Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #3, due Tuesday, 24 February 2009 All references are to Zill & Cullen (3rd edition). Chapter 2: Supplementary Problem dy 1 Observe that the ODE dx = yx is nonlinear in y (x), not s
APMAE 2101
Quiz 1
Feb 25, 2016
No calculator or notes. Write name, uni and HW group number on your exam
book. All answers and work in test book. Turn in exam with test book.
1. Determine the order of the equation and state whether the equation is linear o
Applied Mathematics E2101
Introduction to Applied Mathematics
Course: APMAE2101_001_2017_1
Meeting Time: TR 1:10-2:25pm
Meeting Location: 309 Havemeyer Hall (The Most Filmed College Classroom!)
Instructor: Michael K. Tippett ([email protected])
Course Lo
In 2010, guns took the lives of 31,076 Americans in homicides, suicides and unintentional shootings. This
is the equivalent of more than 85 deaths each day and more than three deaths each hour.1
73,505 Americans were treated in hospital emergency departme
Roco Tair Vzquez:
Gun Control Debate
The pro gun control side in the American debate over the degree to which the government should have the
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typically
3.7
Another substitution
dy
= f (ax + by + c)
dx
Introduce new variable v = ax + by + c
An example
dy
= sin2 (y x)
dx
Let v = y x
dv
dy
=
1
dx
dx
dv
+ 1 = sin2 (v)
dx
dv
= sin2 (v) 1
dx
dv
dv
=
= sec2 (v) = dx
2
2
cos
(v)
sin (v) 1
tan v = x + c
v = tan 1
APMAE 2101
Quiz 2
Apr 7, 2016
No calculator or notes.
Write answers and work in test book. Turn in quiz with test book.
Show all work!
1. (a) (5 points) The equation Ax = b has a solution if b is an element of
.
Solution: the column space of A.
(b) (5 poi
APMAE 2101
Sample questions for topics after Quzi 2
1. (10 points) Suppose that the columns of the m 3 matrix
h
i
Q = q1 q 2 q3
are orthonormal vectors. For what values of m is Q is invertible? What is Q1 ?
Solution: The columns of Q are linearly independ
APMAE 2101
Quiz 1
Feb 25, 2016
No calculator or notes. Write name, uni and HW group number on your exam book. All
answers and work in test book. Turn in exam with test book.
1. Determine the order of the equation and state whether the equation is linear o
Review Session Questions Pertaining to Numerical Methods
2/19/2017
Sources
These notes are based off of Dr. Tippetts lecture slides and the course text.
Questions
1. Differences between explicit and implicit:
(a) Explicit - Approximates a solution, yn+1
,
% function dirfield
% This program plots a direction field for an ODE y'=f(t,y), with the
% option of also plotting solution curves to initial value problems.
% The ODE equation, window values, and optional initial conditions are
% entered by the user.
%-
Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #2, due in class on Thursday, 12 February 2009 All references are to Zill & Cullen (2006 edition). Chapter 2, 2.2: Separable Equations 17 20 30 (a)-(c) Chapter 2, 2.5: Homogeneous,
Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #1, due Tuesday, 3 February 2009 All references are to Zill & Cullen (2006 edition). Chapter 1, 1.1: Classication of ODEs and Verication of Solutions 1 8 11 14 21 27 (a) 28 (a) 33
Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #4, due Thursday, 5 March 2009 All references are to Zill & Cullen (3rd edition). Chapter 2, 2.6: The Euler Method #2 In addition to the two step sizes for h listed, also try to ge
Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #7, due Thursday, 9 April 2009 All references are to Zill & Cullen (3rd edition). Chapter 8, 8.8: The Linear Eigenvalue Problem 5 12 23 27 [You do not need to submit the logs of an
Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #6, due Tuesday, 31 March 2009 All references are to Zill & Cullen (3rd edition). Chapter 8, 8.2: Systems of Linear Algebraic Equations 9 13 Perform these two problems both by hand
Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #8, due Tuesday, 28 April 2009 All references are to Zill & Cullen (3rd edition). Chapter 3, 3.1: Higher-order ODEs 1, 5, 12, 13, 21, 22, 40 Chapter 3, 3.2: Reduction of Order 5 (s
Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #9, due Tuesday, 5 May 2009 All references are to Zill & Cullen (3rd edition). Chapter 3, 3.5: Variation of Parameters 3 21 (Note that both of these problems are perhaps more easil
% Euler's method Demo: exponential decay
% Here we will give some simple matlab code for generating tables of
% results from Euler's method.
%
y' = 2y-1, y(0) = 1.
% Initialize the problem
% start by clearing all variables and closing all figures
clear al