MAC 2312 - Calculus with Analytic Geometry II

Mathematics Department

Credit(s): 5
Contact Hours: 77
Effective Term Spring 2019 (555)

Requisites

Prerequisite MAC 2311 with a minimum grade of C

Course Description

This course is a continuation of MAC 2311 with the study of applications of integration, integration techniques, improper integrals, infinite series and sequences, conics, parametric equations, and polar coordinates. Topics include areas, volumes, centroids, work, fluid pressure, length of arc, trigonometric integrals, integration techniques, polar coordinates, improper integrals, infinite series, plane curves, parametric equations, and conic sections. (Note: Credit is only given for MAC 2312 or MAC 2234.)

Learning Outcomes and Objectives

  1. The student will perform applications of the definite integral by:
    1. solving area problems.
    2. solving volume problems.
    3. solving work problems.
    4. finding the length of an arc of a plane function.
    5. finding the center of mass.
  2. The student will apply integration techniques to evaluate integrals by:
    1. using the methods of parts.
    2. integrating various combinations of trigonometric functions.
    3. using trigonometric substitution.
    4. using partial fractions.
    5. integrating improper integrals with infinite limits of integration.
    6. integrating improper integrals of sectionally continuous functions involving infinite discontinuities.
  3. The student will use polar coordinates, plane curves, parametric equations, and conic sections by:
    1. defining basic terms related to polar coordinates and plotting points in a polar coordinate system.
    2. converting from rectangular to polar coordinates and vice versa.
    3. graphing the limacon, cardioid, rose, spiral, line, and circle.
    4. finding area and arc length in polar coordinates.
    5. obtaining parametric equations of a given plane curve and eliminating the parameter.
    6. finding the slope and concavity of a curve given parametrically.
    7. finding the length of an arc of a curve given parametrically.
    8. graphing parabolas, ellipses, and hyperbolas and extracting useful information from those graphs.
  4. The student will analyze infinite series by:
    1. defining a sequence, determining if it is increasing or decreasing, finding lower and upper bounds, if they exist, and determining convergence or divergence.
    2. defining an infinite series, the sum of a series, and the nth partial sum of a series.
    3. determining the convergence or divergence of infinite series using the:
      1. nth term test
      2. geometric series test
      3. p-series test
      4. integral test
      5. alternating series test
      6. comparison tests
      7. ratio test
      8. root test
    4. being able to do the following with a power series:
      1. find convergence interval using the ratio and root tests
      2. differentiation
      3. integration
    5. stating and using Taylor polynomials.
    6. defining the Taylor and Maclaurin series for a given analytic function.
    7. using the Binomial Theorem as it applies to infinite series.

Criteria Performance Standard

In order to earn a grade of C or better, the student will achieve at the 70% level or higher on classroom measures. Upon successful completion of the course the student will, with a minimum of 70% accuracy, demonstrate mastery of each of the above stated objectives through classroom measures developed by individual course instructors.

History of Changes

Revised 8/84 DBT 11/20/90 Effective Session 19911 3 YR C&I Review 8/94 C&I 3/17/98; DBT 4/20/98 Effective Session 19981 Effective Sess 19981. 3 Year Review 2001. 3 Year Review 2005 eff 20061(0370). 3 Year Review 2009. C&I Approval: 03/17/1998, BOT Approval: 05/29/1998, Effective Term: Fall 2006 (370).
C&I Approval: 07/26/2018, BOT Approval: 09/18/2018, Effective Term: Spring 2019 (555)

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