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The Larson Calculus program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.
- NEW Chapter Openers - Each Chapter Opener highlights five real-life applications of calculus found throughout the chapter. The applications reference the examples or exercises featured. You can find a full listing of the applications in the Index of Applications.
- NEW HOW DO YOU SEE IT? Exercise - The How Do You See It? exercise in each section presents a problem that you will solve by visual inspection using the concepts learned in the lesson.
- NEW LarsonCalculus.com - We’ve created a free website hosting valuable resources. At this website, you can access the following: Proof Videos – Watch co-author Bruce Edwards present theorems and explain their proofs. Calculus Videos – Watch Dana Mosely explain concepts of calculus. Interactive Examples – Explore examples using Wolfram’s free CDF player (plug-in required). Rotatable Graphs – View and rotate three-dimensional graphs using Wolfram’s free CDF player (plug-in required). Biographies – Read biographies of men and women who were instrumental in creating calculus. Web Appendices – Read the web-only appendices that accompany the text. Data Downloads – Use real data to solve problems.
- Table of Contents Changes - We moved Appendix A (Proofs of Selected Theorems) to the website www.LarsonCalculus.com, which also includes videos of co-author Bruce Edwards explaining these proofs.
- CAS Investigation: Many examples throughout the book are accompanied by CAS Investigations. These are collaborative investigations using a computer algebra system (e.g., Maple) to further explore the related example. CAS Investigations are located online and in the Multimedia eBook.
- Writing Style: Simple, mathematically precise instruction and directions are clear and easy to understand for students.
- Linked Examples and Exercises: The Larson program has long been recognized as offering many more examples than most calculus texts. Examples are broken down into critical steps, with careful use of color and design to emphasize the process. Each is linked to problems in the exercise sets, giving students a way to learn or review material as they do their homework.
- Instructor Resource Guide w/Solutions—The instructor's resource contains an abundance of resources keyed to the textbook by chapter and section, including chapter summaries, teaching strategies, multiple versions of chapter tests, final exams, gateway tests, and suggested solutions to the Chapter Openers, Explorations, Section Projects, and Technology features in the text.
- REVISED Remarks - To eliminate any possible confusion, all Study Tips and Notes have been combined into one feature, Remarks. These hints and tips can be used to reinforce or expand upon concepts, help you learn how to study mathematics, caution you about common errors, address special cases, or show alternative or additional steps to a solution of an example.
- REVISED Exercise Sets - The exercise sets have been carefully and extensively examined to ensure they are rigorous, relevant, and cover all topics suggested by our users. The exercises have been reorganized and titled so you can better see the connections between examples and exercises. Multi-step, real-life exercises reinforce problem-solving skills and mastery of concepts by giving you the opportunity to apply the concepts in real-life situations. Putnam Exam questions to push the limits of students’ understanding of calculus. Graphing technology exercises for students to make us of a graphing utility to help find solutions.
- Second Order Differential Equations: Available online, this chapter delves into second order differential equations. This will greatly help engineering and math majors.
- Enhanced WebAssign Course: The Larson EWA course has over 3,900 textbook questions which have been drawn from the book, and offer more coverage of problems and topics than most online homework programs for Calculus. The EWA course for Larson CALCULUS will present numerous section-level video lessons by Dana Mosely and animated tutorials. In addition to these assets, the course includes exercise-level features: Read It, Watch It, Master It, and Chat About It links. These tools benefit students with varied learning styles to ensure they get the most out of their online learning experience.
- Graded Homework Exercises— Online homework and tests are evaluated using powerful Maple software to ensure mathematical accuracy. Instructors control point values, weighting grades, and whether of not an item is graded. An electronic gradebook helps instructors manage course information easily and can be exported to other files, such as Excel.
Vectors in the Plane. Space Coordinates and Vectors in Space. The Dot Product of Two Vectors. The Cross Product of Two Vectors in Space. Lines and Planes in Space. Section Project: Distances in Space. Surfaces in Space. Cylindrical and Spherical Coordinates. Review Exercises. P.S. Problem Solving.
12. VECTOR-VALUED FUNCTIONS.
Vector-Valued Functions. Section Project: Witch of Agnesi. Differentiation and Integration of Vector-Valued Functions. Velocity and Acceleration. Tangent Vectors and Normal Vectors. Arc Length and Curvature. Review Exercises. P.S. Problem Solving.
13. FUNCTIONS OF SEVERAL VARIABLES.
Introduction to Functions of Several Variables. Limits and Continuity. Partial Derivatives. Section Project: Moiré Fringes. Differentials. Chain Rules for Functions of Several Variables. Directional Derivatives and Gradients. Tangent Planes and Normal Lines. Section Project: Wildflowers. Extrema of Functions of Two Variables. Applications of Extrema of Functions of Two Variables. Section Project: Building a Pipeline. Lagrange Multipliers. Review Exercises. P.S. Problem Solving.
14. MULTIPLE INTEGRATION.
Iterated Integrals and Area in the Plane. Double Integrals and Volume. Change of Variables: Polar Coordinates. Center of Mass and Moments of Inertia. Section Project: Center of Pressure on a Sail. Surface Area. Section Project: Capillary Action. Triple Integrals and Applications. Triple Integrals in Cylindrical and Spherical Coordinates. Section Project: Wrinkled and Bumpy Spheres. Change of Variables: Jacobians. Review Exercises. P.S. Problem Solving.
15. VECTOR ANALYSIS.
Vector Fields. Line Integrals. Conservative Vector Fields and Independence of Path. Green's Theorem. Section Project: Hyperbolic and Trigonometric Functions. Parametric Surfaces. Surface Integrals. Section Project: Hyperboloid of One Sheet. Divergence Theorem. Stokes's Theorem. Review Exercises. Section Project: The Planimeter. P.S. Problem Solving.
16. SECOND ORDER DIFFERENTIAL EQUATIONS* ONLINE.
Exact First-Order Equations. Second-Order Homogeneous Linear Equations. Second-Order Nonhomogeneous Linear Equations. Series Solutions of Differential Equations. Review Exercises. P.S. Problem Solving.
A. Proofs of Selected Theorems.
B. Integration Tables.
C. Precalculus Review (Web).
C.1 Real Numbers and the Real Number Line. C.2 The Cartesian Plane. C.3 Review of Trigonometric Functions.
D. Rotation and the General Second-Degree Equation (Web).
E. Complex Numbers (Web).
F. Business and Economic Applications (Web).
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
This manual contains worked-out solutions to all exercises in Chapters 11-16 of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, Seventh Edition.
Microsoft® PowerPoint® slides and image library for the entire book, posted on the Instructor Companion Website, let you incorporate images from the book right into your lectures. Also posted on the Instructor Companion site, is the Complete Solutions Manual for Larson/Edwards, Calculus, 11th manual provides complete solutions to all the exercises from the text.
Instructor's Resource Guide
The robust Instructor’s Resource Guide contains an abundance of resources to aid instructors in preparing and presenting text material in a manner that meets their personal preferences and course needs. It provides a variety of tools keyed to the textbook at the section and chapter level, including section objectives, teaching tips, and chapter projects. An electronic version of the Instructor Guide is available on the PowerLecture DVD.
Cengage Learning Testing, powered by Cognero® Instant Access
Cengage Learning Testing Powered by Cognero® is a flexible, online system that allows you to author, edit, and manipulate content from the text's test bank or elsewhere, including your own favorite test questions; create multiple test versions in an instant; and deliver tests from your LMS, your classroom, or wherever you want. This is available online via www.cengage.com/login.
Student Solutions Manual
This manual contains worked-out solutions for all odd-numbered exercises for Chapters 11-16 in Larson/Edwards' CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 7th Edition.