Calculus

Quarter 2

Assignments:

Assignments:

Learning Objectives:

  • Evaluate an improper integral or determine that the integral diverges.
  • Calculate areas in the plane using the definite integral.

Assignments:

Learning Objectives:

  • Calculate volumes of solids with known cross sections using definite integrals.
  • Calculate volumes of solids of revolution using definite integrals.
  • Determine the length of a curve in the plane defined by a function, using a definite integral.

Assignments:

Learning Objectives:

  • Interpret differential equations via slope fields and show the relationship between slope fields and solution curves.
  • Find numerical solutions to differential equations using Euler's method.

Assignments:

Learning Objectives:

  • Sketch solution curves to logistic differential equations.
  • Determine the intervals where a logistic differential equation's solution is increasing or decreasing.
  • Solve simple logistic differential equations and use them to model population growth and decay.

Assignments:

Learning Objectives:

  • Calculate derivatives of parametric functions.
  • Determine the length of a curve in the plane defined by parametric functions, using a definite integral.
  • Calculate derivatives of vector valued functions.
  • Determine a particular solution given a rate vector and initial conditions.
  • Determine values for positions and rates of change in problems involving planar motion.

Assignments:

Learning Objectives:

  • Calculate derivatives of functions written in polar coordinates.
  • Calculate areas of regions defined by polar curves using definite integrals

Assignments:

Learning Objectives:

  • Show convergence of sequences including decimal expansions.
  • Show convergence or divergence of geometric series.
  • Show the divergence of the harmonic series.
  • Show convergence of p-series using the integral test.
  • Show convergence of series using the comparison tests.

Assignments:

Learning Objectives:

  • Show the interval of convergence of series using the ratio test.
  • Identify a series' radius of convergence.
  • Show the convergence of series using the alternating series test (including the alternating harmonic series).
  • Determine the intervals where a series converges absolutely and conditionally.
  • Use the ratio test (or root test) to find a power series interval of convergence.

Assignments: