Calculus@UTK 142 Table of Contents


142 Syllabus

141 Table of Contents

241 Table of Contents

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4. Applications of Differentiation

  1. Antiderivatives

5. Integrals

  1. Areas and Distances
  2. The Definite Integral
  3. Evaluating Definite Integrals
  4. The Fundamental Theorem of Calculus
  5. The Subsitution Rule
  6. Integration by Parts
  7. Integration using Tables and Computer Algebra Systems
  8. Approximate Integration
  9. Improper Integrals

6. Applications of Integration

  1. More about Areas
  2. Volumes
  3. Arc Length
  4. Average Value of a Function
  5. Applications to Physics and Engineering
  6. Applications to Economics and Biology
  7. Probability

7. Differential Equations

  1. Modeling with Differential Equations
  2. Direction Fields
  3. Euler's Method
  4. Separable Equations
  5. Exponential Growth and Decay
  6. The Logistic Equation
  7. Predator-Prey Systems

8. Infinite Sequences and Series

  1. Sequences
  2. Series
  3. The Integral and Comparison Tests: Estimating Sums
  4. Other Convergence Tests
  5. Power Series
  6. Representation of Functions as Power Series
  7. Taylor and Maclaurin Series
  8. The Binomial Series
  9. Applications of Taylor Polynomials
  10. Using Series to Solve Differential Equations

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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