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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