The first part of the three-part calculus series. Topics include: review of algebra and trigonometry; functions and limits; derivatives and their applications; the integrals and their applicatations. Â Prerequisite: Grade of C or higher in MATH 180 or a score of 26 or higher on the math portion of the ACT or 590 or above SAT score or a passing score on the Columbia College math placement exam. G.E.

Prerequisite(s) / Corequisite(s):

Grade of C or higher in MATH 180 or a score of 26 or higher on the math portion of the ACT or 590 or above SAT score or a passing score on the Columbia College math placement exam.

Course Rotation for Day Program:

Offered Fall and Spring.

Text(s):

Most current editions of the following:

Calculus

By Stewart (Brookes-Cole) Recommended

Course Learning Outcomes

Compute limits, analytically or from a graph, or determine that a limit does not exist.

Determine if functions are continuous, analytically or from a graph, and identify different types of discontinuities.

Compute derivatives of functions or determine that a derivative does not exist.

Relate the graph of a function to properties of its derivative.

Compute definite and indefinite integrals.

Relate the graph of a function to properties of its integral.Â

Solve applied problems using calculus.

Major Topics/Skills to be Covered:

Identify basic algebraic and trigonometric functions from numerical, graphical, symbolic and analytic perspectives.

Apply limit laws to calculate limits of sums, differences, products and quotients of functions.

Distinguish between one-sided and two-sided limits and describe their existence from geometric and analytic points of view.

Evaluate limits using the precise definition of the limit.

Determine if functions are continuous and identify removable, infinite and jump discontinuities.

Apply the Intermediate Value Theorem to prove the existence of roots of functions.

Explain derivatives as instantaneous rates of change.

Differentiate functions explicitly and implicitly and identify cases where functions are not differentiable.

Differentiate composite functions using the Chain Rule.

Apply differential and integral calculus to solve problems in the natural and social sciences.

Compute higher order derivatives and interpret them from a physical point of view.

Use linear approximations and differentials to approximate functions and solve applied problems.

Apply the Mean Value Theorem to establish basic properties of differentiable functions.

Compute limits at infinity and identify horizontal asymptotes.

Sketch graphs of functions based on information about their first and second derivatives.

Solve optimization problems.

Use Newton’s method to solve equations and identify limitations of the method.

Find antiderivatives of functions with and without initial conditions.

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.

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.