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Sep 07, 2024
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MTH 162 - Analytic Geometry and Calculus IICredits: 4 Instructional Contact Hours: 4
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.
Prerequisite(s): MTH 161 with grade of "C" or higher Corequisite(s): None Lecture Hours: 60 Lab Hours: 0 Meets MTA Requirement: Math Pass/NoCredit: Yes
Outcomes and Objectives
- The student will develop an understanding of hyperbolic functions.
- 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.
- 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.
- 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.
- 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.
- 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.
- Verbally describe solutions to problems using appropriate terminology.
- Provide complete written solutions to problems using appropriate terminology.
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