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Latest revision as of 15:03, 3 April 2013
Contents
Catalog Information
Title
Calculus 2.
(Credit Hours:Lecture Hours:Lab Hours)
(4:5:0)
Offered
F, W, Sp, Su
Prerequisite
Math 112 or equivalent.
Description
Techniques and applications of integration; sequences, series, convergence tests, power series; parametric equations; polar coordinates.
Note
Honors also.
Desired Learning Outcomes
This course is designed for students majoring in the mathematical and physical sciences, engineering, or mathematics education and for students minoring in mathematics or mathematics education. Calculus is the foundation for most of the mathematics studied at the university level. The mastery of calculus requires welldeveloped skills, clear conceptual understanding, and the ability to model phenomena in a variety of settings. Calculus 2 develops techniques of integration, applications of integration, infinite sequences and series, parametric curves, polar coordinates, and conic sections. This course contributes to all the expected learning outcomes of the Mathematics BS (see [1]).
Prerequisites
Students are expected to have completed Math 112 or equivalent. A student with a 4 or 5 on the AB calculus exam can receive credit for Math 112.
Minimal learning outcomes
Students should achieve mastery of the topics below. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve nontrivial problems related to these concepts, and prove simple theorems in analogy to proofs given by the instructor. Previous final exams (see [2]) give specific examples of the level of understanding that is expected.
 Techniques of integration
 Integration by parts
 Trigonometric substitution
 Partial fractions
 Integration using a computer algebra system
 Approximation of integrals including Simpson’s and trapezoidal rules
 Improper integrals
 Applications of integration
 Area between curves
 Volumes from slice method (includes washer method) and shell method
 Work
 Average value of a function
 Arc Length
 Area of a surface of revolution
 Hydrostatic force
 Moments and centers of mass for regions in the plane
 Using centroids to compute volume, hydrostatic force, and work.
 Infinite sequences and series
 Infinite sequences including definition, limit laws, and the theorem on monotonic sequences
 Infinite series including definition with partial sums, the geometric and harmonic series
 Tests for convergence of series including the test for divergence, and the integral, comparison, limit comparison, ratio and root tests.
 Alternating series test and bounding the sum of an alternating series between successive partial sums
 Absolute and conditional convergence
 Functions defined by power series including the radius of convergence, differentiation, and integration
 Taylor and Maclaurin series
 Parametric equations and polar coordinates
 Curves defined by parametric equations
 Tangent lines, arc length and area for curves defined by parametric equations
 Polar coordinates including graphs, tangent lines, arc lengths and areas
 Conic sections in Cartesian and polar coordinates
Textbooks
Possible textbooks for this course include (but are not limited to):
Additional topics
These are at the instructor's discretion as time allows. Some suggested topics are applications to economics and biology, probability, centroids of curves and solids, and the logarithm defined as an integral.
Courses for which this course is prerequisite
This course is required for Math 300, Math 302, Math 314, Math 334, and Math 341.