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Emphasizes conceptual understanding over rote drill. The problems are organized in groups that parallel traditional grouping of ideas, making it possible to use them as supplements to most texts. Most of the problems can be done without the use of a calculator or computer.
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
Functions and Graphs
Domain and Range. Elementary Functions
Trigonometric Functions
Exponential and Logarithmic Functions
Composite Functions
Functions Described by Tables or Graphs
Parametric Equations
Polar Coordinates
The Derivative
Average Rates of Change
Introduction to the Derivative
Graphical Differentiation Problems
Limits
Continuity
Power, Sum and Product Rules
The Chain Rule
Implicit Differentiation and Derivatives of Inverses
Derivatives of Trigonometric, Log, and Exponential Functions
Root Finding Methods
Related Rates
Extreme Values
Increasing and Decreasing Functions and Relative Extrema
Concavity and the Second Derivative
Max-Min Story Problems
Antiderivatives and Differential Equations
Antiderivatives
Introduction to Differential Equations
The Definite Integral
Riemann Sums
Properties of Integrals
Geometric Integrals
The Fundamental Theorem of Calculus
Functions Defined by Integrals
The Definite Integral Revisited
Exact Values from the Fundamental Theorem of Calculus
Techniques of Integration
Approximation Techniques and Error Analysis
Sequences and Series of Numbers
Sequences of Numbers
Series of Numbers. Geometric Series
Convergence Tests: Positive Series
Convergence Tests: All Series
Newton’s Method
Improper Integrals
Sequences and Series of Functions
Sequences of Functions. Taylor Polynomials
Series of Functions. Taylor Series
Power Series
The Integral in IR2 and R3
Real-valued Functions of Two and Three Variables
Definition of Double and Triple Integrals
Evaluation of Double Integrals
Vectors and Vector Geometry
Vectors
Velocity and Acceleration
Arc Length
The Derivative in Two and Three Variables
Partial Derivatives
Gradient and Directional Derivatives
Equation of the Tangent Plane
Optimization
Line Integrals
Line Integrals
Conservative Vector Fields and Green’s Theorem