Librería Portfolio

NEW EXPLANATIONS AND EXAMPLES: Careful refinements throughout provide even greater clarity on key concepts such as computing volumes of revolution and setting up triple integrals.
NEW SCAFFOLDED EXERCISES: At the beginning of problem sets, new basic exercises reinforce key skills and build student confidence to prepare them for more rigorous exercises and conceptual understanding.
NEW SUBHEADINGS: Additional subsections within chapters help instructors and students find key content more easily to make the text an even more helpful teaching and learning tool.
NEW WEBASSIGN RESOURCES: New digital resources in WebAssign include Explore It interactive learning modules, the MindTap reader for interactive and mobile ebook access, enhanced remediation support, and improved problem types.
PROBLEM-SOLVING EMPHASIS: George Polya's problem-solving methodology is introduced at the beginning and reinforced throughout. ´Strategies´ sections help students select what techniques they´ll need to solve problems in situations where the choice is not obvious and help them develop true problem-solving skills and intuition.
CLEAR EXPOSITION: Dan Clegg and Saleem Watson have remained true to James Stewart´s writing style speaking clearly and directly to students, guiding them through key ideas, theorems, and problem-solving steps, and encouraging them to think as they read and learn calculus.
STEM APPLICATIONS: Stewart/Clegg/Watson answers ´When will I use this?´ by showing how calculus is used as a problem-solving tool in fields such as physics, engineering, chemistry, biology, medicine, and the social sciences.
PREREQUISITE SUPPORT: Four diagnostic tests in algebra, analytic geometry, functions, and trigonometry enable students to test their preexisting knowledge and brush up on skills. Quick Prep and Just-in-Time exercises in WebAssign refresh and reinforce prerequisite knowledge.
HELPFUL EXAMPLES: Every concept is supported by thoughtfully worked examples that encourage students to develop an analytic view of the subject. To provide further insight into mathematical concepts, many detailed examples display solutions graphically, analytically, and/or numerically. Margin notes expand on and clarify the steps of the solution.
QUALITY EXERCISES: Each exercise set carefully progresses from skill-development problems to more challenging problems involving applications and proofs. Conceptual exercises encourage the development of communication skills by explicitly requesting descriptions, conjectures, and explanations. More challenging "Problems Plusö exercises reinforce concepts by requiring students to apply techniques from more than one chapter of the text, and by patiently showing them how to approach a challenging problem.
ENGAGING PROJECTS: A wealth of engaging projects reinforce concepts. ´Writing Projects´ ask students to compare present-day methods with those of the founders of calculus. ´Discovery Projects´ anticipate results to be discussed later. ´Applied Projects´ feature real-world use of mathematics. ´Laboratory Projects´ anticipate results to be discussed later or encourage discovery through pattern recognition.



Preface.
To the Student.
Diagnostic Tests.
A Preview of Calculus.
1. FUNCTIONS AND MODELS.
Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving.
2. LIMITS AND DERIVATIVES.
The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. Problems Plus.
3. DIFFERENTIATION RULES.
Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Discovery Project: Families of Implicit Curves. Derivatives of Logarithmic Functions and Inverse Trigonometric Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Applied Project: Controlling Red Blood Cell Loss During Surgery. Related Rates. Linear Approximations and Differentials. Discovery Project: Taylor Polynomials. Hyperbolic Functions. Review. Problems Plus.
4. APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. What Derivatives Tell Us about the Shape of a Graph. Indeterminate Forms and l´Hospital´s Rule. Writing Project: The Origins of l´Hospital´s Rule. Summary of Curve Sketching. Graphing with Calculus and Technology. Optimization Problems. Applied Project: The Shape of a Can. Applied Project: Planes and Birds: Minimizing Energy. Newton´s Method. Antiderivatives. Review. Problems Plus.
5. INTEGRALS.
The Area and Distance Problems. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus.
6. APPLICATIONS OF INTEGRATION.
Areas Between Curves. Applied Project: The Gini Index. Volumes. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Calculus and Baseball. Applied Project: Where to Sit at the Movies. Review. Problems Plus.
7. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Technology. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus.
8. FURTHER APPLICATIONS OF INTEGRATION.
Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Problems Plus.
9. DIFFERENTIAL EQUATIONS.
Modeling with Differential Equations. Direction Fields and Euler´s Method. Separable Equations. Applied Project: How Fast Does a Tank Drain? Models for Population Growth. Linear Equations. Applied Project: Which is Faster, Going Up or Coming Down? Predator-Prey Systems. Review. Problems Plus.
10. PARAMETRIC EQUATIONS AND POLAR COORDINATES.
Curves Defined by Parametric Equations. Discovery Project: Running Circles Around Circles. Calculus with Parametric Curves. Discovery Project: Bézier Curves. Polar Coordinates. Discovery Project: Families of Polar Curves. Calculus in Polar Coordinates. Coni