Calculus 2

MS4022

Calculus II

MATH 166

International Credits:

6.0

Converted Credits:

3.5

Semester:

Country:

Ireland

Language:

English

Course Description:

Sequences and series: Limit of a sequence, convergence of a sequence; series, convergence, tests for convergence, absolute and conditional convergence. Power series. MacLaurin and Taylor series: Order notation, big-O, little-O notation, asymptotic equivalence, Taylor's Theorem and remainders, applications. Indefinite Integral: Integration of standard functions, techniques including integration by parts, substitution and partial fractions. Definite Integral: The limit of a Riemann sum, fundamental theorem of calculus, Area between two curves, Volumes of revolution, Improper integrals. Introduction to ordinary differential equations: Definition of an ODE, Linearity, first order variables separable, solution technique by integration. Introduction to functions of two real variables: Continuity, partial derivatives and their geometrical interpretation, Leibniz's rule, conditions (without proof) for maximum, minimum, saddle-point.