The fifth edition of Calculus brings together the best of both new and traditional curricula in an effort to meet the needs of even more instructors teaching calculus. The author team's extensive experience teaching from both traditional and innovative books and their expertise in developing innovative problems put them in an unique position to make this new curriculum meaningful to students going into mathematics and those going into the sciences and engineering. Calculus: Single Variable, 5e exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students. The fifth edition includes even more problems and additional skill-building exercises.
Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the "Rule of Four" - graphical, numeric, symbolic/algebraic, and verbal/applied presentations - to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique.
Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the "Rule of Four" - graphical, numeric, symbolic/algebraic, and verbal/applied presentations - to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique.
1 A LIBRARY OF FUNCTIONS
1.1 Functions and Change
1.2 Exponential Functions
1.3 New Functions from Old
1.4 Logarithmic Functions
1.5 Trigonometric Functions
1.6 Powers, Polynomials, and Rational Functions
1.7 Introduction to Continuity
1.8 Limits
Review Problems
Check Your Understanding
Projects: Matching Functions to Data, Which Way Is the Wind Blowing?
2 KEY CONCEPT: THE DERIVATIVE
2.1 How Do We Measure Speed?
2.2 The Derivative at a Point
2.3 The Derivative Function
2.4 Interpretations of the Derivative
2.5 The Second Derivative
2.6 Differentiability
Review Problems
Check Your Understanding
Projects: Hours of Daylight as a Function of Latitude, US Population
3 SHORT-CUTS TO DIFFERENTIATION
3.1 Powers and Polynomials
3.2 The Exponential Function
3.3 The Product and Quotient Rules
3.4 The Chain Rule
3.5 The Trigonometric Functions
3.6 The Chain Rule and Inverse Functions
3.7 Implicit Functions
3.8 Hyperbolic Functions
3.9 Linear Approximation and the Derivative
3.10 Theorems about Differentiable Functions
Review Problems
Check Your Understanding
Projects: Rule of 70, Newton? ?s Method
4 USING THE DERIVATIVE
4.1 Using First and Second Derivatives
4.2 Optimization
4.3 Families of Functions
4.4 Optimization, Geometry, and Modeling
4.5 Applications to Marginality
4.6 Rates and Related Rates
4.7 L? ?hopital? ?s Rule, Growth, and Dominance
4.8 Parametric Equations
Review Problems
Check Your Understanding
Projects: Building a Greenhouse, Fitting a Line to Data, Firebreaks
5 KEY CONCEPT: THE DEFINITE INTEGRAL
5.1 How Do We Measure Distance Traveled?
5.2 The Definite Integral
5.3 The Fundamental Theorem and Interpretations
5.4 Theorems about Definite Integrals
Review Problems
Check Your Understanding
Projects: The Car and the Truck, An Orbiting Satellite
6 CONSTRUCTING ANTIDERIVATIVES
6.1 Antiderivatives Graphically and Numerically
6.2 Constructing Antiderivatives Analytically
6.3 Differential Equations
6.4 Second Fundamental Theorem of Calculus
6.5 The Equations of Motion
Review Problems
Check Your Understanding
Projects: Distribution of Resources, Yield from an Apple Orchard, Slope Fields
7 INTEGRATION
7.1 Integration by Substitution
7.2 Integration by Parts
7.3 Tables of Integrals
7.4 Algebraic Identities and Trigonometric Substitutions
7.5 Approximating Definite Integrals
7.6 Approximation Errors and Simpson? ?s Rule
7.7 Improper Integrals
7.8 Comparison of Improper Integrals
Review Problems
Check Your Understanding
Projects: Taylor Polynomial Inequalities
8 USING THE DEFINITE INTEGRAL
8.1 Areas and Volumes
8.2 Applications to Geometry
8.3 Area and Arc Length in Polar Coordinates
8.4 Density and Center of Mass
8.5 Applications to Physics
8.6 Applications to Economics
8.7 Distribution Functions
8.8 Probability, Mean, and Median
Review Problems
Check Your Understanding
Projects: Volume Enclosed by Two Cylinders, Length of a Hanging Cable, Surface Area of an Unpaintable Can of Paint, Maxwell? ?s Distribution of Molecular Velocities
9 SEQUENCES AND SERIES
9.1 Sequences
9.2 Geometric Series
9.3 Convergence of Series
9.4 Tests for Convergence
9.5 Power Series and Interval of Convergence
Review Problems
Check Your Understanding
Projects: A Definition of e, Probability of Winning in Sports, Prednisone
10 APPROXIMATING FUNCTIONS USING SERIES
10.1 Taylor Polynomials
10.2 Taylor Series
10.3 Finding and Using Taylor Series
10.4 The Error in Taylor Polynomial Approximations
10.5 Fourier Series
Review Problems
Check Your Understanding
Projects: Shape of Planets, Machin? ?s Formula and the Value of pi, Approximation the Derivative
11 DIFFERENTIAL EQUATIONS
11.1 What Is a Differential Equation?
11.2 Slope Fields
11.3 Euler? ?s Method
11.4 Separation of Variables
11.5 Growth and Decay
11.6 Applications and Modeling
11.7 The Logistic Model
11.8 Systems of Differential Equations
11.9 Analyzing the Phase Plane
11.10 Second-Order Differential Equations: Oscillations
11.11 Linear Second-Order Differential Equations
Review Problems
Check Your Understanding
Projects: SARS Predictions for Hong Kong, A S-I-R Model for SARS, Pareto? ?s Law, Vibrations in a Molecule