### ALA-B, 2003, week 1

Home, w 1, w 2, w 3, w 4, w 5, w 6, w 7. Matlab: analysis, linear algebra, facit.

Obs: boken finns nu på Cremona. Pris: 800 kr för 3 volymer.

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: AMBS Chapter 27 and Chapter 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.)

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 Un.
2. Proof that Un 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. Show this to one of your teachers during week 2 or 3.

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

Last modified: Wed Oct 29 08:07:21 MET 2003