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.
Reading: Ch 27 and Ch 28.
Exercises:
basic 27: 1, 2, 3, 4, 7, 8, 9, 11.
28: 1, 2, 3, 4, 5, 6, 7, 8,
9, 13, 14, 15,
advanced 27: 5, 6, 10. 28: 10, 11, 12, 16, 17, 18
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.
Lecture 2.1: Linear algebra in R3.
Studio 2.1: Newton's method - the conclusion.
Lecture 2.2: The Fundamental Theorem of Calculus.
Studio 2.2: Linear algebra in R3.
Lecture 2.3: Properties of the integral.
Studio 2.3:
Exercises on the integral.
/stig