COURSE SYLLABUS
Course Number: MATH1620
Course Title: CALCULUS II
Credit Hours: 4
Prerequisites: MATH1610
Corequisite:
Bulletin Description:
CALCULUS II (4). Pr., MATH1610. Techniques of integration, applications of the integral, parametric equations, polar coordinates. Vectors, lines and planes in space. Infinite sequences and series.
Students may receive credit for only one of MATH1620, MATH1627, MATH1720.
Objectives:
To develop students' mathematical and analytic skills. To further students' understanding of integral calculus and the applications of the integral. To develop students' conception of infinite sequences and series, to master techniques of analyzing convergence, and to apply this knowledge in the study of sequences and series of functions.
Course Content:
Techniques of Integration. [14 days]
Integration by Parts, Trigonometric Integrals, Trigonometric Substitution, Partial Fractions, Improper Integrals.
Applications of the Integral. [8 days]
Areas of Regions Between Curves, Volumes, Volumes by Cylindrical Shells, Work, Arc Length.
Vectors. [4 days]
Vectors in the plane and space, lines and planes in space.
Parametric Equations and Polar Coordinates. [5 days]
Curves and Parametric Equations, Tangents and Areas in Polar Coordinates.
Sequences and Series. [24 days]
Definitions, Integral Test, Comparison Test, Alternating Series, Absolute Convergence, Ratio and Root test and Absolute Convergence, Strategy for Testing Convergence, Power Series, Functions as Power Series, Taylor Series and Maclaurin Series, Applications of Taylor Polynomial.
Tests and review. [5 days]