222 - Calculus and Analytic Geometry

Prerequisites: 

Calculus and Analytic Geometry 2. Prereqs < Math 221. Open to Fr.

Frequency: 
Fall (I), Winter (II), Summer (SS)
Student Body: 

This course is intended for students in the sciences, mathematics, computer science and engineering, or for other students who want preparation for higher level math courses or courses in allied fields.

Credits: 
4. (r-N-I)
Recent Texts: 

The UW Madison on-line calculus text

Course Coordinator: 
Sigurd Angenent
Background and Goals: 

Math 222 is the second course in the standard Calculus series at UW Madison, Math 221-222-234. This series is designed for students in the Sciences and Engineering. Depending on their major, students in the School of Business might be asked to take 211-213 instead of 221-222. Honors students interested in a theoretical approach should consider the Honors sequence 275-276-375-376 instead.

Alternatives: 
Students in the School of Business are sometimes asked to take 211-213 instead of 221-222 as part of their major requirements. Math 276 is a theoretical version of Math 222 and it is aimed at Honors students.
Subsequent Courses: 
Math 234.
Course Content: 
  • Techniques of integration: substitution, integration by parts, trigonometric integrals, trigonometric substitutions, partial fraction decompositions, improper integrals
  • Applications of integration to arc length, moments and center of mass, pressure and force, and elementary differential equations
  • Differential equations, linear first order
  • Definitions and relations between infinite sequences and series, algebraic and geometric series
  • Convergence tests for series: integral, comparison and ratio tests. Absolute convergence and alternating series
  • Power series and radius of convergence
  • Taylor and Maclaurin series. Taylor's formula, exp, cosine and sine expansions
  • Error bounds for Taylor approximations
  • Vectors and parametric equations
  • Lines and planes
  • Dot and cross products