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Integral Calculus

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Description

Integrals

  • Antiderivatives
  • Riemann sum
  • Definite integral
  • Fundamental theorem of calculus

Integration Techniques

  • U-Substitution
  • Integration by parts
  • Integration using trigonometric identities
  • Trigonometric substitution
  • Integration of rational functions by partial fractions
  • Improper integrals
  • Numerical integration

Integration Applications

  • Areas between curves
  • Volumes of solid with known cross-sections
  • Volumes of solids of revolution – Disc method
  • Volumes of solids of revolution – Shell method
  • Average value of a function
  • Arc length

Differential Equations

  • Introduction to differential equations
  • Separable equations
  • Applications to differential equations
  • Slope fields
  • Euler’s method

Sequence and Series

  • Introduction to sequences
  • Monotonic and bounded sequences
  • Introduction to infinite series
  • Convergence and divergence of normal infinite series
  • Convergence & divergence of geometric series
  • Convergence & divergence of telescoping series
  • Divergence of harmonic series
  • P Series
  • Alternating series test
  • Divergence test
  • Comparison & limit comparison test
  • Integral test
  • Ratio test
  • Root test
  • Absolute & conditional convergence
  • Radius and interval of convergence with power series
  • Functions expressed as power series
  • Taylor series and Maclaurin series
  • Approximating functions with Taylor polynomials and error bounds

Parametric Equations and Polar Coordinates

  • Defining curves with parametric equations
  •  Tangent and concavity of parametric equations
  • Area of parametric equations
  • Arc length and surface area of parametric equations
  • Polar coordinates
  • Tangents of polar curves
  • Area of polar curves
  • Arc length of polar curves

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