Mathematics - MATH 151

Course Description

This course includes the study of derivatives and integrals of transcendental functions, techniques of integration, indeterminate forms, improper integrals, infinite series, conics, polar coordinates and applications.

Prerequisites

(A requirement that must be completed before taking this course.)

Course Competencies

Upon successful completion of the course, the student should be able to:

• Apply the definite integral in computing areas and surface areas.
• Apply the definite integral in computing volumes.
• Determine the derivative of hyperbolic and inverse hyperbolic functions.
• Evaluate the integral of a rational function using long division and/or partial fraction decomposition.
• Evaluate integrals using various techniques such as: parts, rationalizing substitutions, trigonometric substitution, completing the square.
• Evaluate improper integrals.
• Identify convergence or divergence of various sequences.
• Identify convergence or divergence of an infinite series using an appropriate test.
• Investigate the limit of a geometric, telescoping, alternating or p-series.
• Determine the interval of convergence for a power series.
• Determine a power series representation of various functions.
• Approximate certain non-polynomial function values and definite integrals using power series.
• Compute the arc length of a parametric or polar curve.
• Compute the slope of a tangent line to a parametric or polar curve.
• Compute the area of a region enclosed by polar curves.
• Analyze conic sections.

Course Schedule