Miami-Dade Community College
Course Description Topics include: Techniques of integration; differentiation and integration of inverse trigonometric, exponential, logarithmic, and hyperbolic functions; sequences and power series; parametric equations and polar coordinates; improper integrals; applications. (4 hrs. lecture)
Pre-requisite: MAC 2311 with a grade of C or better or equivalent.
Course Competencies:
Competency 1:
The Student will demonstrate knowledge of integrating functions by:
a. using integration by parts,
b. computing trigonometric integrals,
c. using appropriate trigonometric substitutions,
d. using partial fractions,
e. using rationalizing substitutions.
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Competency 2: The Student will demonstrate knowledge of approximate integration by:
a. using mid-point rule,
b. using trapezoidal rule,
c. using Simpson’s rule
Competency 3: The Student will demonstrate knowledge of improper integrals and their convergence by:
a. computing convergent improper integrals of type-1 and type-2,
b. identifying improper integrals that are divergent,
c. using comparison theorems to test their convergence.
Competency 4: The Student will demonstrate knowledge of applications of integrals by:
a. finding the arc length,
b. finding the area of surface of revolution,
c. finding moments and centers of mass
Competency 5: The Student will demonstrate knowledge of differential equations by:
a. modeling differential equations,
b. solving separable equations.
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Competency 6: The Student will demonstrate knowledge of curves defined by parametric and polar equations by:
a. drawing graphs of such curves,
b. finding tangents and areas that involve such curves,
c. finding arc lengths and areas of surface of revolutions of such curves.
Competency 7: The Student will demonstrate knowledge of sequences and series by:
a. determining the convergence or divergence of a sequence with different techniques,
b. computing the limits of convergent sequences,
c. recognizing types of series, such as, geometric, telescopic, harmonic, alternating, p-series, power series etc.,
d. determining convergence or divergence of a series by comparison test, limit-comparison test, integral test, alternating series test, p-series test,
e. determining the absolute convergence or conditional convergence by ratio test and/or root test,
f. determining the radius of convergence and the interval of convergence of a power series,
g. finding the Taylor and Maclaurin series of an analytic function ,
h. finding binomial series.