Chapter | Topics | Lecture 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 function | 8 |
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 |