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Analytic Geometry and Calculus II

MTH 162

Analytic Geometry and Calculus II

MTH 162

Course Description

Prerequisite: MTH 161 with a grade of "C" or better. Includes applications of integrals, integration techniques, limits and indeterminate forms, improper integrals, infinite series, polar coordinates, parametric equations, as well as differentiation and integration of trigonometric and hyperbolic functions. A TI 89 GRAPHING CALCULATOR IS REQUIRED. (60-0)

Outcomes and Objectives

The student will develop an understanding of hyperbolic functions.

Objectives:

  • Evaluate derivatives of hyperbolic functions .
  • Evaluate integrals related to hyperbolic functions.

The student will use integration to solve applied problems in a variety of settings.

Objectives:

  • Find the area between two curves.
  • Find volumes of solids of revolution.
  • Find lengths of curves.
  • Find the surface area of a solid of revolution.
  • Solve applied problems which may include work, fluid pressure, and centers of mass.

The student will use a variety of integration techniques to solve problems in various settings.

Objectives:

  • Determine which integration technique is appropriate to solve a given problem.
  • Evaluate integrals using integration by parts.
  • Evaluate integrals using the method of partial fraction decomposition.
  • Evaluate integrals using trigonometric substitution.
  • Evaluate integrals using trigonometric identities where appropriate.
  • Evaluate integrals using integration tables.
  • Evaluate improper integrals.
  • Estimate definite integrals using the trapezoid rule and Simpson's rule.
  • Evaluate integrals using a computer algebra system (CAS).

The student will develop an understanding of sequences and series.

Objectives:

  • Differentiate and integrate perform numerical estimates using power series.
  • Determine whether a sequence converges or diverges.
  • Determine the sum of a convergent geometric series.
  • Use the following tests to determine the convergence, absolute convergence, or divergence of an infinite series: comparison test, integral test, and ratio test.
  • Determine which test is appropriate to use on a given problem.
  • Determine the radius and interval of convergence for power series.
  • Determine the Taylor or Maclaurin series for a variety of functions.

The student will develop an understanding of the calculus of conic sections, parametric curves and polar equations.

Objectives:

  • Determine parametric equations for a curve.
  • Sketch graphs of parametric curves.
  • Evaluate derivatives of curves defined parametrically.
  • Find lengths of curves defined parametrically.
  • Find the surface area of a solid of revolution for a parametric curve.
  • Sketch graphs of polar equations.
  • Determine the area enclosed by a polar curve or between 2 polar curves.
  • Determine the length of a polar curve and the surface area of a solid of revolution for a polar curve.

The student will use technology appropriately to do mathematics.

The student will communicate effectively about mathematics.

Objectives:

  • Verbally describe solutions to problems using appropriate terminology.
  • Provide complete written solutions to problems using appropriate terminology.