Mathematics 121 (Honours Calculus), Spring 2002

Tentative schedule

ChapterTopicsLecture hours
5 Definite Integrals and the Fundamental Theorem of Calculus: area under curves, Riemann sums and the definite integral, properties of the definite integral, the Fundamental Theorem of Calculus, the average value of a function8
6 Techniques of Integration: substitution, integration by parts, integrals of trig functions and inverse trig substitutions, partial fractions 4
6 Improper Integrals: improper integrals and comparison 2
6 Approximate Integration: trapezoidal rule and error estimate, Simpson's Rule 4
7 Applications of Definite Integrals: areas, volumes, arc length, surface area, continuous probability density functions, expectation, variance, separable first order differential equations 9
8 Parametric and Polar Curves: sketching and derivatives of parrametric and polar curves 7
9 Infinite Series: convergence of series, comparison and integral tests, alternating series, power series, Taylor's theorem with integral remainder 8