# Mathematics Classes 2012-2013

Introduction to Systems Biology

Fundamentals of Bioinformatics

## Contents

### Study material

**Calculus**

- Brief Calculus and its applications - BC

- Wiskundige Methoden Toegepast - WMT

- http://www.sosmath.com/ - SOS

**Linear algebra**

- Lectures by Gilbert Strang (highly recommended): MIT OpenCourseWare

- "Linear algebra and its applications" by Gilbert Strang (bit expensive but very good)

### General Remarks

This class is mainly to refresh mathematics from highschool. Near the end new topics will be discussed that are relevant for systems biology. If the material is new, some extra study will be necessary. We provided some suggested books and a website but other materials will do as well. On the internet there is a lot of material for basic calculus.

Homework is optional (max 1 bonuspoint for the exam can be earned) and has to be handed in latest the Monday after the class. It can be emailed or brought to F246 or put in Evert's or Meike's mailbox in M246. For questions about the assignments or the mathematics explained in class you can always sent an email or drop by F246.

### First Class

*Functions and Exponentials*

- BC Chapter 0 (0.1 - 0.5), Chapter 4 (4.1, 4.2, 4.4)
- WMT 1.1, 1.3
- SOS Quadratic Equations, Logarithms and Exponential Functions and Solving Equations

**Assignments**: Media:Functions2012.pdf Media: FunctionsII_2012.pdf

These are the new versions. In the version we handed out there were two mistakes in question 9 of Functions. In 9a, there is suppost to be ln(b^x) + ln(c^x) in stead of ln(b^x) * ln(c^x) and in 9c a z at the end is missing, it is supposed to be ln(z) in stead of just ln.

Homework (for Monday September 10th): Functions: 4, 7; Functions II: 7, 9a,b,f

### Second class

*Differentiation*

- BC Chapter 1 (1.1, 1.3 p 87-88, 1.4, 1.5, 1.6, 1.7, 1.8)
- WMT 1.2, 1.3, 1.4, 1.5
- SOS Inverse Functions, The Defenition of the Derivative, Using the Definition to Compute the Derivative, Techniques of Differentiation, The Chain Rule, Critical Points, Concavity and Points of Inflection

**Assignment**: **1.** Media:differentiation2012.pdf **2.** Media:differentiation2012part2.pdf

These are the new versions. In the version we handed out there was a mistake in question 3b. In stead of f(x) there should have been f(t).

Homework (for Monday September 10th - at latest Tuesday 11 o'clock): 3, 4, 10

### Third class

*Integration*

**Assignment**: Media:integration2012.pdf

Homework (for Monday September 17th): 2, 3, 4

### Fourth class

*Differential equations*

**Assignment**: Media:differential_equations2012.pdf
*Some extra hints are added for question 6 and 8 in this file!*

Homework (for Monday September 17th - at latest 11 AM Tuesdaymorning!): 1, 4, 5, 8

**Some links where to study differential equation (what is covered in this course):**

A pdf for a differential equation course. You can read through chapter 1 for general information about differential equations. Don't read the rest, only the last paragraph on page 20 and page 21 are also covered in class, but probably better explained on other websites. [1]

Youtube videos explaining step by step how to test a function is a solution of a differential equation: [2] and [3]

Drawing the graph of y'(t) against y(t) to find stable and unstable equilibria: [4] (starting form: "The Linear Stability Test")

(The SOS math website [5] actually goes a bit further then we went in class)

### Fifth class

*Questions*

### Sixth class

*Calculus test*

13:45 - 16:00

*The room will be announce asap.*

You have 2 hours for the test. You only have to bring a pen (calculators are not allowed). You will be tested on the ability to work with powers and logaritms, to do differentiation and integration and sketch graphs (find minima/maxima and intersections). Also, you have to know how to check if a solution of a differential equation is correct (you don't have to know how to solve them!) and draw a graph of a function against its derivative and use the graph to find the equilibria and know if they are stable or unstable. Furthermore, you are expected to understand that x(t) = x_0 e^(a t) is a solution to the differential equation x'(t) = a x(t).

### Linear Algebra

Media:Exercices_linear_algebra.pdf

### Date and time re-exam linear algebra

The re-exam for linear algebra will take place on Wednesday October 24-th, 9:00 - 11:00, room F-612, W&N building.