Matematik och Datavetenskap, Chalmers Tekniska Högskola och Göteborgs Universitet
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 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.
/stig