Calculus: A Complete Course

Name: Calculus: A Complete Course
Price: 4490 ISK
Availability: InStock
Author: Robert A. Adams; Christopher Essex
ISBN: 9781292498997

Höfundar: Robert A. Adams; Christopher Essex (Útgáfa: 11)

Kaup valmöguleikar

Learn everything you need to know about Calculus and practice your reasoning and practical skills with a high-end textbook suitable for a wide range of course levels. Calculus: A Complete Course, 10th Edition by Robert Adams and Christopher Essex is the ultimate guide written by two leading authors in the field that continues to build its solid core following the successful pattern of its previous editions.

With its reader-friendly language, the textbook holds a reputation for excellent accuracy and mathematical rigour, offering you study material suitable to cover a standard semester course, as well as high-end content that will help you further explore some of the unique topics and approaches in the landscape of Mathematics. Adding important, but overlooked topics while clarifying old ones, this edition will help you develop and practice your reasoning skills and apply techniques you have learned to concrete situations.

Some of the topics this edition explores include: Sufficient conditions for maxima and minima in higher dimensions: this is the only mainstream textbook that covers the topic sufficiently. The fuzzy topic of metrics: the text explores and addresses any issues and questions, leading to new gateway topics, including spherical geometry (as in navigation) and special relativity, which emerge rather effortlessly once the metric concept is in place properly.

Computers and mathematics through Maple and now Python: there is no other Calculus book that deals better with the topic while treating unique but important applications from information theory to Lévy distributions. With a wide variety of exercises and useful features to support your learning, this unique edition continues to aspire to the definition of its subtitle of “A Complete Course.” Also available with MyLab® Math MyLab is the teaching and learning platform that empowers you to reach every student.

By combining trusted author content with digital tools and a flexible platform, MyLabMath personalises the learning experience and improves results for each student. If you would like to purchase both the physical text and MyLab® Math, search for: 9780135732595 Calculus: A Complete Course, 10th Edition plus MyLab Math with Pearson eText -- Access Card Package Package consists of: 9780135732588 Calculus: A Complete Course, 10th Edition 9780135732526 Calculus: A Complete Course, 10th Edition MyLab® Math -- Standalone Access Card MyLab® Math is not included.

Students, if MyLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. MyLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

Nánar um bókina

Útgefandi: Pearson International Content

ISBN: 9781292498997

Print ISBN: 9781292499000

Format: ePub

Útgáfa: 11

Höfundar: Robert A. Adams; Christopher Essex

Tungumál: English

Útgefið: 2026-10-06

Prent takmörkun á líftíma: 100

Prent takmörkun: 2

Afritunar takmörkun: 2

Kaflar

Cover
Cover
Front Matter
Title Page
Copyright
Dedication
Contents
Preface
About the Cover
To the Student
To the Instructor
Acknowledgments
What Is Calculus
What Is Calculus?
Chapter P: Preliminaries
Introduction: Real Numbers and the Real Line
P.1 Real Numbers and the Real Line
P.2 Cartesian Coordinates in the Plane
P.3 Graphs of Quadratic Equations
P.4 Functions and Their Graphs
P.5 Combining Functions to Make New Functions
P.6 Polynomials and Rational Functions
P.7 The Trigonometric Functions
Chapter 1: Limits and Continuity
Introduction: Limits and Continuity
1.1 Examples of Velocity, Growth Rate, and Area
1.2 Limits of Functions
1.3 Limits at Infinity and Infinite Limits
1.4 Continuity
1.5 The Formal Definition of Limit
Chapter Review
Chapter 2: Differentiation
Introduction: Differentiation
2.1 Tangent Lines and Their Slopes
2.2 The Derivative
2.3 Differentiation Rules
2.4 The Chain Rule
2.5 Derivatives of Trigonometric Functions
2.6 Higher-Order Derivatives
2.7 Using Differentials and Derivatives
2.8 The Mean-Value Theorem
2.9 Implicit Differentiation
2.10 Antiderivatives and Initial-Value Problems
2.11 Velocity and Acceleration
Chapter Review
Chapter 3: Transcendental Functions
Introduction: Transcendental Functions
3.1 Inverse Functions
3.2 Exponential and Logarithmic Functions
3.3 The Natural Logarithm and Exponential Functions
3.4 Growth and Decay
3.5 The Inverse Trigonometric Functions
3.6 Hyperbolic Functions
3.7 Second-Order Linear DEs with Constant Coefficients
Chapter Review
Chapter 4: More Applications of Differentiation
Introduction: More Applications of Differentiation
4.1 Related Rates
4.2 Finding Roots of Equations
4.3 Indeterminate Forms
4.4 Extreme Values
4.5 Concavity and Inflections
4.6 Sketching the Graph of a Function
4.7 Graphing with Computers
4.8 Extreme-Value Problems
4.9 Linear Approximations
4.10 Taylor Polynomials
4.11 Roundoff Error, Truncation Error, and Computers
Chapter Review
Chapter 5: Integration
Introduction: Integration
5.1 Sums and Sigma Notation
5.2 Areas as Limits of Sums
5.3 The Definite Integral
5.4 Properties of the Definite Integral
5.5 The Fundamental Theorem of Calculus
5.6 The Method of Substitution
5.7 Areas of Plane Regions
Chapter Review
Chapter 6: Techniques of Integration
Introduction: Techniques of Integration
6.1 Integration by Parts
6.2 Integrals of Rational Functions
6.3 Inverse Substitutions
6.4 Other Methods for Evaluating Integrals
6.5 Improper Integrals
6.6 The Trapezoid and Midpoint Rules
6.7 Simpson’s Rule
6.8 Other Aspects of Approximate Integration
Chapter Review
Chapter 7: Applications of Integration
Introduction: Applications of Integration
7.1 Volumes by Slicing—Solids of Revolution
7.2 More Volumes by Slicing
7.3 Arc Length and Surface Area
7.4 Mass, Moments, and Centre of Mass
7.5 Centroids
7.6 Other Physical Applications
7.7 Applications in Business, Finance, and Ecology
7.8 Probability
7.9 First-Order Differential Equations
Chapter Review
Chapter 8: Conics, Parametric Curves, and Polar Curves
Introduction: Conics, Parametric Curves, and Polar Curves
8.1 Conics
8.2 Parametric Curves
8.3 Smooth Parametric Curves and Their Slopes
8.4 Arc Lengths and Areas for Parametric Curves
8.5 Polar Coordinates and Polar Curves
8.6 Slopes, Areas, and Arc Lengths for Polar Curves
Chapter Review
Chapter 9: Sequences, Series, and Power Series
Introduction: Sequences, Series, and Power Series
9.1 Sequences and Convergence
9.2 Infinite Series
9.3 Convergence Tests for Positive Series
9.4 Absolute and Conditional Convergence
9.5 Power Series
9.6 Taylor and Maclaurin Series
9.7 Applications of Taylor and Maclaurin Series
9.8 The Binomial Theorem and Binomial Series
9.9 Fourier Series
Chapter Review
Chapter 10: Vectors and Coordinate Geometry in 3-Space
Introduction: Vectors and Coordinate Geometry in 3-Space
10.1 Analytic Geometry in Three Dimensions
10.2 Vectors
10.3 The Cross Product in 3-Space
10.4 Planes and Lines
10.5 Quadric Surfaces
10.6 Cylindrical and Spherical Coordinates
10.7 A Little Linear Algebra
10.8 Using Maple for Vector and Matrix Calculations
Chapter Review
Chapter 11: Arc Length, Metric Spaces, and Applications
Introduction: Arc Length, Metric Spaces, and Applications
11.1 Spherical Geometry and Trigonometry
11.2 Relativity and Minkowskian Geometry
Chapter 12: Vector Functions and Curves
Introduction: Vector Functions and Curves
12.1 Vector Functions of One Variable
12.2 Some Applications of Vector Differentiation
12.3 Curves and Parametrizations
12.4 Curvature, Torsion, and the Frenet Frame
12.5 Curvature and Torsion for General Parametrizations
12.6 Kepler’s Laws of Planetary Motion
Chapter Review
Chapter 13: Partial Differentiation
Introduction: Partial Differentiation
13.1 Functions of Several Variables
13.2 Limits and Continuity
13.3 Partial Derivatives
13.4 Higher-Order Derivatives
13.5 The Chain Rule
13.6 Linear Approximations, Differentiability, and Differentials
13.7 Gradients and Directional Derivatives
13.8 Implicit Functions
13.9 Taylor’s Formula, Taylor Series, and Approximations
Chapter Review
Chapter 14: Applications of Partial Derivatives
Introduction: Applications of Partial Derivatives
14.1 Extreme Values
14.2 Extreme Values of Functions Defined on Restricted Domains
14.3 Lagrange Multipliers
14.4 Lagrange Multipliers in n-Space
14.5 The Method of Least Squares
14.6 Parametric Problems
14.7 Newton’s Method
14.8 Calculations with Maple
14.9 Entropy in Statistical Mechanics and Information Theory
Chapter Review
Chapter 15: Multiple Integration
Introduction: Multiple Integration
15.1 Double Integrals
15.2 Iteration of Double Integrals in Cartesian Coordinates
15.3 Improper Integrals and a Mean-Value Theorem
15.4 Double Integrals in Polar Coordinates
15.5 Triple Integrals
15.6 Change of Variables in Triple Integrals
15.7 Applications of Multiple Integrals
Chapter Review
Chapter 16: Vector Fields
Introduction: Vector Fields
16.1 Vector and Scalar Fields
16.2 Conservative Fields
16.3 Line Integrals
16.4 Line Integrals of Vector Fields
16.5 Surfaces and Surface Integrals
16.6 Oriented Surfaces and Flux Integrals
Chapter Review
Chapter 17: Vector Calculus
Introduction: Vector Calculus
17.1 Gradient, Divergence, and Curl
17.2 Some Identities Involving Grad, Div, and Curl
17.3 Green’s Theorem in the Plane
17.4 The Divergence Theorem in 3-Space
17.5 Stokes’s Theorem
17.6 Some Physical Applications of Vector Calculus
17.7 Orthogonal Curvilinear Coordinates
Chapter Review
Chapter 18: Differential Forms and Exterior Calculus
Introduction: Differential Forms and Exterior Calculus
18.1 k-Forms
18.2 Differential Forms and the Exterior Derivative
18.3 Integration on Manifolds
18.4 Orientations, Boundaries, and Integration of Forms
18.5 The Generalized Stokes’s Theorem
Chapter 19: Ordinary Differential Equations
Introduction: Ordinary Differential Equations
19.1 Classifying Differential Equations
19.2 Solving First-Order Equations
19.3 Existence, Uniqueness, and Numerical Methods
19.4 Differential Equations of Second Order
19.5 Linear Differential Equations with Constant Coefficients
19.6 Nonhomogeneous Linear Equations
Chapter Review
Chapter 20: More Topics in Differential Equations
Introduction: More Topics in Differential Equations
20.1 The Laplace Transform
20.2 Series Solutions of Differential Equations
20.3 Orthogonal Function Expansions and Boundary Value Problems
20.4 Dynamical Systems, Phase Space, and the Phase Plane
20.5 Calculus of Variations
20.6 Computation and Symmetry in Differential Equations
Appendix I: Complex Numbers
Introduction: Complex Numbers
Definition of Complex Numbers
Graphical Representation of Complex Numbers
Complex Arithmetic
Roots of Complex Numbers
Appendix II: Complex Functions
Introduction: Complex Functions
Limits and Continuity
The Complex Derivative
The Exponential Function
The Fundamental Theorem of Algebra
Appendix III: Continuous Functions
Introduction: Continuous Functions
Limits of Functions
Continuous Functions
Completeness and Sequential Limits
Continuous Functions on a Closed, Finite Interval
Appendix IV: The Riemann Integral
Introduction: The Riemann Integral
Uniform Continuity
Appendix V: Doing Calculus with Maple
Introduction: Doing Calculus with Maple
List of Maple Examples and Discussion
Appendix VI: Doing Calculus with Python
Introduction: Doing Calculus with Python
Sympy and Elementary Algebra
Calculus with Sympy
Vector Calculus with Sympy
Mathematical Graphics Using Matplotlib
Answers to Odd-Numbered Exercises
Chapter P Preliminaries
Chapter 1 Limits and Continuity
Chapter 2 Differentiation
Chapter 3 Transcendental Functions
Chapter 4 More Applications of Differentiation
Chapter 5 Integration
Chapter 6 Techniques of Integration
Chapter 7 Applications of Integration
Chapter 8 Conics, Parametric Curves, and Polar Curves
Chapter 9 Sequences, Series, and Power Series
Chapter 10 Vectors and Coordinate Geometry in 3-Space
Chapter 11 Arc Length, Metric Spaces, and Applications
Chapter 12 Vector Functions and Curves
Chapter 13 Partial Differentiation
Chapter 14 Applications of Partial Derivatives
Chapter 15 Multiple Integration
Chapter 16 Vector Fields
Chapter 17 Vector Calculus
Chapter 18 Differential Forms and Exterior Calculus
Chapter 19 Ordinary Differential Equations
Chapter 20 More Topics in Differential Equations
Appendix I Complex Numbers
Appendix II Complex Functions
Appendix III Continuous Functions
Appendix IV The Riemann Integral
Appendix V Doing Calculus with Maple
Appendix VI Doing Calculus with Python
Rules and Formulas
Rules and Formulas