# (Honours) Integral Calculus

### Department of Mathematics,  Undergraduate Math courses,  University of British Columbia

Math 121 is the honours version of Math 101, covering mostly the same topics, but in greater foundational depth and with more emphasis on harder and/or theoretical exercises. Some precise definitions and statements of theorems will be given, but only limited theoretical facility will be expected of students.

Prerequisite: A grade of 68% in Math 120 or 80% in Math 100, 102 or 104, or a score of 5 in AP Calculus AB, or permision of the Head of the Department.

## Text

Adams, Single Variable Calculus, fifth edition.

I will post all handouts, problem sets, final grades, etc. on the web here.

## Topics

1. Definite Integrals and the Fundamental Theorem: 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. [Chapter 5]
2. Techniques of Integration: substitution, integration by parts, integrals of trig functions and inverse trig substitutions, partial fractions. [Chapter 6]
3. Improper Integrals: improper integrals and comparison. [Chapter 6]
4. Approximate Integration: midpoint and trapezoidal rules and error estimates, Simpson's rule. [Chapter 6]
5. Applications of Definite Integrals: areas, volumes, arc length, surface area, continuous probability density functions, expectation, variance, differential equations. [Chapter 7]
6. Parametric and Polar Curves: sketching and derivatives of parametric and polar curves. [Chapter 8]
7. Infinite Series: convergence of series, comparison and integral tests, alternating series, power series, Taylor's theorem with integral remainder. [Chapter 9]