Course Description
Volumes, arclength, work, separable differential equations. Techniques of integration. Sequences and series, convergence tests, power series, and Taylor series. Vectors in three-dimensional space, dot product, cross product, lines, and planes.
Athena Title
Calc II Sci and Eng Honors
Equivalent Courses
Not open to students with credit in MATH 2260, MATH 2260E, MATH 2310H
Prerequisite
(MATH 2250 or MATH 2250E or MATH 2300H or MATH 2400 or MATH 2400H) and permission of Honors
Semester Course Offered
Offered fall
Grading System
A - F (Traditional)
Course Objectives
The student will learn how to solve a variety of applied problems using the integral, including modeling problems by differential equations. The student will learn how to test numerical series for convergence and then apply this to power series and Taylor series approximations. The student will, lastly, acquire familiarity with vector algebra and geometry and apply this to lines and planes in three-dimensional space. This honors course will feature somewhat more challenging problems than the non-honors equivalent.
Topical Outline
1. Review of the definition of the integral, Fundamental Theorem of Calculus, area, and integration by substitution 2. Volumes: cross-sections, cylindrical shells, Arclength and surface area, Work 3. Separable differential equations 4. Methods of integration: integration by parts, trigonometric substitutions, and partial fractions, Improper integrals 5. Sequences, series, convergence tests, Power series, Taylor series, and applications 6. Vectors in three dimensions, Dot product, cross product, lines, and planes
General Education Core
CORE III: Quantitative Reasoning