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.
Prerequisite
MATH 170 with a grade of 'C' or better.
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 with a grade of 'C' or better.
Grading Method
Letter grade
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