ANNOUNCEMENTS

Drop in tutor hours:

M-Tu-W-Th 4-10pm, Baskin 379

Homework due Monday at end of class. Stapled, name of student and name of TA and section you attend.

ANNOUNCEMENTS

SECTIONS CHANGE OF TIMES/LOCATIONM/W 8-9:50am section with Wenyi moved to

M/W 4-5:50 in Baskin 360.

Tu/Th 8-9:50am section with Deboja moved to M/W 6-7:50 in Baskin 295

M/W 5-6:50pm section with Shubhra moved by 10 minutes to M/W 5:10-7:00pm

Chapter IIfunctions and variables

II.1 the concept of variables

II.1.1 introduction

the ultimate scientific aim is to understand causal links between events:

WHY ?or

HOW ?

methods used to achieve that aim:• measurement• analysis• modeling• prediction• control

measurement & analysis

• all experiments/measurements provides data

• human brain specifically designed to process images efficiently

analysis usually involves graphic representation of data.

examples

one quantity measured as a function of another

examples

one quantity measured as a function of another

examples

two quantities measured as a function of another

examples

one quantity measured as a function of two others

examples

one quantity measured as a function of two others

examples

one quantity measured as a function of two others

examples

one quantity measured as a function of three others

Examples

one quantity measured as a function of three others

modeling

to model and study complex problems one needs a rigorous mathematical framework

II.1.2 definitions

• independent variables:control parameters, the quantities that can

be varied at will.

• dependent variables:the quantities that change as a consequence

of the independent variable being varied.

but sometimes it’s all relative!

II.2 Graphing

2 possible scales: linear and logarithmic

II.2.1 the linear scale• use it when the variable has small range• the interval [a,b] has the same length as the

interval [a+c,b+c]

II.2.1 the logarithmic scale• use it when the variable has large range• the interval [a,b] has the same length as the

interval [a x c, b x c]

3 example types of plots

• linear - linear

3 example types of plots

• log - linear

3 example types of plots

• log - log

II.3 Functions