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Calculus for Scientists and Engineers, CourseSmart eTextbook

By Bill Briggs, Lyle Cochran, Bernard Gillett

Published by Pearson

Published Date: Jul 9, 2012

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Briggs/Cochran is the most successful new calculus series published in the last two decades. The authors’ years of teaching experience resulted in a text that reflects how students generally use a textbook: they start in the exercises and refer back to the narrative for help as needed. The text therefore builds from a foundation of meticulously crafted exercise sets, then draws students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students’ geometric intuition to introduce fundamental concepts, laying a foundation for the rigorous development that follows.

Table of Contents

1. Functions

1.1 Review of functions

1.2 Representing functions

1.3 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 inverse trigonometric functions

3.9 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 Hyperbolic functions



7. Logarithmic and Exponential Functions

7.1 Inverse functions

7.2 The natural logarithm and exponential functions

7.3 Logarithmic and exponential functions with general bases

7.4 Exponential models

7.5 Inverse trigonometric functions

7.6 L'Hôpital's rule and growth rates of functions



8. Integration Techniques

8.1 Basic approaches

8.2 Integration by parts

8.3 Trigonometric integrals

8.4 Trigonometric substitutions

8.5 Partial fractions

8.6 Other integration strategies

8.7 Numerical integration

8.8 Improper integrals



9. Differential Equations

9.1 Basic ideas

9.2 Direction fields and Euler's method

9.3 Separable differential equations

9.4 Special first-order differential equations

9.5 Modeling with differential equations



10. Sequences and Infinite Series

10.1 An overview

10.2 Sequences

10.3 Infinite series

10.4 The Divergence and Integral Tests

10.5 The Ratio, Root, and Comparison Tests

10.6 Alternating series



11. Power Series

11.1 Approximating functions with polynomials

11.2 Properties of power series

11.3 Taylor series

11.4 Working with Taylor series



12. Parametric and Polar Curves

12.1 Parametric equations

12.2 Polar coordinates

12.3 Calculus in polar coordinates

12.4 Conic sections



13. Vectors and Vector-Valued Functions

13.1 Vectors in the plane

13.2 Vectors in three dimensions

13.3 Dot products

13.4 Cross products

13.5 Lines and curves in space

13.6 Calculus of vector-valued functions

13.7 Motion in space

13.8 Length of curves

13.9 Curvature and normal vectors



14. Functions of Several Variables

14.1 Planes and surfaces

14.2 Graphs and level curves

14.3 Limits and continuity

14.4 Partial derivatives

14.5 The Chain Rule

14.6 Directional derivatives and the gradient

14.7 Tangent planes and linear approximation

14.8 Maximum/minimum problems

14.9 Lagrange multipliers



15. Multiple Integration

15.1 Double integrals over rectangular regions

15.2 Double integrals over general regions

15.3 Double integrals in polar coordinates

15.4 Triple integrals

15.5 Triple integrals in cylindrical and spherical coordinates

15.6 Integrals for mass calculations

15.7 Change of variables in multiple integrals



16. Vector Calculus

16.1 Vector fields

16.2 Line integrals

16.3 Conservative vector fields

16.4 Green's theorem

16.5. Divergence and curl

16.6 Surface integrals

16.6 Stokes' theorem

16.8 Divergence theorem


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Calculus for Scientists and Engineers, CourseSmart eTextbook
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$108.99 | ISBN-13: 978-0-321-82673-2