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Lecturer | Dr. Cornelia Busch | Lecture | Tue 8-10, HCI D4 | |
Assistant | Claire Burrin | Exercise class | Fr 15-16, HG G26.5 |
Lectures start on Tuesday, September 16
Exercises classes start on Friday, September 26
This lecture will present an overview of the following fundamentals of mathematics : linear algebra, calculus, multivariable calculus, differential equations, examples of partial differential equations.
Some supplementary references to the lecture notes, for both theory and exercises : Thomas' Calculus, Otto Bretscher's Linear Algebra with Applications.
Relevant information to the exam can be found here.
Week | Topic | Exercise sheet | Solutions |
1 (Sep 16) | Linear algebra : linear systems, Gauss elimination |
Ex 1 |
Sol 1 |
2 (Sep 23) | Linear algebra : linear (in)dependance of vectors; matrix algebra |
Ex 2 |
Sol 2 |
3 (Sep 30) |
Linear algebra : inverses, introduction to bases Calculus : review of derivation and integration rules |
Ex 3 |
Sol 3 |
4 (Oct 7) | Calculus : methods of integration, cont'd; parametrization of curves and computation of the arc length |
Ex 4 |
Sol 4 |
5 (Oct 14) | Multivariable calculus : functions in several variables, level surfaces, partial derivatives ; vector fields, work along curves |
Ex 5 |
Sol 5 |
6 (Oct 21) |
Multivariable calculus : chain rule for partial derivatives Linear algebra : determinants, change of bases |
Ex 6 |
Sol 6 |
7 (Oct 28) | Linear algebra : change of basis, cont'd; eigenvalues and eigenvectors |
Ex 7 |
Sol 7 |
8 (Nov 4) | Multivariable calculus : finding extrema |
Ex 8 |
Sol 8 |
9 (Nov 14) | Multivariable calculus : parametrizing surfaces |
Ex 9 |
Sol 9 |
10 (Nov 18) | Midterm on Friday ! | ||
11 (Nov 25) | Multivariable calculus : surface areas, surfaces integrals, flux across a surface |
Ex 10 |
Sol 10 |
12 (Dec 2) | First order differential equations |
Ex 11 |
Sol 11 |
13 (Dec 9) | Linear differential equations |
Ex 12 |
Sol 12 |
14 (Dec 16) |
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