Department of Mathematics

Course Objectives

By the end of Calculus II, students should have significant fundamental knowledge and skills so they can apply calculus to future STEM academic training and professional practice.

Fundamental calculus knowledge and skills will be learned and evaluated based on specific objectives related to:

Limits and Derivatives

  • Apply L'Hospital's Rule to calculate limits of various indeterminate forms.
  • Calculate derivatives of:
    • inverse trigonometric functions,
    • hyperbolic trigonometric functions,
    • exponential and logarithmic functions.
  • Recognize when to apply logarithmic differentiation.
  • Calculate slope of tangent lines for curves given parametrically or in polar coordinates.

Integrals and Applications

  • Calculate volumes of solids of revolution.
  • Apply integration to force functions to calculate work.
  • Apply exponentials to solve real world problems such as: population growth, decay of radioactive elements, and Newton's Law of Cooling.
  • Solve initial value problems for separable differential equations.
  • Recognize when to apply integration techniques such as:
    • integration by parts,
    • trigonometric substitution,
    • partial fractions.
  • Compute arc length of a function given:
    • in Cartesian coordinates,
    • in polar coordinates,
    • parametrically.
  • Solve for the area between polar curves.

Sequences and Series

  • Determine the limit of a sequence by applying previous calculus knowledge.
  • Calculate the limit of a geometric series.
  • Apply tests to determine convergence/divergence of series including:
    • n-th term test,
    • p-series test,
    • alternating series test,
    • ratio test,
    • integral test,
    • comparison tests.
  • Apply the ratio test to determine the interval of convergence for a power series.
  • Memorize common power series representations of functions.
  • Determine power series representations of more complicated functions by manipulating known power series representations.
  • Apply the Taylor series formula to calculate even more power series representations of various functions.