Matematik och Datavetenskap, Chalmers Tekniska Högskola och Göteborgs Universitet

ALA-B, 2002, week 1

Goal: Understand the Fundamental Theorem of Calculus and its proof. Learn the basic properties of the integral. Write a Matlab program for computing the integral.

Reading: Ch 27 and Ch 28.

Exercise 1.1
basic 27: 1, 2, 3, 8, 9, 10
advanced 27: 5, 6, 11, 12
demo 27: 1c, 8b, 9b

Exercise 1.2
basic 28: 1, 2, 3, 4, 5, 6, 14
advanced 28: 11, 13, 15, 16, 17, 18
demo 28: 1b, 2b, 4b

David's tutorial 1.
More integrals (by Fredrik B.)
Even more integrals (by Tomas H.)

Obligatory work: Write down the proof of The Fundamental Theorem of Calculus and put it in your individual folder. Emphasize the following steps:
1. Construction of U_n.
2. Proof that U_n is a Cauchy sequence.
3. Proof that u(x) satisfies the differential equation.
4. u is unique.
This proof is a very important part of the course and you must understand it well. Then the later parts of the course will be much easier.

Lecture 1.1: The Fundamental Theorem of Calculus.

Studio 1.1: The integral.

Lecture 1.2: Properties of the integral.

Studio 1.2: The integral (again).

/stig