Work
5.8 Moments and Center of Mass
Chapter 6 Techniques of Integration
6.1 Integration by Parts
6.2 Trigonometric Integrals
6.3 Trigonometric Substitutions
6.4 Partial Fractions
6.5 Integrals via a Computer Algebra System
6.6 Improper Integrals
Chapter 7 Differential Equations
7.1 Introduction to Differential Equations
7.2 Separable DEs and Modeling
7.3 First-Order Linear DEs
Chapter 8 Sequences and Series
8.1 Sequences
8.2 Infinite Series
8.3 The nth Term and Integral Tests
8.4 The Comparison Tests
8.5 The Ratio and Root Tests
8.6 Absolute and Conditional Convergence
8.7 Power Series
8.8 Taylor and Maclaurin Series
8.9 Operations on Power Series
Chapter 9 Plane Curves and Polar Coordinates
9.1 Parametric Equations
9.2 Parametric Calculus - Derivatives
9.3 Parametric Calculus - Integrals
9.4 Polar Coordinates
9.5 Polar Coordinate Calculus
9.6 Conic Sections
Chapter 10 Vectors and Geometry
10.1 Three-Dimensional Coordinate Systems
10.2 Vectors
10.3 The Dot Product
10.4 The Cross Product
10.5 Lines and Planes in Space
10.6 Cylinders and Quadric Surfaces
Chapter 11 Partial Derivatives
11.1 Functions of Two or More Variables
11.2 Multivariable Limits and Continuity
11.3 Partial Derivatives
11.4 The Chain Rule
11.5 Directional Derivatives & Gradients
11.6 Tangent Planes
11.7 Local Extrema and Saddle Points
Chapter 12 Multiple Integrals
12.1 Double Integrals and Iterated Integrals
12.2 Double Integrals over General Regions
12.3 Double Integrals in Polar Coordinates
12.4 Applications of Double Integrals
12.5 Triple Integrals
12.6 Triple Integrals in Cylindrical and Spherical Coordinates
Chapter 13 Geometry of Curves and Surfaces
13.1 Space Curves and Arc Length
13.2 Surfaces and Surface Area
Chapter 14 Vector Analysis
14.1 Vector Fields & Differential Operators
14.2 Line Integrals
14.3 The Fundamental Theorem of Line Integrals
14.4 Surface Integrals
14.5 Stokes’ Theorem - Green’s Theorem
14.6 The Divergence Theorem
Answers to Odd Exercises OA-1
Index I-1
Mylan Redfern received her BS in mathematics from Augusta College and her PhD in mathematics from Louisiana State University. She has authored numerous refereed publications in stochastic analysis and has published two books on Mathematical Computing and Calculus. She has taught all levels of mathematics at the University of Southern Mississippi, Valdosta State University, and the University of Texas, Permian Basin.
David Betounes received his BArch in architecture from the University of Southern California and his PhD in mathematics from Florida State University. He has authored numerous refereed publications in differential geometry and mathematical physics and has published four books on DEs, PDEs, Mathematical Computing, and Calculus. He has taught all levels of mathematics at the University of Southern Mississippi, Valdosta State University, and the University of Texas, Permian Basin.
The book presents the essential calculus material using a traditional approach and organization of the canonical collection of concepts. The writing style is clear and concise, oriented toward students’ understanding, and augmented by numerous figures, drawings, animations (movies), and lecture videos.
A major feature of the book is the abundance of new examples and exercises, both traditional and computational, which can be blended into the calculus sequence according to the instructor’s preferences.
Features of the Book
- Can be bundled with a detailed and elaborate electronic Solutions Manuals (SMs) for the odd-numbered exercises in Chapters 1–14. The SMs, written by the authors, contain all the steps in the progression toward the answer and many comments on the underlying algebra (and calculus). NOTE: These SMs are titled Calculus Single Variable Solutions Manual and Calculus Multivariable Solutions Manual and may be purchased separately.
- Includes unique sections: An Alternative to Trig Substitutions, A New Class of Arc Length Problems, A New Class of Surface Area Problems, An Overlooked Class of Solids of Revolution, and A Simplified, Rigorous Approach to the Theorems of Stokes, Green, and Gauss.
- Contains thoughtfully designed exercise sets, with exercises ranging from basic to hard, both computational and theoretical
Preface
Chapter 1 Limits
1.1 Limits: An Informal View
1.2 Limit Tools: The Graphical Method
1.3 Limit Tools: The Numerical Method
1.4 Limit Tools: The Algebraic Method
1.5 Limit Laws
1.6 One-Sided Limits
1.7 Continuous Functions
1.8 Limits Involving Infinity
1.9 The Definition of a Limit
Chapter 2 Derivatives
2.1 The Tangent Line Problem
2.2 The Derivative Function
2.3 Derivatives of Power Functions
2.4 Velocity
2.5 Differentials and Higher Derivatives
2.6 The Product and Quotient Rules
2.7 Derivatives of Trig Functions
2.8 The Chain Rule
2.9 Derivatives of Exponential and Logarithmic Functions
2.10 Implicit Differentiation
2.11 Derivatives of Inverse Functions
2.12 Hyperbolic Functions
2.13 Related Rates
Chapter 3 Applications of Derivatives
3.1 Curve Sketching: 1st Derivatives
3.2 Curve Sketching: 2nd Derivatives
3.3 Maximum and Minimum Values
3.4 Optimization
3.5 The Mean Value Theorem
3.6 L’ Hospital’s Rule
3.7 Antiderivatives and Integrals
Chapter 4 Integrals
4.1 Areas and Sums
4.2 Riemann Sums
4.3 Definite Integrals
4.4 The Fundamental Theorem of Calculus
4.5 The Substitution Method
Chapter 5 Applications of Integrals
5.1 Areas of Planar Regions
5.2 Solids with Known Sectional Area
5.3 Solids of Revolutions–Disk Method
5.4 The Washer and Shell Methods
5.5 Lengths of Curves
5.6 Surface Area of Solids of Revolutions
5.7 Force and Work
5.8 Moments and Center of Mass
Chapter 6 Techniques of Integration
6.1 Integration by Parts
6.2 Trigonometric Integrals
6.3 Trigonometric Substitutions
6.4 Partial Fractions
6.5 Integrals via a Computer Algebra System
6.6 Improper Integrals
Chapter 7 Differential Equations
7.1 Introduction to Differential Equations
7.2 Separable DEs and Modeling
7.3 First-Order Linear DEs
Chapter 8 Sequences and Series
8.1 Sequences
8.2 Infinite Series
8.3 The nth Term and Integral Tests
8.4 The Comparison Tests
8.5 The Ratio and Root Tests
8.6 Absolute and Conditional Convergence
8.7 Power Series
8.8 Taylor and Maclaurin Series
8.9 Operations on Power Series
Chapter 9 Plane Curves and Polar Coordinates
9.1 Parametric Equations
9.2 Parametric Calculus - Derivatives
9.3 Parametric Calculus - Integrals
9.4 Polar Coordinates
9.5 Polar Coordinate Calculus
9.6 Conic Sections
Chapter 10 Vectors and Geometry
10.1 Three-Dimensional Coordinate Systems
10.2 Vectors
10.3 The Dot Product
10.4 The Cross Product
10.5 Lines and Planes in Space
10.6 Cylinders and Quadric Surfaces
Chapter 11 Partial Derivatives
11.1 Functions of Two or More Variables
11.2 Multivariable Limits and Continuity
11.3 Partial Derivatives
11.4 The Chain Rule
11.5 Directional Derivatives & Gradients
11.6 Tangent Planes
11.7 Local Extrema and Saddle Points
Chapter 12 Multiple Integrals
12.1 Double Integrals and Iterated Integrals
12.2 Double Integrals over General Regions
12.3 Double Integrals in Polar Coordinates
12.4 Applications of Double Integrals
12.5 Triple Integrals
12.6 Triple Integrals in Cylindrical and Spherical Coordinates
Chapter 13 Geometry of Curves and Surfaces
13.1 Space Curves and Arc Length
13.2 Surfaces and Surface Area
Chapter 14 Vector Analysis
14.1 Vector Fields & Differential Operators
14.2 Line Integrals
14.3 The Fundamental Theorem of Line Integrals
14.4 Surface Integrals
14.5 Stokes’ Theorem - Green’s Theorem
14.6 The Divergence Theorem
Answers to Odd Exercises OA-1
Index I-1
Mylan Redfern received her BS in mathematics from Augusta College and her PhD in mathematics from Louisiana State University. She has authored numerous refereed publications in stochastic analysis and has published two books on Mathematical Computing and Calculus. She has taught all levels of mathematics at the University of Southern Mississippi, Valdosta State University, and the University of Texas, Permian Basin.
David Betounes received his BArch in architecture from the University of Southern California and his PhD in mathematics from Florida State University. He has authored numerous refereed publications in differential geometry and mathematical physics and has published four books on DEs, PDEs, Mathematical Computing, and Calculus. He has taught all levels of mathematics at the University of Southern Mississippi, Valdosta State University, and the University of Texas, Permian Basin.