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Calculus 2:

 

Integrals

 

  • Riemann Sums and Trapezoidal Sums to calculate area under a curve
  • Integration Rules for all functions using Indefinite Integrals
  • Fundamental Theorem of Calculus 1 and 2
     – definite integrals
     – derivative of an integral
  • Integration using Partial Fractions, Integration by Parts, and Improper Integrals
  • Trig Substitution
  • Advanced Trigonometric Integration

 

Application of Integrals

  •  Area between curves
  • Finding Volume using known cross sections
  • Solids of Revolution (finding volume using the disk and washer methods)
  • Particle Motion

 

Differential Equations

 

  • Separable Differential Equations
  • Slope Fields and Growth and Decay

 

Polar Functions

  • Slope and Arc Length
  • Area of Polar Functions

 

Parametric and Vector Functions

  

  • Slope and Arc Length
  • Horizontal and Vertical Tangents
  • Particle Motion

 

Sequences and Series

 

  •  Sequences
  • Convergence and Divergence for Infinite Series (9 series tests)
  • Radius and Interval of Convergence
  • Taylor Polynomials and Expansions
  • Error and Lagrange Error Bound

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