Math 33B-1, Spring 2017
Practice Problem Set 1
Disclaimer: The actual midterm will vary from this problem set in content and length. This
practice set should not be considered a comprehensive study guide.
1.
Find the general solution of the ODE below.
(x2
Math 33B-3, Spring 2015
Practice Midterm 1
Midterm 1 will be given Monday, April 20. Please be on time; no make-up exam will be given.
No notes, calculators, cell phones, or any other outside material devices will be allowed on the
exam. Disclaimer: the a
Math 33B-1, Spring 2017
Selected Solutions, Practice Problem Set 1
1.
This equation is homogeneous of degree 2. Using the substitution y = xv,
(x2 + x2 v 2 )dx + (x2 x2 v)(xdv + vdx) = 0
this simplifies to the separable
1
v1
dx =
dv
x
v+1
Use long divisio
Math 33B-1, Spring 2017
Practice Problem Set 2
Disclaimer: This practice problem set should not be considered a comprehensive study guide.
1.
Find the general solution of the ODE below.
y 00 6y 0 + 9y = 6x2 + 2 12e3x
2.
A mass of 5 kg stretches a spring 1
Outline
Math 33B: Differential Equations, Lecture 12
Last time: finished 4.1; started Section 4.3 (second-order
linear homogeneous ODEs with constant coefficients)
Today: finish Section 4.3; start Section 4.4 (unforced
harmonic motion) if time
Math 33B, L
Math 33B: Differential Equations, Lecture 18
Math 33B, Lecture 18
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Outline
Last time: began systems of first-order ODEs
Today: section 9.1; start section 9.2 (planar systems)
Math 33B, Lecture 18
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Characteristic polynomials and eigenvalues
For
Outline
Math 33B: Differential Equations, Lecture 13
Last time: Section 4.3
Today: briefly finish Section 4.3; Section 4.4 (unforced
harmonic motion)
Math 33B, Lecture 13
Example of repeated roots
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Example
Example, continued
Math 33B, Lecture 13
Rew
Math 33B: Differential Equations, Lecture 17
Math 33B, Lecture 17
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Outline
Last time: Section 4.6 (variation of parameters)
Today: briefly finish Section 4.5, then do Section 9.1 (systems
of first-order ODEs with constant coefficients)
Math 33B, Lec
Outline
Math 33B: Differential Equations, Lecture 11
Last time: sections 4.1 and 4.2
Today: briefly finish 4.1; start Section 4.3 (second-order linear
homogeneous ODEs with constant coefficients)
Math 33B, Lecture 11
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Main theorem on general solutio
Math 33B: Differential Equations, Lecture 13
Math 33B, Lecture 13
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Outline
Last time: Section 4.3
Today: briefly finish Section 4.3; Section 4.4 (unforced
harmonic motion)
Math 33B, Lecture 13
2 / 27
Example of repeated roots
Example
Find the genera
Math 33B: Differential Equations, Lecture 20
Math 33B, Lecture 20
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Outline
Last time: began section 9.2 (planar systems)
Today: finish section 9.2 (hopefully)
Math 33B, Lecture 20
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Complex eigenvalues, real solutions, continued
Let A be a real
Math 33B: Differential Equations, Lecture 26
Math 33B, Lecture 26
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Outline
Last time: started Section 9.6
Today: finish Section 9.6 and course
Math 33B, Lecture 26
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Computing the matrix exponential
Key idea: if ~v is a generalized eigenvector
HOMEWORK, WEEK 7
This assignment is due Friday, February 24 in lecture. Show your work clearly and concisely. An (unannounced) subset of the problems will be graded.
We will cover the relevant material on systems of equations / linear algebra on Wednesday
HOMEWORK, WEEK 10
This assignment is due Friday, March 17 in lecture. Show your work clearly and concisely.
An (unannounced) subset of the problems will be graded.
Many problems ask you to use a computer for linear algebra; indicate when you have done
thi
HOMEWORK, WEEK 8
This assignment is due Friday, March 3 in lecture. Show your work clearly and concisely.
An (unannounced) subset of the problems will be graded.
Section 9.1, Problems 17, 20, 25
Section 9.2, Problems 1, 6, 7, 12, 14, 16, 17, 20, 22, 23,
HOMEWORK, WEEK 5
This assignment is due Friday, February 10 in lecture. Show your work clearly and concisely. An (unannounced) subset of the problems will be graded.
Note: there are a lot of problems this week, but many of them require very little computa
HOMEWORK, WEEK 9
This assignment is due Friday, March 10 in lecture. Show your work clearly and concisely.
An (unannounced) subset of the problems will be graded.
You dont need to include any Sage printouts with your solutions.
Section 9.2, Problems 33,
PIC 16 Python with Applications
Lecture 3
Puck Rombach
Regular Expressions
Regular expressions are a language to describe patterns in strings. They are extremely useful when
working with data sets. To start, we need the module re, and two functions from i
PIC 16 Python with Applications
Lecture 5
Puck Rombach
Captured Groups in Regular Expressions
Recall that we use parentheses (.) to capture groups in a regular expression. The groups are numbered 1,2,3,. by the appearance of their opening parenthesis. We
PIC 16 Python with Applications
Homework 2
Puck Rombach
Challenge 1 mytype(v)
Write a function that performs the same action as type(), and can recognize integers, floats, strings,
and lists. Do this by first using str(v), and then reading the string. Ass
PIC 16 Python Spring 2017
Lecturer: Puck Rombach ([email protected])
Overview
The course will cover the following topics (one per week):
1. Basics
2. Regular Expressions
3. Visualizations
4. Image Processing
5. Data Analysis
6. Symbolic Math
7.