Upon successful completion of this course, the student should be able to:

• In Applications of Integration
  • Compute Volumes by cross-section
  • Compute Volumes by disk-washer
  • Compute Volumes by shells
  • Compute Work (spring, rope)
  • Compute Work (pumping liquids)
  • Compute Arc length
  • Compute Areas of surfaces of revolution
  • Compute Application (center of mass)
• In Techniques of Integration
  • Integrate by parts
  • Calculate trigonometric integrals
  • Calculate integrals by trigonometric substitution
  • Define the indeterminate form and apply L'Hopital's Rule.
  • Calculate improper integrals
  • Integrate by partial fractions
  • Integrate using Tables and Software
  • Approximate integrals (Trapezoidal, Simpson) with error estimation.
• In Infinite Sequences and Series
  • Write definition of and understand Sequences
  • Write definition of and understand Series (intro)
  • Determine convergence by integral test
  • Determine convergence by comparison test
  • Determine convergence of alternating series
  • Determine absolute convergence (ratio, root tests)
  • Apply strategies for testing series
  • Work with power series
  • Represent functions as power series
  • Find Taylor, Maclaurin series & polynomials
  • Calculate Taylor and Maclaurin series
• In Parametric Curves and Polar Coordinates
  • Represent curves by parametric equations
  • Perform calculus with parametric curves
  • Use and graph with polar system
  • Calculate areas and lengths in polar coordinates
  • Define the conic forms in polar form