# (Honours) Integral Calculus

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

This is an honours version of Math 101, covering mostly the same topics, but in greater depth and with more emphasis on harder 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 5 in AP Calculus AB or 75% on the Calculus Challenge exam. Registration is only possible through the Mathematics department. For registration please email lamb@math.ubc.ca or phone 604-822-2666.

## 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. [Chapter 6]
4. Approximate Integration: trapezoidal rule and error estimate, Simpson's Rule. [Chapter 6]
5. Applications of Definite Integrals: areas, volumes, arc length, surface area, continuous probability density functions, expectation, variance, complex numbers, differential equations. [Chapter 7]

• There will be weekly problem sets. The best seven of these will account for about 10% of the final mark.
• There will be two midterms (Wednesday, Oct 9 and Wednesday, Nov 6) accounting for about 40% of the final mark.
• The final exam will account for about 50% of the final mark.
• Grades will probably be scaled.