Calculus: Single Variable, 5th Edition
Calculus: Single Variable, 5th Edition
ISBN: 978-0-470-08915-6
Dec 2008
736 pages
Description
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.
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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, Newtonâ ?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 Lâ ?hopitalâ ?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 Simpsonâ ?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, Maxwellâ ?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, Machinâ ?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 Eulerâ ?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, Paretoâ ?s Law, Vibrations in a Molecule
- Expanded Skills and Practice: The 5th edition includes a number new of skill-building and practice exercises, as well as additional problems.
- Updated Data and Models: References to dates, prices, and other time-bound quantities have been updated for contemporary applied examples, problems, and projects. For example, Section 11.7 now introduces the current debate on Peak Oil production, underscoring the importance of mathematics in understanding the world's economic and social problems.
- New Projects: There are new projects in Chapter 1:Which way is the Wind Blowing?; Chapter 5: The Car and the Truck; Chapter 9: Prednisone; and Chapter 10: The Shape of Planets.
- More Problems: 10% more "problem"-type questions now included in the test banks and instructor's manuals.
- Chapter 4 Reorganization: This chapter has been reorganized to smooth the approach to optimization.
- New ConcepTests: Promote active learning in the classroom. These can be used with or without clickers, and have been shown to dramatically improve student learning. Available in a book or on theweb at www.wiley.com/college/hugheshallett.
- Expanded Appendices: A new Appendix D introducing vectors in the plane has been added. This can be covered at any time, but may be particularly useful in the conjunction with Section 4.8 on parametric equations.
- Foundations: The 5th edition of the text provides students with a clear understanding of the ideas of calculus as a solid foundation for subsequent courses in mathematics and other disciplines.
- Rule of Four: Encourages students with a variety of learning styles to expand their knowledge by presenting ideas and concepts graphically, numerically, symbolically, and verbally.
- Balanced Approach: The authors understand the important balance between concepts and skills. As instructors themselves, they know that the balance that an instructor chooses depends on the students they have: sometimes a focus on conceptual understanding is best; sometimes more drill is appropriate. The flexibility of the Fifth Edition allows instructors to tailor the course to their students.
- Problems: Creative problems, of great variety, probe student understanding.
- Emphasis on modeling
- Student Understanding: Exposition written in a way that students can actually read and more easily understand.
- Flexible approach to technology