Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacher’s voice beyond the classroom. That voice—evident in the narrative, the figures, and the questions interspersed in the narrative—is a master teacher leading readers to deeper levels of understanding. The authors appeal to readers’ geometric intuition to introduce fundamental concepts and lay the foundation for the more rigorous development that follows. Comprehensive exercise sets have received praise for their creativity, quality, and scope. This book covers chapters single variable topics (chapters 1—10) of Calculus for Scientists and Engineers: Early Transcendentals, which is an expanded version of Calculus: Early Transcendentals by the same authors.
Les mer
1. Functions
1.1 Review of functions
1.2 Representing functions
1.3 Inverse, exponential, and logarithmic functions
1.4 Trigonometric functions and their inverses
2. Limits
2.1 The idea of limits
2.2 Definitions of limits
2.3 Techniques for computing limits
2.4 Infinite limits
2.5 Limits at infinity
2.6 Continuity
2.7 Precise definitions of limits
3. Derivatives
3.1 Introducing the derivative
3.2 Rules of differentiation
3.3 The product and quotient rules
3.4 Derivatives of trigonometric functions
3.5 Derivatives as rates of change
3.6 The Chain Rule
3.7 Implicit differentiation
3.8 Derivatives of logarithmic and exponential functions
3.9 Derivatives of inverse trigonometric functions
3.10 Related rates
4. Applications of the Derivative
4.1 Maxima and minima
4.2 What derivatives tell us
4.3 Graphing functions
4.4 Optimization problems
4.5 Linear approximation and differentials
4.6 Mean Value Theorem
4.7 L’Hôpital’s Rule
4.8 Newton’s Method
4.9 Antiderivatives
5. Integration
5.1 Approximating areas under curves
5.2 Definite integrals
5.3 Fundamental Theorem of Calculus
5.4 Working with integrals
5.5 Substitution rule
6. Applications of Integration
6.1 Velocity and net change
6.2 Regions between curves
6.3 Volume by slicing
6.4 Volume by shells
6.5 Length of curves
6.6 Surface area
6.7 Physical applications
6.8 Logarithmic and exponential functions revisited
6.9 Exponential models
6.10 Hyperbolic functions
7. Integration Techniques
7.1 Integration Strategies
7.2 Integration by parts
7.3 Trigonometric integrals
7.4 Trigonometric substitutions
7.5 Partial fractions
7.6 Other integration strategies
7.7 Numerical integration
7.8 Improper integrals
8. Differential Equations
8.1 Basic ideas
8.2 Direction fields and Euler’s method
8.3 Separable differential equations
8.4 Special first-order differential equations
8.5 Modeling with differential equations
9. Sequences and Infinite Series
9.1 An overview
9.2 Sequences
9.3 Infinite series
9.4 The Divergence and Integral Tests
9.5 The Ratio, Root, and Comparison Tests
9.6 Alternating series
10. Power Series
10.1 Approximating functions with polynomials
10.2 Properties of Power series
10.3 Taylor series
10.4 Working with Taylor series
11. Parametric and Polar Curves
11.1 Parametric equations
11.2 Polar coordinates
11.3 Calculus in polar coordinates
11.4 Conic sections
Les mer
Topics are introduced through concrete examples, geometric arguments, applications, and analogies rather than through abstract arguments. The authors appeal to students’ intuition and geometric instincts to make calculus natural and believable.
Figures are designed to help today’s visually oriented learners. They are conceived to convey important ideas and facilitate learning, annotated to lead students through the key ideas, and rendered using the latest software for unmatched clarity and precision.
Comprehensive exercise sets provide for a variety of student needs and are consistently structured and labeled to facilitate the creation of homework assignments by inspection.
Review Questions check that students have a general conceptual understanding of the essential ideas from the section.
Basic Skills exercises are linked to examples in the section so students get off to a good start with homework.
Further Explorations exercises extend students’ abilities beyond the basics.
Applications present practical and novel applications and models that use the ideas presented in the section.
Additional Exercises challenge students to stretch their understanding by working through abstract exercises and proofs.
Examples are plentiful and stepped out in detail. Within examples, each step is annotated to help students understand what took place in that step.
Quick Check exercises punctuate the narrative at key points to test understanding of basic ideas and encourage students to read with pencil in hand.
The MyMathLab course for the text features the following:
More than 7,000 assignable exercises provide you with the options you need to meet the needs of students. Most exercises can be algorithmically regenerated for unlimited practice.
Learning aids include guided exercises, additional examples, and tutorial videos. You control how much help your students can get and when.
700 Interactive Figures in the eBook can be manipulated to shed light on key concepts. The figures are also ideal for in-class demonstrations.
Interactive Figure Exercises provide a way for you make the most of the Interactive Figures by including them in homework assignments.
A “Getting Ready for Calculus” chapter, with built-in diagnostic tests, identifies each student’s gaps in skills and provides individual remediation directly to those skills that are lacking.
Ready to Go Courses designed by experienced instructors minimize the start-up time for new MyMathLab users.
Guided Projects, available for each chapter, require students to carry out extended calculations (e.g., finding the arc length of an ellipse), derive physical models (e.g., Kepler’s Laws), or explore related topics (e.g., numerical integration). The “guided” nature of the projects provides scaffolding to help students tackle these more involved problems.
The Instructor’s Resource Guide and Test Bank provides a wealth of instructional resources including Guided Projects, Lecture Support Notes with Key Concepts, Quick Quizzes for each section in the text, Chapter Reviews, Chapter Test Banks, Tips and Help for Interactive Figures, and Student Study Cards.
This book is an expanded version of Calculus: Early Transcendentals by the same authors. It contains an entire chapter devoted to differential equations and additional sections on other topics (Newton’s method, surface area of solids of revolution, and hyperbolic functions). Most sections also contain additional exercises, many of them mid-level skills exercises.
Les mer
Produktdetaljer
ISBN
9780321785503
Publisert
2012-04-05
Utgiver
Vendor
Pearson
Vekt
1570 gr
Høyde
276 mm
Bredde
212 mm
Dybde
26 mm
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
912