Matematik och Datavetenskap,
Chalmers Tekniska Högskola och
Göteborgs Universitet

###
ALA-B, 2004, week 1

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

Answers to AMBS problems
(postscript).
Corrections AMBS problems, ch 31.
Corrections AMBS problems, ch 32.

David's tutorial 1.

More integrals (by Fredrik B.)
(postscript)

**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. 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.

`/stig`

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