Calculus II

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Calculus II starts with a review of limits, differentiation, and integration. We then continue on to an introduction to differential equations, applications of integration, more advanced integration techniques, infinite series, and conics/paremetric equations/polar coordinates.

Grading

  • Daily Work: 20%
  • Projects: 20%
  • Quizzes: 30%
  • Exams: 30%

Contents

Session 1: Calculus Review

  • Finding derivatives using the limit method.
  • Basic derivative formulas and rules (chain rule/product rule/quotient rule)
  • Implicit Differentiation
  • Basic integration formulas and applications (finding areas and integration by substitution)
  • Numerical Integration
  • Log, exponential and other transcendental functions

Session 2: Differential Equations

  • Slope fields and Euler's method
  • Growth and Decay
  • Separation of variables and the logistic equation
  • First-order linear differential equations

Session 3: Applications of Integration

  • Areas between curves
  • Volume (Disk and Shell methods)
  • Arc length and surfaces of revolution
  • Work
  • Moments, centers of mass, and centroids
  • Fluid pressure and fluid force

Session 4: Integration techniques, L'Hopital's Rule, and Improper Integrals

  • Basic Integration Rules
  • Integration by parts
  • Trigonometric Integrals
  • Trigonometric substitutions
  • Partial fractions
  • Integration by tables and other integration techniques
  • Indeterminate forms and L'Hopital's Rule
  • Improper Integrals

Session 5: Infinite Series

  • Sequences
  • Series and Convergence
  • The integral test and p-Series
  • Harmonic series
  • Comparisons of sets
  • Alternating series
  • Ratio and root tests
  • Taylor polynomials and approximations
  • Power series
  • Taylor and Maclaurin Series

Session 6: Conics, Parametric Equations, and Polar Coordinates

  • Conics and calculus
  • Plane curves and Parametric equations
  • Parametric equations and calculus
  • Polar coordinates and polar graphs
  • Anamorphic art
  • Area, arc length in polar coordinates
  • Polar equations of conics and Kepler's Laws
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