Calculus@UTK 141 Table of Contents
141 Syllabus

142 Table of Contents

241 Table of Contents

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A Preview of Calculus

1. Functions and Models

  1. Four Ways to Represent a Function
  2. New Functions from Old Functions
  3. Graphing Calculators and Computers
  4. Parametric Curves
  5. Exponential Functions
  6. Inverse Functions and Logarithms
  7. Models and Curve Fitting

2. Limits and Derivatives

  1. The Tangent and Velocity Problems
  2. The Limit of a Function
  3. Calculating Limits Using the Limit Laws
  4. Continuity
  5. Limits Involving Infinity
  6. Tangents, Velocities, and Other Rates of Change
  7. Derivatives
  8. The Derivative as a Function
  9. Linear Approximations
  10. What Does f' Say about f?

3. Differentiation Rules

  1. Derivatives of Polynomials and Exponential Functions
  2. The Product and Quotient Rules
  3. Rates of Change in the Natural and Social Sciences
  4. Derivatives of Trigonometric Functions
  5. The Chain Rule
  6. Implicit Differentiation
  7. Derivatives of Logarithmic Functions
  8. Linear Approximations and Differentials

4. Applications of Differentiation

  1. Related Rates
  2. Maximum and Minimum Values
  3. Derivatives and the Shape of Curves
  4. Graphing with Calculus and Calculators
  5. Indeterminate Forms and L'Hospital's Rule
  6. Optimization Problems
  7. Applications to Economics
  8. Newton's Method
  9. Antiderivatives (Covered in 142)

Appendices

  1. Intervals, Inequalities and Absolute Values
  2. Coordinate Geometry
  3. Trigonometry
  4. Precise Definitions of Limits
  5. A Few Proofs
  6. Integration of Rational Functions by Partial Fractions
  7. Polar Coordinates
  8. Complex Numbers


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