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University Calculus: Alternate Edition, Part One (Single Variable, Chapters 1-9)

University Calculus: Alternate Edition, Part One (Single Variable, Chapters 1-9) - 08 edition

University Calculus: Alternate Edition, Part One (Single Variable, Chapters 1-9) - 08 edition

ISBN13: 9780321475190

ISBN10: 0321475194

University Calculus: Alternate Edition, Part One (Single Variable, Chapters 1-9) by Joel D. Hass, Maurice D. Weir and George B. Thomas - ISBN 9780321475190
Edition: 08
Copyright: 2008
Publisher: Addison-Wesley Longman, Inc.
Published:
International: No
University Calculus: Alternate Edition, Part One (Single Variable, Chapters 1-9) by Joel D. Hass, Maurice D. Weir and George B. Thomas - ISBN 9780321475190

ISBN13: 9780321475190

ISBN10: 0321475194


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Summary

Calculus hasn't changed, but your students have. Many of today's students have seen calculus before at the high school level. However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. University Calculus: Alternate Edition, Part One responds to the needs of today's students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course.

University Calculus: Alternate Edition, Part One is suitable for the first two semesters or three quarters of a calculus course. The Alternate Edition is the perfect alternative for instructors who want the same quality and quantity of exercises as Thomas' Calculus, Media Upgrade, Eleventh Edition but prefer a faster-paced presentation.

Table of Contents

Table of Contents

1. Functions

1.1 Functions and Their Graphs
1.2 Combining Functions; Shifting and Scaling Graphs
1.3 Trigonometric Functions
1.4 Graphing with Calculators and Computers

2. Limits and Continuity

2.1 Rates of Change and Tangents to Curves
2.2 Limit of a Function and Limit Laws
2.3 The Precise Definition of a Limit
2.4 One-Sided Limits and Limits at Infinity
2.5 Infinite Limits and Vertical Asymptotes
2.6 Continuity
2.7 Tangents and Derivatives at a Point

3. Differentiation

3.1 The Derivative as a Function
3.2 Differentiation Rules
3.3 The Derivative as a Rate of Change
3.4 Derivatives of Trigonometric Functions
3.5 The Chain Rule
3.6 Implicit Differentiation
3.7 Related Rates
3.8 Linearization and Differentials
3.9 Parametrizations of Plane Curves

4. Applications of Derivatives

4.1 Extreme Values of Functions
4.2 The Mean Value Theorem
4.3 Monotonic Functions and the First Derivative Test
4.4 Concavity and Curve Sketching
4.5 Applied Optimization
4.6 Newton's Method
4.7 Antiderivatives

5. Integration

5.1 Area and Estimating with Finite Sums
5.2 Sigma Notation and Limits of Finite Sums
5.3 The Definite Integral
5.4 The Fundamental Theorem of Calculus
5.5 Indefinite Integrals and the Substitution Rule
5.6 Substitution and Area Between Curves

6. Applications of Definite Integrals

6.1 Volumes by Slicing and Rotation About an Axis
6.2 Volumes by Cylindrical Shells
6.3 Lengths of Plane Curves
6.4 Areas of Surfaces of Revolution
6.5 Work
6.6 Moments and Centers of Mass
6.7 Fluid Pressures and Forces

7. Transcendental Functions

7.1 Inverse Functions and Their Derivatives
7.2 Natural Logarithms
7.3 Exponential Functions
7.4 Inverse Trigonometric Functions
7.5 Exponential Change and Separable Differential Equations
7.6 Indeterminate Forms and L'Hopital's Rule
7.7 Hyperbolic Functions

8. Techniques of Integration

8.1 Integration by Parts
8.2 Trigonometric Integrals
8.3 Trigonometric Substitutions
8.4 Integration of Rational Functions by Partial Fractions
8.5 Integral Tables and Computer Algebra Systems
8.6 Numerical Integration
8.7 Improper Integrals

9. Infinite Sequences and Series

9.1 Sequences
9.2 Infinite Series
9.3 The Integral Test
9.4 Comparison Tests
9.5 The Ratio and Root Tests
9.6 Alternating Series, Absolute and Conditional Convergence
9.7 Power Series
9.8 Taylor and Maclaurin Series
9.9 Convergence of Taylor Series
9.10 The Binomial Series

10. Polar Coordinates and Conics

10.1 Polar Coordinates
10.2 Graphing in Polar Coordinates
10.3 Areas and Lengths in Polar Coordinates
10.4 Conic Sections
10.5 Conics in Polar Coordinates
10.6 Conics and Parametric Equations; The Cycloid