Computing with formulas - GitHub Pages

Computing with formulas

FC CK0030 2019.1

A formula

Programs and programming Variables Comments, text and numbers formatting

Another formula

Integer division Objects in Python Integer division Arithmetic operators

Mathematical functions

Examples Rounding errors

Interactive computing

The shell Type conversion IPython

019 Computing with formulas 2 Foundation of programming (CK0030) R 20F,C ? Francesco Corona A? M

Computing with formulas

FC CK0030 2019.1

A formula

Programs and programming Variables Comments, text and numbers formatting

Another formula

Integer division Objects in Python Integer division Arithmetic operators

Mathematical functions

Examples Rounding errors

Interactive computing

The shell Type conversion IPython

FdP

19 Intro to variables, objects, modules, and text formatting 0 Programming with WHILE- and FOR-loops, and lists 2 Functions and IF-ELSE tests 0, ? Data reading and writing

Error handling

R 2FC Making modules A ? Arrays and array computing

Plotting curves and surfaces

M

Computing with formulas

FC CK0030 2019.1

A formula

Programs and programming Variables Comments, text and numbers formatting

Another formula

Integer division Objects in Python Integer division Arithmetic operators

Mathematical functions

Examples Rounding errors

Interactive computing

The shell Type conversion IPython

, 2019 A formula R 20FC ? Computing with formulas A? M

Computing with formulas

A formula

FC

CK0030 2019.1

A formula

Programs and programming Variables Comments, text and numbers formatting

Another formula

Integer division Objects in Python Integer division Arithmetic operators

Mathematical functions

Examples Rounding errors

Interactive computing

The shell Type conversion

9 Example 1 The vertical motion of a ball thrown up in the air 0 We can set up a mathematical model for the motion of the ball 2 ? From Newton's second law of motion

, The vertical position of the ball, called y, varies with time t

20 ? y(t)

=

v0t

-

1 gt2 2

R FC v0 is the initial velocity of the ball

A ? g is the acceleration of gravity

t is time

(1)

IPython

M The y axis is chosen such that the ball starts from y = 0 at t = 0

Computing with formulas

FC CK0030 2019.1

A formula

Programs and programming Variables Comments, text and numbers formatting

Another formula

Integer division Objects in Python Integer division Arithmetic operators

Mathematical functions

Examples Rounding errors

Interactive computing

The shell Type conversion IPython

A formula (cont.)

19 The time for the ball to move upwards and return to the ground again

0 We are interested in the solutions to equation y(t) = 0

, 2 v0t

-

1 gt

2

2

=

t (v0

-

1 gt )

2

=

0

0 ? t = 0

(2)

2 t = 2v0 Cg

R F The ball returns to ground level in 2v0/g (seconds) A ? ? We can focus in the interval t [0, 2v0/g]

M

Computing with formulas

FC CK0030 2019.1

A formula

Programs and programming Variables Comments, text and numbers formatting

Another formula

Integer division Objects in Python Integer division Arithmetic operators

Mathematical functions

Examples Rounding errors

Interactive computing

The shell Type conversion IPython

A formula (cont.)

y (t )

=

v0t

-

1 gt2 2

We evaluate the formula for some values of v0 and g

9 ? v0 = 5 ms-1 1 ? g = 9.81 ms-2

0 We want to compute the ball's height for t = 0.6 s

2 1.4 0, ? 1.2 2 1 R FC 0.8

A ? 0.6

M0.4 0.2

0

0

0.5

1

1.5

Computing with formulas

A formula (cont.)

FC

CK0030 2019.1

A formula

Programs and programming Variables Comments, text and numbers formatting

Another formula

Integer division Objects in Python Integer division Arithmetic operators

Mathematical functions

Examples Rounding errors

Interactive computing

The shell Type conversion

9 y = 5 ? 0.6 - 1 ? 9.81 ? 0.62 2

1 v0

t

g

t2

0 1 print 5*0.6 - 0.5*9.81*0.6**2

, 2 Remark 0 ? The four standard arithmetic operators

2 +, -, * and / R FC Exponentiation employs a double asterisk ** notation

A ? The arithmetic expression is easily evaluated and printed

(3)

IPython

M ? A one-line Python program

The ball comes back after some time t = 2v0/g 1 [s]

Computing with formulas

FC CK0030 2019.1

A formula

Programs and programming Variables Comments, text and numbers formatting

Another formula

Integer division Objects in Python Integer division Arithmetic operators

Mathematical functions

Examples Rounding errors

Interactive computing

The shell Type conversion IPython

, 2019 Programs and programming R 20FC ? A formula

A? M

Computing with formulas

FC CK0030 2019.1

A formula

Programs and programming Variables Comments, text and numbers formatting

Another formula

Integer division Objects in Python Integer division Arithmetic operators

Mathematical functions

Examples Rounding errors

Interactive computing

The shell Type conversion IPython

Programs and programming

9 Our task is to create programs/code and run it 1 There are three main types of tools for writing Python code 0 ? A plain text editor 2 ? An IPython notebook

? An integrated development environment (IDE) with a text editor

20, ? Remark C What you choose depends on how you access Python R F There are various possibilities

? Access a plain installation on your own computer

A ? ? Access a pre-installed environment (distribution) M ? Access Python in a cloud service

Computing with formulas

Programs and programming (cont.)

FC CK0030 2019.1

A formula

Programs and programming Variables Comments, text and numbers formatting

Another formula

Integer division Objects in Python Integer division Arithmetic operators

Mathematical functions

Examples Rounding errors

Interactive computing

The shell Type conversion IPython

2019 t = 0.6s , v0 = 5 ms-1 0 ? g = 9.81 ms-2

y (t )

=

v0t

-

1 gt2 2

2 1 print 5*0.6 - 0.5*9.81*0.6**2 R FC This line is a complete Python program for evaluating the formula A ? ? Copy the line in a text file

M ? Save the text file with name ball1.py

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