Calculus Problems for a New Century ( MAA Notes Series #28: Resources for Calculus ), Vol. 2 Book

Introduction: Resources for Calculus Collection
The Five Volumes of the Resources for Calculus Collection
Acknowledgements
Foreword
Acknowledgements for Volume II
Suggestions to the Student
Suggestions to the Instructor

I. Functions and Graphs
1. Domain and Range. Elementary Functions
2. Trigonometric Functions
3. Exponential and Logarithmic Functions
4. Composite Functions
5. Functions Described by Tables or Graphs
6. Parametric Equations
7. Polar Coordinates

II. The Derivative
1. Average Rates of change
2. Introduction to the Derivative
3. Graphical Differential Problems
4. Limits
5. Continuity
6. Power, Sum, and Product Rules
7. The Chain Rule
8. Implicit Differentiation and Derivatives of Inverse
9. Derivatives of Trigonometric, Log, and Exponential Functions
10. Root Finding Methods
11. Related Rates

III. Extreme Values
1. Increasing and Decreasing Functions and Relative Extrema
2. Concavity and the Second Derivative
3. Man-Min Story Problems

IV. Antiderivatives and Differential Equations
1. Antiderivatives
2. Introduction to Differential Equations

V. The Definite Integral
1. Riemann Sums
2. Properties of Integrals
3. Geometric Integrals
4. The Fundamental Theorem of Calculus
5. Functions Defined by Integrals

VI. The Definite Integral Revisited
1. Exact Values from the Fundamental Theorem of Calculus
2. Techniques of Integration
3. Approximation Techniques and Error Analysis

VII. Sequences and Series of Numbers
1. Sequences of Numbers
2. Series of Numbers. Geometric Series
3. Convergence Tests: Positive Series
4. Newton's Method
5. Improper Integrals

VIII. Sequences and Series of Functions
1. Sequences of Functions. Taylor Polynomials
2. Series of Functions. Taylor Series
3. Power Series

IX. The Integral of R Squared and R Cubed
1. Real-valued Functions of Two and Three Variables
2. Definition of Double and Triple Integrals
3. Evaluation of Double Integrals

X. Vectors and Vector Geometry
1. Vectors
2. Velocity and Acceleration
3. Arc Length

XI. The Derivative in Two and Three Variables
1. Partial Derivatives
2. Gradient and Directional Derivatives
3. Equation of the Tangent Plane
4. Optimization

XII. Line Integrals
1. Line Integrals
2. Conservative Vector Fields and Green's Theorem