Computation Fundamentals

This borrows heavily from the UC Berkeley ERG Toolkits.

Numerical Computing Environment

• Matlab

• Scientific Python

• Julia

• Sage Math Cloud

Learning Objectives

• Able to use numerical computing environment to create and narrate computations

• Able to use spreadsheets to create computations

Written

• Explanation of unit factor with inches and centimeters

Unit Factor

$1 \textrm{inch} = 2.54 \textrm{cm}$ Dividing, we get $\frac{2.54\textrm{cm}}{\textrm{inch}} = 1$ Note that 2.54 does not equal one, but with the units the two physical quantities of length are equal.

Combinations of units

• We often combine units to express new quantities

Scientific Notation

$6 \cdot 10^3$ is entered as 6E3.

Units

Computation of physical quantities often relies on the human to define and use a consistent set of units of measurement. There are tools that allow us to add physical quantities to our calculations, but they are not as rich as I could like them to be. One good practice is to explicitly include the unit name in the variable name.

power_watt = 100
time_sec = 30
energy_joule = power_watt * time_sec

Units

There are also computer libraries that allow you to include units in the definition of your variables.

• Pint python library

Defining Functions

A custom function can be created and used. The syntax for this often varies but the idea is usually the same.

m = 1
b = 10
f(x) = m * x + b
f(5) => 15

For Julia:

m = 1
b = 10
f(x) = m * x + b

Python has a different syntax but it is the same idea.

Narration

• You can add text and mathematics to your document

• # Title makes bold text

• $$ \frac{1}{2} $$ creates mathematics $\frac{1}{2}$

Google Docs

• be sure you have access to your new sonoma.edu drive account

• access the template file that I shared

• fill in the different values and sheets

Pandas

• assumes mastery of single variables

• now we do vector calculations (numpy or pandas?)

• to do TMY calculation we need to take difference and plot

• then we need to add up only the positive values

Energy Units

• Joule

  • SI Unit. One Newton-Meter.

• Kilowatt-Hour

  • Energy consumed by 1 kW load over one hour

• Calorie

  • Energy to heat one gram of water one degree Celsius

• Kilo-calorie

  • One thousand calories. Used in food energy content.

• British Thermal Unit (BTU)

  • Energy to heat one pound of water by one degree Fahrenheit

• Quad

  • One quadrillion ($10^{15}$) BTU

Unit Conversions

• We may wish to compare energy units that are not consistent

• Often you can look up conversions in a table

• Other times you may need to recreate the conversion

Variables

• single values

• math expressions with variables

• sympy creation of math expressions?

• arrays

• linspace?

• treating an array like a variable

• data frames (groups of arrays)

• first use of conditionals (only add up positives or negatives)

• fancy indexing to get positives or negatives

Worked Exercises

Exercise

• Estimate the yearly use of gasoline in the US

• What is our strategy?

Exercise

• How many gallons do you consume?

• How many persons in the US?

Problems