The second course in a three part calculus sequence. Topics include: the Riemann integral, applications of integration, techniques of integration, and transcendental functions. Prerequisite: MATH 215 with grade of C or higher.
Prerequisite(s) / Corequisite(s):
MATH 215 with a grade of C or higher.
Course Rotation for Day Program:
Not offered in the day program.
Most current editions of the following:
A TI-84 calculator is required for this course. This calculator will be allowed on most assessment opportunities in this course.
By Stewart (Brookes-Cole) Recommended
Course Learning Outcomes
Compute definite and indefinite integrals.
Relate the graph of a function to properties of its integral.
Solve applied problems using calculus.
Demonstrate understanding of the calculus of logarithmic and exponential functions.
Demonstrate understanding of the calculus of inverse trigonometric functions.
Analyze indeterminate forms and apply L’Hospital’s rule to evaluate limits of such forms.
Apply integration rules including substitution, integration by parts, trigonometric identities, trigonometric substitution and partial fractions to evaluate integrals.
Major Topics/Skills to be Covered:
Compute definite integrals as the limit of Riemann sums and approximate integrals using finite Riemann sums.
Evaluate definite and indefinite integrals using the Fundamental Theorem of Calculus and the method of substitution.
Compute areas and volumes using definite integrals.
Identify the natural exponential and logarithmic functions as inverses of each other and find their derivatives and integrals.
Solve exponential growth and decay problems arising from biology, physics, chemistry, and other sciences.
Compute derivatives and integrals of functions containing inverse trigonometric functions.
Analyze various indeterminate forms and apply L’Hospital’s rule to evaluate limits of such forms.
Use the Substitution Rule and the Integration by Parts formula to evaluate indefinite and definite integrals.
Describe and explain special methods required to integrate trigonometric and rational functions.
Apply numerical methods of integration such as Simpson's Rule and the trapezoidal rule to approximate definite integrals.
Recommended maximum class size for this course: 30
NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by
the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this
course for Columbia College are expected to facilitate learning pursuant to the course learning outcomes and cover the subjects listed in the Major Topics/Skills to be Covered section.
However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's
subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.