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简介
The wide-ranging debate brought about by the calculus reform movement has had a significant impact on calculus textbooks. In response to many of the questions and concerns surrounding this debate, the authors have written a modern calculus textbook, intended for students majoring in mathematics, physics, chemistry, engineering and related fields. The text is written for the average student -- one who does not already know the subject, whose background is somewhat weak in spots, and who requires a significant motivation to study calculus.The authors follow a relatively standard order of presentation, while integrating technology and thought-provoking exercises throughout the text. Some minor changes have been made in the order of topics to reflect shifts in the importance of certain applications in engineering and science. This text also gives an early introduction to logarithms, exponentials and the trigonometric functions. Wherever practical, concepts are developed from graphical, numerical, and algebraic perspectives (the "Rule of Three") to give students a full understanding of calculus. This text places a significant emphasis on problem solving and presents realistic applications, as well as open-ended problems.
目录
Preliminaries
The Real Numbers and the Cartesian Plane
Lines and Functions
Graphing Calculators and Computer Algebra Systems
Solving Equations
Trigonometric Functions
Exponential and Logarithmic Functions
Transformations of Functions
Preview of Calculus
Limits and Continuity
The Concept of Limit
Computation of Limits
Continuity and its Consequences
Limits Involving Infinity
Formal Definition of the Limit
Limits and Loss-of-Significance Errors
Differentiation
Tangent Lines and Velocity
The Derivative
Computation of Derivatives: The Power Rule
The Product and Quotient Rules
Derivatives of Trigonometric Functions
Derivatives of Exponential and Logarithmic Functions
The Chain Rule
Implicit Differentiation and Related Rates
The Mean Value Theorem
Applications of Differentiation
Linear Approximations adn L'Hopital's Rule
Newton's Method
Maximum and Minimum Values
Increasing and Decreasing Functions
Concavity
Overview of Curve Sketching
Optimization
Rates of Change in Applications
Integration
Antiderivatives
Sums and Sigma Notation
Area
The Definite Integral
The Fundamental Theorem of Calculus
Integration by Substitution
Numerical Integration
Applications of the Definite Integral
Area Between Curves
Volume
Volumes by Cylindrical Shells
Arc Length and Surface Area
Projectile Motion
Work, Moments, and Hydrostatic Force
Probability
Exponentials, Logarithms, and Other Transcendental Functions
The Natural Logarithm Revisited
Inverse Functions
The Exponential Function Revisited
Growth and Decay Problems
Separable Differential Equations
Euler's Method
The Inverse Trigonometric Functions
The Calculus of the Inverse Trigonometric Functions
The Hyperbolic Functions
Integration Techniques
Review of Formulas and Techniques
Integration by Parts
Trigonometric Techniques of Integration
Integration of Rational Functions using Partial Fractions
Integration Tables and Computer Algebra Systems
Indeterminate Forms and L'Hopital's Rule
Improper Integrals
Infinite Series
Sequences of Real Numbers
Infinite Series
The Integral Test and Comparison Tests
Alternating Series
Absolute Convergence and the Ratio Test
Power Series
Taylor Series
Fourier Series
Parametric Equations and Polar Coordinates
Plane Curves and Parametric Equations
Calculus and Parametric Equations
Arc Length and Surface Area in Parametric Equations
Polar Coordinates
Calculus and Polar Coordinates
Conic Sections
Conic Sections in Polar Coordinates
The Real Numbers and the Cartesian Plane
Lines and Functions
Graphing Calculators and Computer Algebra Systems
Solving Equations
Trigonometric Functions
Exponential and Logarithmic Functions
Transformations of Functions
Preview of Calculus
Limits and Continuity
The Concept of Limit
Computation of Limits
Continuity and its Consequences
Limits Involving Infinity
Formal Definition of the Limit
Limits and Loss-of-Significance Errors
Differentiation
Tangent Lines and Velocity
The Derivative
Computation of Derivatives: The Power Rule
The Product and Quotient Rules
Derivatives of Trigonometric Functions
Derivatives of Exponential and Logarithmic Functions
The Chain Rule
Implicit Differentiation and Related Rates
The Mean Value Theorem
Applications of Differentiation
Linear Approximations adn L'Hopital's Rule
Newton's Method
Maximum and Minimum Values
Increasing and Decreasing Functions
Concavity
Overview of Curve Sketching
Optimization
Rates of Change in Applications
Integration
Antiderivatives
Sums and Sigma Notation
Area
The Definite Integral
The Fundamental Theorem of Calculus
Integration by Substitution
Numerical Integration
Applications of the Definite Integral
Area Between Curves
Volume
Volumes by Cylindrical Shells
Arc Length and Surface Area
Projectile Motion
Work, Moments, and Hydrostatic Force
Probability
Exponentials, Logarithms, and Other Transcendental Functions
The Natural Logarithm Revisited
Inverse Functions
The Exponential Function Revisited
Growth and Decay Problems
Separable Differential Equations
Euler's Method
The Inverse Trigonometric Functions
The Calculus of the Inverse Trigonometric Functions
The Hyperbolic Functions
Integration Techniques
Review of Formulas and Techniques
Integration by Parts
Trigonometric Techniques of Integration
Integration of Rational Functions using Partial Fractions
Integration Tables and Computer Algebra Systems
Indeterminate Forms and L'Hopital's Rule
Improper Integrals
Infinite Series
Sequences of Real Numbers
Infinite Series
The Integral Test and Comparison Tests
Alternating Series
Absolute Convergence and the Ratio Test
Power Series
Taylor Series
Fourier Series
Parametric Equations and Polar Coordinates
Plane Curves and Parametric Equations
Calculus and Parametric Equations
Arc Length and Surface Area in Parametric Equations
Polar Coordinates
Calculus and Polar Coordinates
Conic Sections
Conic Sections in Polar Coordinates
Calculus / 2nd ed.
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