MATH 175 Calculus 2*

This is the second course in the calculus sequence. It covers techniques of integration, improper integrals, Simpson’s Rule, Trapezoid Rule, arc length, surface area, other applications of integration, direction (slope) fields, parametric equations, polar calculus, conic sections, infinite sequences and series, power series and Taylor’s formula.

Credits

4 Credits

Semester Contact Hours Lecture

60

Prerequisite

MATH 170

MATH 175Calculus 2*

Please note: This is not a course syllabus. A course syllabus is unique to a particular section of a course by instructor. This curriculum guide provides general information about a course.

I. General Information

Department

Mathematics & Engineering

II. Course Specification

Course Type

Program Requirement

Credit Hours Narrative

4 Credits

Semester Contact Hours Lecture

60

Prerequisite Narrative

MATH 170

Grading Method

Letter grade

Repeatable

N

III. Catalog Course Description

This is the second course in the calculus sequence. It covers techniques of integration, improper integrals, Simpson’s Rule, Trapezoid Rule, arc length, surface area, other applications of integration, direction (slope) fields, parametric equations, polar calculus, conic sections, infinite sequences and series, power series and Taylor’s formula.

IV. Student Learning Outcomes

Upon completion of this course, a student will be able to:

• Apply techniques of integration to improper integrals, arc length, area of a surface revolution, and other real-world applications.
• Apply theirtrigonometric knowledge of parametric equations to polar calculus and conic sections. They will apply that knowledge to skill-based and real-world problems.
• Use sequences, series and techniques for determining convergence and divergence. They will apply those techniques to analyze and evaluate power, Taylor, and Maclaurin series representations.

V. Topical Outline (Course Content)

Simpson’s Rule Trapezoid Rule Arc length Surface area of solids of revolution Differentiation and integration of inverse trigonometric functions Integration by parts Integrals involving powers of trig functions Integration using trig substitutions Integration using partial fractions Integration by tables Improper integrals Direction (slope) fields Sequences Series and tests for convergence Taylor polynomials and approximations Power series Representing functions by power series Taylor and Maclaurin series Conics sections, including rotated conics Parametric equations of plane curves Derivative, slope of tangent, arc length and surface area for parametric equations Polar coordinates and graphs Area and arc length for polar curves

VI. Delivery Methodologies