Difference between revisions of "EGR 103/Concept List Fall 2019"
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\(
y=e^x=\sum_{n=0}^{\infty}\frac{x^n}{n!}
\)
\(
\begin{align}
y_{init}&=1\\
y_{new}&=y_{old}+\frac{x^n}{n!}
\end{align}
\)
Line 180: | Line 180: | ||
* Taylor series fundamentals | * Taylor series fundamentals | ||
* Maclaurin series approximation for exponential | * Maclaurin series approximation for exponential | ||
− | * Newton Method for finding square roots | + | <center><math> |
+ | y=e^x=\sum_{n=0}^{\infty}\frac{x^n}{n!} | ||
+ | </math> | ||
+ | </center> | ||
+ | :so | ||
+ | <center><math> | ||
+ | \begin{align} | ||
+ | y_{init}&=1\\ | ||
+ | y_{new}&=y_{old}+\frac{x^n}{n!} | ||
+ | \end{align} | ||
+ | </math> | ||
+ | </center> | ||
+ | * Newton Method for finding square roots - to find <math>y</math> where <math>y=\sqrt{x}</math>: <center><math> | ||
+ | \begin{align} | ||
+ | y_{init}&=1\\ | ||
+ | y_{new}&=\frac{y_{old}+\frac{x}{y_{old}}}{2} | ||
+ | \end{align} | ||
+ | </math> | ||
* See Python version of Fig. 4.2 and modified version of 4.2 in the Resources section of Sakai page under Chapra Pythonified | * See Python version of Fig. 4.2 and modified version of 4.2 in the Resources section of Sakai page under Chapra Pythonified | ||
− | |||
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Revision as of 16:09, 7 February 2019
This page will be used to keep track of the commands and major concepts for each lecture in EGR 103.
Contents
Lecture 1 - Introduction
- Class web page: EGR 103L; assignments, contact info, readings, etc - see slides on Errata/Notes page
- Sakai page: Sakai 103L page; grades, surveys and tests, some assignment submissions
- Piazza page: Piazza 103L page; message board for questions
Lecture 2 - Programs and Programming
- To play with Python:
- Install it on your machine or a public machine: Download
- Quick tour of Python
- Editing window, variable explorer, and console
- Variable explorer is your friend
- From Dewey - programming language typically have ability to work with input, output, math, conditional execution, and repetition
- Hilton and Bracy Seven Steps
- Class work developing algorithm for program to determine if a number is prime
- Inputs in Python using input() command - always grab strings
- Convert strings containing integer characters to integers using int()
- Some commands are only available by importing from modules;
import numpy as np
will bring in all the functions of the numpy module. Access these commands by typing np.VALUE or np.FUNCTION (for example, np.pi or np.cos(2))
Lecture 3
- Python has several different variable types, each with their own purpose and operators.
- Main ones this lecture: int, float, string, tuple, list.
Lecture 4
- Brief discussion of disctionaries, how to build, and how to access.
- Two main types of function - lambda functions and defined functions
- Lambda functions are one line of code; can have multiple inputs but only one expression.
- c = lambda a,b: np.sqrt(a**2 + b**2)
- Defined functions can be multiple lines of code and have multiple outputs.
- Four different types of argument:
- Required (listed first)
- Named with defaults (second)
- Additional positional arguments ("*args") (third)
- Function will create a tuple containing these items in order
- Additional keyword arguments ("**kwargs") (last)
- Function will create a dictionary of keyword and value pairs
- Four different types of argument:
Lecture 5
- Creating formatted strings using {} and .format() (format strings, standard format specifiers -- focus was on using e or f for type, minimumwidth.precision, and possibly a + in front to force printing + for positive numbers.
- Basics of decisions using if...elif...else
- Basics of loops using for and while
- Building a program to count the number of numbers, vowels, consonants, and other characters in a phrase
# letter_counter.py from class:
def counter(phrase):
counts = [0, 0, 0, 0]
nums = "0123456789"
vowels = "aeiou"
cons = "bcdfghjklmnpqrstvwxyz"
for k in phrase.lower():
#print(k)
if k in nums:
# print('{:s} is a number!'.format(k))
counts[0] += 1
elif k in vowels:
counts[1] += 1
elif k in cons:
counts[2] += 1
else:
counts[3] += 1
return counts
c = counter("Hello! Go 2022! East Campus Rocks!")
print(c)
Lecture 6
- The Price Is Right - Clock Game:
# tpir.py from class:
# -*- coding: utf-8 -*-
"""
The Price Is Right - Clock Game
"""
import numpy as np
import time
def create_price(low, high):
return np.random.randint(low, high+1)
def get_guess():
guess = int(input('Guess: '))
return guess
def check_guess(new_guess, price):
if new_guess > price:
print('${:0.0f} is too high - Lower!'.format(new_guess))
elif new_guess < price:
print('Higher!')
else:
print('You win!')
price = create_price(100, 1000)
# print(price)
new_guess = price + 1
start_time = time.clock()
while new_guess != price and (time.clock()-start_time)<30:
new_guess = get_guess()
# print(new_guess)
check_guess(new_guess, price)
if new_guess != price:
print('You lose :( '))
Lecture 7
- Robust programming
- isinstance to check type
# validator.py from class:
def check_for_int(x):
'''
returns true if string contains an valid int
returns false otherwise
'''
for k in x:
if k not in '0123456789':
return False
return True
def get_good():
x = input('Integer between 0 and 10: ')
bad = True
''' not quite
while bad:
if check_for_int(x) is False:
pass
elif int(x)>=0 and int(x)<=10:
bad = False
return int(x)
'''
while bad:
if check_for_int(x) is False:
print('Wrong type of input')
x = input('INTEGER between 0 and 10: ')
elif int(x) < 0 or int(x) > 10:
print('Invalid value')
x = input('Integer BETWEEN 0 and 10: ')
else:
bad = False
return int(x)
if __name__ == "__main__":
check_for_int('1.1')
y = get_good()
print(y)
- Note: my_string.isdigit() works like check_for_int() above
Lecture 8
- Taylor series fundamentals
- Maclaurin series approximation for exponential
- so
- Newton Method for finding square roots - to find \(y\) where \(y=\sqrt{x}\):
\( \begin{align} y_{init}&=1\\ y_{new}&=\frac{y_{old}+\frac{x}{y_{old}}}{2} \end{align} \) - See Python version of Fig. 4.2 and modified version of 4.2 in the Resources section of Sakai page under Chapra Pythonified