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Math 222 - Calculus and Analytic Geometry 2    vanvleck.gif (8145 bytes)
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Timetable Information
Current Syllabus
Older Calculus Sequence Syllabus (out of date in many ways but contains more details)
Catalog Description

Techniques of integration, introductory ordinary differential equations, conic sections, polar coordinates, vectors, two and three dimensional analytic geometry, infinite series.
Prerequisites: Math 221. Students may not receive full degree credit for Math 222 & 213. Open to Freshmen.
Course Prerequisite(s)

Mathematics 221, or advanced placement

Prerequisite knowledge and/or skills

Ability to differentiate combinations of elementary functions, integration formulas for elementary functions and their inverses, and facts about differential and integral calculus such as the intermediate value theorem, the mean value theorem, and the Fundamental Theorem of Calculus.

Textbook(s) and/or other required material
Calculus 8th edition, by Varberg, Purcell, and Rigdon, Prentice Hall, 1999 (Linked to publisher's web pages)
Course objectives

This course builds on the skills from Mathematics 221. Those skills are extended and new skills are added, and the resulting tools are applied to new applications. As specific skills, the student will be able to:

Evaluate integrals analytically, using substitutions, integration by parts, partial fractions, and trigonometric identities
Approximate integrals numerically
Evaluate convergent improper integrals
Test a proposed solution to a differential equation, and derive the solution to an initial value problem from a general solution
Find solutions of differential equations if the variables are separable
Solve first order linear differential equations
Use Euler's method to solve differential equations numerically
Set up and solve differential equations which model behavior of a real-world system, and interpret the solutions in the problem domain
Use slope fields to describe the behavior of solutions to differential equations
Parametrize motion along a path, and compute length of a parametrically given curve
Translate between rectangular and polar coordinates, and use integration in polar coordinates
Find equations for conic sections in standard forms, and translate between the equation, a graph, and a verbal description of the curve
Use the comparison, ratio, alternating series, and integral tests to test convergence of an infinite series, and understand the role of the sequence of partial sums in determining convergence
Test for absolute vs. conditional convergence, and estimate the sum, of an alternating series
Find Taylor polynomials and bound the error in using such a polynomial to approximate a function
Find a power series representation for a function, determine where it converges, and use the series to evaluate an integral
Calculate with vectors in 2- and 3-space, represented graphically or as combinations of standard unit vectors or as pairs or triples of numbers
Compute length, dot products, cross products, and projections of vectors
Find a unit vector with given direction, the angle between two vectors, and the distance between points in space
Find equations for lines and planes in space
Topics covered
Techniques of integration: Integration by parts, trigonometric integrals, trigonometric substitutions, partial fraction decompositions, and numerical techniques
Applications of integration to arc length, moments and center of mass, pressure and force, and solving differential equations
The calculus of parametric curves
Polar coordinates, and finding areas and lengths in polar coordinates
Conic sections in rectangular coordinates
Definitions and relations between infinite sequences and series
Convergence tests for series
Power series and radius of convergence
Taylor and Maclaurin series
Applications and error bounds for Taylor approximations
Coordinates and vectors in 3-space
Dot and cross products, and applications to equations for lines and planes
Class/laboratory schedule

Three hours of lecture each week (either 50 minutes MWF or 75 minutes TR) and two hours in discussion section.

Contribution of course to professional development of engineers and scientists:

This course contributes primarily to the students' knowledge of college-level mathematics and/or basic sciences, but does not provide experimental evidence.
(Some laboratory exercises will make use of real data from experiments, but they are provided to the student rather than being measured by the student personally.)

Calculus is a fundamental tool both in the science and engineering courses which the student will take and also in professional applications. Even when the practicing engineer may use a calculator or computer to carry out a calculation, it is important that he/she knows what the technology is being asked to perform and how to tell if the answer is reasonable.This course is the second in a sequence and provides more advanced skills and understanding as well as additional applications.

Relationship of course to undergraduate engineering objectives:

This course serves students in a variety of engineering majors. The paragraph below describes how the course contributes to the college's educational objectives.

The skills learned in this course are essential to success in most science and engineering courses the student will be taking, and the course uses examples which feed into those courses. In addition, the course builds an understanding of how abstract foundations support and frequently evolve into concrete technologies.

Assessment of student progress toward course objectives
Two or three examinations during the semester (typically 90 minutes, given in the evenings) and a two hour final examination
Homework, participation in discussion section, and quiz grades from discussion section
(some sections) Computer laboratory assignments, done in small groups and handed in as a group effort
(some sections) Term projects, which may be term papers or in-depth mathematical investigations
Person(s) who prepared this description
Robert L. Wilson