MATH& 152 - Calculus II

Credits: 5
Variable Credit Course: No

Lecture Hours: 55
Lab Hours: 0
Worksite/Clinical Hours: 0
Other Hours (LIA/Internships): 0

Course Description: This is the second in a sequence of four calculus courses for students who are planning to major in engineering, mathematics, or the sciences, and expands on the concept of the antiderivative and integration. Topics include integration of algebraic and transcendental functions, improper integrals, applications of integration including areas, volumes, work, hydrostatic force, centers of mass, and differential equations. Graphing technology required.

Prerequisite: MATH& 151 with a grade of C or higher.
Distribution Requirements:

Natural Sciences Distribution Requirement
Quantitative

Meets FQE Requirement: No
Integrative Experience Requirement: No

Student Learning Outcomes

Evaluate definite integrals using the Fundamental Theorem of Calculus.
Calculate areas and volumes of revolution using integration.
Evaluate integrals using various techniques of integration: Substitution; Integration by parts; Partial fractions; Tables.
Approximate definite integrals using the Trapezoid Rule and Simpson’s Rule.
Solve applied problems including arc length, work, hydrostatic force, and centers of mass using techniques of integration.
Solve basic differential equations such as first order linear and separable.

Course Contents

Integrals. The Fundamental Theorem of Calculus. Calculate areas and distances. Indefinite integrals. Improper integrals.
Techniques of Integration. The substitution rule. Integration by parts. Trigonometric integrals. Trigonometric substitution. Partial fractions. Numerical Integration: Riemann Sums, Trapezoid Rule, Simpson’s Rule, Error estimation. Integration using computer algebra systems and other technology (optional).
Applications of Integration. Area between curves: Type I and Type II. Volumes of revolution. Work. Average value of a function. Arclength. Surface area of revolution. Hydrostatic pressure and force. Center of mass and centroids.
Differential Equations. Direction fields. Euler’s method. First order linear. Separable.

Instructional Units: 5