9781429231893

Single Variable Calculus (Paper) Chapters 1-12

by
  • ISBN13:

    9781429231893

  • ISBN10:

    1429231890

  • Edition: 2nd
  • Format: Paperback
  • Copyright: 4/1/2011
  • Publisher: W. H. Freeman

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Summary

What’s the ideal balance?  How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning?   With your teaching—supported by Rogawski’s Calculus, Second Edition—the most successful new calculus text in 25 years!
 
Widely adopted in its first edition, Rogawski’s Calculus worked for instructors and students by balancing formal precision with a guiding conceptual focus. Rogawski engages students while reinforcing the relevance of calculus to their lives and future studies.  Precise mathematics, vivid examples, colorful graphics, intuitive explanations, and extraordinary problem sets all work together to help students grasp a deeper understanding of calculus.
 
Now Rogawski’s Calculus success continues in a meticulously updated new edition.  Revised in response to user feedback and classroom experiences, the new edition provides an even smoother teaching and learning experience.
 
This paperback volume includes chapters 1-12 of the Second Edition, for instructors who just want the book's coverage of topics in single variable calculus.

Table of Contents

Chapter 1:  Precalculus Review
1.1 Real Numbers, Functions, and Graphs
1.2 Linear and Quadratic Functions
1.3 The Basic Classes of Functions
1.4 Trigonometric Functions
1.5 Technology Calculators and Computers

Chapter 2:  Limits
2.1 Limits, Rates of Change, and Tangent Lines
2.2 Limits:  A Numerical and Graphical Approach
2.3 Basic Limit Laws
2.4 Limits and Continuity
2.5 Evaluating Limits Algebraically
2.6 Trigonometric Limits
2.7 Limits at Infinity
2.8 Intermediate Value Theorem
2.9 The Formal Definition of a Limit

Chapter 3:  Differentiation
3.1 Definition of the Derivative
3.2 The Derivative as a Function
3.3 Product and Quotient Rates
3.4 Rates of Change
3.5 Higher Derivatives
3.6 Trigonometric Functions
3.7 The Chain Rule
3.8 Implicit Differentiation
3.9 Related Rates

Chapter 4: Applications of the Derivative
4.1 Linear Approximation and Applications
4.2 Extreme Values
4.3 The Mean Value Theorem and Monotonicity
4.4 The Shape of a Graph
4.5 Graph Sketching and Asymptotes
4.6 Applied Optimizations
4.7 Newton’s Method
4.8 Antiderivatives

Chapter 5:  The Integral
5.1 Approximating and Computing Area
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus, Part I
5.4 The Fundamental Theorem of Calculus, Part II
5.5 Net Change as the Integral of a Rate
5.6 Substitution Method                                         

Chapter 6:  Applications of the Integral
6.1 Area Between Two Curves
6.2 Setting Up Integrals:  Volume, Density, Average Value
6.3 Volumes of Revolution
6.4 The Method of Cylindrical Shells
6.5   Work and Energy

Chapter 7:  The Exponential Function
7.1 Derivative of f(x) = bx and the Number e
7.2 Inverse Functions
7.3 Logarithms and Their Derivatives
7.4 Exponential Growth and Decay
7.5 Compound Interest and Present Value
7.6 Models Involving y? = k ( y – b
7.7 L’Hôpital’s Rule
7.8 Inverse Trigonometric Functions
7.9 Hyperbolic Functions

Chapter 8:  Techniques of Integration
8.1 Integration by Parts
8.2 Trigonometric Integral
8.3 Trigonometric Substitution
8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
8.5 The Method of Partial Fractions
8.6 Improper Integrals
8.7 Probability and Integration
8.8 Numerical Integration

Chapter 9:  Further Applications of the Integral and Taylor Polynomials
9.1 Arc Length and Surface Area
9.2 Fluid Pressure and Force
9.3 Center of Mass
9.4 Taylor Polynomials

Chapter 10:  Introduction to Differential Equations
10.1 Solving Differential Equations
10.2 Graphical and Numerical Method
10.3 The Logistic Equation
10.4 First-Order Linear Equations

Chapter 11:  Infinite Series
11.1 Sequences
11.2 Summing an Infinite Series
11.3 Convergence of Series with Positive Terms
11.4 Absolute and Conditional Convergence
11.5 The Ratio and Root Tests
11.6 Power Series
11.7 Taylor Series

Chapter 12:  Parametric Equations, Polar Coordinates, and Conic Sections?
12.1 Parametric Equations
12.2 Arc Length and Speed
12.3 Polar Coordinates
12.4 Area and Arc Length in Polar Coordinates
12.5 Conic Sections

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