Description

Book Synopsis


Table of Contents
1. Functions
  • 1.1 Functions and Their Graphs
  • 1.2 Combining Functions; Shifting and Scaling Graphs
  • 1.3 Trigonometric Functions
  • 1.5 Exponential Functions
  • 1.6 Inverse Functions and Logarithms
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
2. Limits and Continuity
  • 2.1 Rates of Change and Tangent Lines to Curves
  • 2.2 Limit of a Function and Limit Laws
  • 2.3 The Precise Definition of a Limit
  • 2.4 One-Sided Limits
  • 2.5 Continuity
  • 2.6 Limits Involving Infinity; Asymptotes of Graphs
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
3. Derivatives
  • 3.1 Tangent Lines and the Derivative at a Point
  • 3.2 The Derivative as a Function
  • 3.3 Differentiation Rules
  • 3.4 The Derivative as a Rate of Change
  • 3.5 Derivatives of Trigonometric Functions
  • 3.6 The Chain Rule
  • 3.7 Implicit Differentiation
  • 3.8 Derivatives of Inverse Functions and Logarithms
  • 3.9 Inverse Trigonometric Functions
  • 3.10 Related Rates
  • 3.11 Linearization and Differentials
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
4. Applications of Derivatives
  • 4.1 Extreme Values of Functions on Closed Intervals
  • 4.2 The Mean Value Theorem
  • 4.3 Monotonic Functions and the First Derivative Test
  • 4.4 Concavity and Curve Sketching
  • 4.5 Indeterminate Forms and L'Hôpital's Rule
  • 4.6 Applied Optimization
  • 4.7 Newton's Method
  • 4.8 Antiderivatives
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
5. Integrals
  • 5.1 Area and Estimating with Finite Sums
  • 5.2 Sigma Notation and Limits of Finite Sums
  • 5.3 The Definite Integral
  • 5.4 The Fundamental Theorem of Calculus
  • 5.5 Indefinite Integrals and the Substitution Method
  • 5.6 Definite Integral Substitutions and the Area Between Curves
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
6. Applications of Definite Integrals
  • 6.1 Volumes Using Cross-Sections
  • 6.2 Volumes Using Cylindrical Shells
  • 6.3 Arc Length
  • 6.4 Areas of Surfaces of Revolution
  • 6.5 Work and Fluid Forces
  • 6.6 Moments and Centers of Mass
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
7. Integrals and Transcendental Functions
  • 7.1 The Logarithm Defined as an Integral
  • 7.2 Exponential Change and Separable Differential Equations
  • 7.3 Hyperbolic Functions
  • 7.4 Relative Rates of Growth
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
8. Techniques of Integration
  • 8.1 Using Basic Integration Formulas
  • 8.2 Integration by Parts
  • 8.3 Trigonometric Integrals
  • 8.4 Trigonometric Substitutions
  • 8.5 Integration of Rational Functions by Partial Fractions
  • 8.6 Integral Tables and Computer Algebra Systems
  • 8.7 Numerical Integration
  • 8.8 Improper Integrals
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
9. Infinite Sequences and Series
  • 9.1 Sequences
  • 9.2 Infinite Series
  • 9.3 The Integral Test
  • 9.4 Comparison Tests
  • 9.5 Absolute Convergence; The Ratio and Root Tests
  • 9.6 Alternating Series and Conditional Convergence
  • 9.7 Power Series
  • 9.8 Taylor and Maclaurin Series
  • 9.9 Convergence of Taylor Series
  • 9.10 Applications of Taylor Series
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
10. Parametric Equations and Polar Coordinates
  • 10.1 Parametrizations of Plane Curves
  • 10.2 Calculus with Parametric Curves
  • 10.3 Polar Coordinates
  • 10.4 Graphing Polar Coordinate Equations
  • 10.5 Areas and Lengths in Polar Coordinates
  • 10.6 Conic Sections
  • 10.7 Conics in Polar Coordinates
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
11. Vectors and the Geometry of Space
  • 11.1 Three-Dimensional Coordinate Systems
  • 11.2 Vectors
  • 11.3 The Dot Product
  • 11.4 The Cross Product
  • 11.5 Lines and Planes in Space
  • 11.6 Cylinders and Quadric Surfaces
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
12. Vector-Valued Functions and Motion in Space
  • 12.1 Curves in Space and Their Tangents
  • 12.2 Integrals of Vector Functions; Projectile Motion
  • 12.3 Arc Length in Space
  • 12.4 Curvature and Normal Vectors of a Curve
  • 12.5 Tangential and Normal Components of Acceleration
  • 13.6 Velocity and Acceleration in Polar Coordinates
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
13. Partial Derivatives
  • 13.1 Functions of Several Variables
  • 13.2 Limits and Continuity in Higher Dimensions
  • 13.3 Partial Derivatives
  • 13.4 The Chain Rule
  • 13.5 Directional Derivatives and Gradient Vectors
  • 13.6 Tangent Planes and Differentials
  • 13.7 Extreme Values and Saddle Points
  • 13.8 Lagrange Multipliers
  • 13.9 Taylor's Formula for Two Variables
  • 13.10 Partial Derivatives with Constrained Variables
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
14. Multiple Integrals
  • 14.1 Double and Iterated Integrals over Rectangles
  • 14.2 Double Integrals over General Regions
  • 14.3 Area by Double Integration
  • 14.4 Double Integrals in Polar Form
  • 14.5 Triple Integrals in Rectangular Coordinates
  • 14.6 Applications
  • 14.7 Triple Integrals in Cylindrical and Spherical Coordinates
  • 14.8 Substitutions in Multiple Integrals
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
15. Integrals and Vector Fields
  • 15.1 Line Integrals of Scalar Functions
  • 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
  • 15.3 Path Independence, Conservative Fields, and Potential Functions
  • 15.4 Green's Theorem in the Plane
  • 15.5 Surfaces and Area
  • 15.6 Surface Integrals
  • 15.7 Stokes' Theorem
  • 15.8 The Divergence Theorem and a Unified Theory
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
16. First-Order Differential Equations
  • 16.1 Solutions, Slope Fields, and Euler's Method
  • 16.2 First-Order Linear Equations
  • 16.3 Applications
  • 16.4 Graphical Solutions of Autonomous Equations
  • 16.5 Systems of Equations and Phase Planes
  • Questions to Guide Your Review
  • Practice Exercises
  • Technology Application Projects
17. Second-Order Differential Equations
  • 17.1 Second-Order Linear Equations
  • 17.2 Nonhomogeneous Linear Equations
  • 17.3 Applications
  • 17.4 Euler Equations
  • 17.5 Power-Series Solutions
  • Questions to Guide Your Review
  • Practice Exercises
  • Additional and Advanced Exercises
  • Technology Application Projects
18. Complex Functions (online)
  • 18.1 Complex Numbers
  • 18.2 Limits and Continuity
  • 18.3 Complex Derivatives
  • 18.4 The Cauchy-Riemann Equations
  • 18.5 Complex Series
  • 18.6 Conformal Maps
19. Fourier Series and Wavelets (online)
  • 19.1 Periodic Functions
  • 19.2 Summing Sines and Cosines
  • 19.3 Vectors and Approximation in Three and More Dimensions
  • 19.4 Approximation of Functions
  • 19.5 Advanced Topic: The Haar System and Wavelets
Appendix A
  • A.1 Real Numbers and the Real Line
  • A.2 Graphing with Software
  • A.3 Mathematical Induction
  • A.4 Lines, Circles, and Parabolas
  • A.5 Proofs of Limit Theorems
  • A.6 Commonly Occurring Limits
  • A.7 Theory of the Real Numbers
  • A.8 The Distributive Law for Vector Cross Products
  • A.9 Probability
  • A.10 The Mixed Derivative Theorem and the Increment Theorem
Appendix B
  • B.1 Determinants
  • B.2 Extreme Values and Saddle Points for Functions of More than Two Variables
  • B.3 The Method of Gradient Descent
Answers to Odd-Numbered Exercises Applications Index Subject Index A Brief Table of Integrals Credits

Thomas Calculus Early Transcendentals SI Units

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      Book details

      Publisher Pearson Education Limited
      Published 1 June 2023
      ISBN-13 9781292725901
      978-1292725901
      ISBN-10 1292725907
      Also in:
      Mathematics Calculus and mathematical analysis

      Description

      Book Synopsis


      Table of Contents
      1. Functions
      • 1.1 Functions and Their Graphs
      • 1.2 Combining Functions; Shifting and Scaling Graphs
      • 1.3 Trigonometric Functions
      • 1.5 Exponential Functions
      • 1.6 Inverse Functions and Logarithms
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      2. Limits and Continuity
      • 2.1 Rates of Change and Tangent Lines to Curves
      • 2.2 Limit of a Function and Limit Laws
      • 2.3 The Precise Definition of a Limit
      • 2.4 One-Sided Limits
      • 2.5 Continuity
      • 2.6 Limits Involving Infinity; Asymptotes of Graphs
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      3. Derivatives
      • 3.1 Tangent Lines and the Derivative at a Point
      • 3.2 The Derivative as a Function
      • 3.3 Differentiation Rules
      • 3.4 The Derivative as a Rate of Change
      • 3.5 Derivatives of Trigonometric Functions
      • 3.6 The Chain Rule
      • 3.7 Implicit Differentiation
      • 3.8 Derivatives of Inverse Functions and Logarithms
      • 3.9 Inverse Trigonometric Functions
      • 3.10 Related Rates
      • 3.11 Linearization and Differentials
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      4. Applications of Derivatives
      • 4.1 Extreme Values of Functions on Closed Intervals
      • 4.2 The Mean Value Theorem
      • 4.3 Monotonic Functions and the First Derivative Test
      • 4.4 Concavity and Curve Sketching
      • 4.5 Indeterminate Forms and L'Hôpital's Rule
      • 4.6 Applied Optimization
      • 4.7 Newton's Method
      • 4.8 Antiderivatives
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      5. Integrals
      • 5.1 Area and Estimating with Finite Sums
      • 5.2 Sigma Notation and Limits of Finite Sums
      • 5.3 The Definite Integral
      • 5.4 The Fundamental Theorem of Calculus
      • 5.5 Indefinite Integrals and the Substitution Method
      • 5.6 Definite Integral Substitutions and the Area Between Curves
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      6. Applications of Definite Integrals
      • 6.1 Volumes Using Cross-Sections
      • 6.2 Volumes Using Cylindrical Shells
      • 6.3 Arc Length
      • 6.4 Areas of Surfaces of Revolution
      • 6.5 Work and Fluid Forces
      • 6.6 Moments and Centers of Mass
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      7. Integrals and Transcendental Functions
      • 7.1 The Logarithm Defined as an Integral
      • 7.2 Exponential Change and Separable Differential Equations
      • 7.3 Hyperbolic Functions
      • 7.4 Relative Rates of Growth
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      8. Techniques of Integration
      • 8.1 Using Basic Integration Formulas
      • 8.2 Integration by Parts
      • 8.3 Trigonometric Integrals
      • 8.4 Trigonometric Substitutions
      • 8.5 Integration of Rational Functions by Partial Fractions
      • 8.6 Integral Tables and Computer Algebra Systems
      • 8.7 Numerical Integration
      • 8.8 Improper Integrals
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      9. Infinite Sequences and Series
      • 9.1 Sequences
      • 9.2 Infinite Series
      • 9.3 The Integral Test
      • 9.4 Comparison Tests
      • 9.5 Absolute Convergence; The Ratio and Root Tests
      • 9.6 Alternating Series and Conditional Convergence
      • 9.7 Power Series
      • 9.8 Taylor and Maclaurin Series
      • 9.9 Convergence of Taylor Series
      • 9.10 Applications of Taylor Series
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      10. Parametric Equations and Polar Coordinates
      • 10.1 Parametrizations of Plane Curves
      • 10.2 Calculus with Parametric Curves
      • 10.3 Polar Coordinates
      • 10.4 Graphing Polar Coordinate Equations
      • 10.5 Areas and Lengths in Polar Coordinates
      • 10.6 Conic Sections
      • 10.7 Conics in Polar Coordinates
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      11. Vectors and the Geometry of Space
      • 11.1 Three-Dimensional Coordinate Systems
      • 11.2 Vectors
      • 11.3 The Dot Product
      • 11.4 The Cross Product
      • 11.5 Lines and Planes in Space
      • 11.6 Cylinders and Quadric Surfaces
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      12. Vector-Valued Functions and Motion in Space
      • 12.1 Curves in Space and Their Tangents
      • 12.2 Integrals of Vector Functions; Projectile Motion
      • 12.3 Arc Length in Space
      • 12.4 Curvature and Normal Vectors of a Curve
      • 12.5 Tangential and Normal Components of Acceleration
      • 13.6 Velocity and Acceleration in Polar Coordinates
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      13. Partial Derivatives
      • 13.1 Functions of Several Variables
      • 13.2 Limits and Continuity in Higher Dimensions
      • 13.3 Partial Derivatives
      • 13.4 The Chain Rule
      • 13.5 Directional Derivatives and Gradient Vectors
      • 13.6 Tangent Planes and Differentials
      • 13.7 Extreme Values and Saddle Points
      • 13.8 Lagrange Multipliers
      • 13.9 Taylor's Formula for Two Variables
      • 13.10 Partial Derivatives with Constrained Variables
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      14. Multiple Integrals
      • 14.1 Double and Iterated Integrals over Rectangles
      • 14.2 Double Integrals over General Regions
      • 14.3 Area by Double Integration
      • 14.4 Double Integrals in Polar Form
      • 14.5 Triple Integrals in Rectangular Coordinates
      • 14.6 Applications
      • 14.7 Triple Integrals in Cylindrical and Spherical Coordinates
      • 14.8 Substitutions in Multiple Integrals
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      15. Integrals and Vector Fields
      • 15.1 Line Integrals of Scalar Functions
      • 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
      • 15.3 Path Independence, Conservative Fields, and Potential Functions
      • 15.4 Green's Theorem in the Plane
      • 15.5 Surfaces and Area
      • 15.6 Surface Integrals
      • 15.7 Stokes' Theorem
      • 15.8 The Divergence Theorem and a Unified Theory
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      16. First-Order Differential Equations
      • 16.1 Solutions, Slope Fields, and Euler's Method
      • 16.2 First-Order Linear Equations
      • 16.3 Applications
      • 16.4 Graphical Solutions of Autonomous Equations
      • 16.5 Systems of Equations and Phase Planes
      • Questions to Guide Your Review
      • Practice Exercises
      • Technology Application Projects
      17. Second-Order Differential Equations
      • 17.1 Second-Order Linear Equations
      • 17.2 Nonhomogeneous Linear Equations
      • 17.3 Applications
      • 17.4 Euler Equations
      • 17.5 Power-Series Solutions
      • Questions to Guide Your Review
      • Practice Exercises
      • Additional and Advanced Exercises
      • Technology Application Projects
      18. Complex Functions (online)
      • 18.1 Complex Numbers
      • 18.2 Limits and Continuity
      • 18.3 Complex Derivatives
      • 18.4 The Cauchy-Riemann Equations
      • 18.5 Complex Series
      • 18.6 Conformal Maps
      19. Fourier Series and Wavelets (online)
      • 19.1 Periodic Functions
      • 19.2 Summing Sines and Cosines
      • 19.3 Vectors and Approximation in Three and More Dimensions
      • 19.4 Approximation of Functions
      • 19.5 Advanced Topic: The Haar System and Wavelets
      Appendix A
      • A.1 Real Numbers and the Real Line
      • A.2 Graphing with Software
      • A.3 Mathematical Induction
      • A.4 Lines, Circles, and Parabolas
      • A.5 Proofs of Limit Theorems
      • A.6 Commonly Occurring Limits
      • A.7 Theory of the Real Numbers
      • A.8 The Distributive Law for Vector Cross Products
      • A.9 Probability
      • A.10 The Mixed Derivative Theorem and the Increment Theorem
      Appendix B
      • B.1 Determinants
      • B.2 Extreme Values and Saddle Points for Functions of More than Two Variables
      • B.3 The Method of Gradient Descent
      Answers to Odd-Numbered Exercises Applications Index Subject Index A Brief Table of Integrals Credits

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