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Viser: Single Variable Calculus
Single Variable Calculus
William Briggs, Lyle Cochran og Bernard Gillett
(2014)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- 2. Udgave
- Paperback: 896 sider
- Udgiver: Pearson Education, Limited (Marts 2014)
- Forfattere: William Briggs, Lyle Cochran og Bernard Gillett
- ISBN: 9780321954893
This much anticipated second edition of the most successful new calculus text published in the last two decades retains the best of the first edition while introducing important advances and refinements. Authors Briggs, Cochran, and Gillett build from a foundation of meticulously crafted exercise sets, then draw 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 development that follows.
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0321954890 / 9780321954893 Single Variable Calculus, 2/e
1.1 Review of functions
1.2 Representing functions
1.3 Trigonometric functions
1.4 Trigonometric functions
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 Working with derivatives
3.3 Rules of differentiation
3.4 The product and quotient rules
3.5 Derivatives of trigonometric functions
3.6 Derivatives as rates of change
3.7 The Chain Rule
3.8 Implicit differentiation
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
7. Logarithmic and Exponential Functions
7.1 Inverse functions
7.2 The natural logarithmic and exponential functions
7.3 Logarithmic and exponential functions with other bases
7.4 Exponential models
7.5 Inverse trigonometric functions
7.6 L'' Hôpital''s Rule and growth rates of functions
7.7 Hyperbolic 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
8.9 Introduction to 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
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