APMA 2101 Problem Set #4 Sample Solution Set (due 9 March 2007) Section 3.1: Theory of Higher-order ODEs
Section 7.6: Vector Spaces
Section 7.7: Gram-Schmidt
Historical Research (a) Jorgen Pederson Gram was born in Denmark, and lived from 1850 to

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 #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

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 #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 #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 #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

APMA 2101 Problem Set #1 Sample Solution Set (due 3 February 2009) Section 1.1
Section 1.2
Section 2.3
Historical Research (a) Newton was approximately 23 or 24 years old when he invented calculus. He graduated from Cambridge in 1665, at the age of 22, an

APMA 2101 Problem Set #2 Sample Solution Set (due 12 February 2009) Section 2.2
Section 2.5
Section 2.5, #8 (continued)
Historical Research (a) In 1754, the year that Kings College was founded on Wall Street, Daniel Bernoulli was teaching physics at the U

APMA 2101 Problem Set #3 Sample Solution Set (due 24 February 2009) Chapter 2: Supplementary Problem (2 points) For x(y), we have dx/dy + x = y, with integrating factor exp(y). Integrating both sides and using integration by parts once on the right-hand s

APMA 2101 Problem Set #4 Sample Solution Set (due 5 March 2009) Section 2.6.: The Euler Method (5 pts]
Trying to get to the endpoint in just one step, h=0.2, is trivial, y(0.2)=0. Of course, we expect the finest mesh step h=0.05 to be best, since all calc

APMA 2101 Problem Set #8 Sample Solution Set (due 28 April 2009): 40 points total Section 3.1: Theory of Higher-order ODEs [8 pts., 1 pt. each numbered or lettered part]
Section 3.2; Reduction of Order [9 pts., 3 pts. each]
Section 3.3: Constant-coefficie

APMA 2101 Problem Set #7 Sample Solution Set (due 14 April 2009): 40 points total Section 8.8; The Linear Eigenvalue Problem [9 pts., 2 pts. each #5, 12, 23; 1 pt. #27(a), 2 pts. #27(b)]
Section 8.9: Powers of Matrices [6 pts., 2 pts. each]
Section 8.10:

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

APMA 2101 Problem Set #1 Sample Solution Set (due 25 January 2007) Section 1.1
Section 1.2
Section 2.3
Historical Research (a) Newton was approximately 23 or 24 years old when he invented calculus. He graduated from Cambridge in 1665, at the age o

APMA 2101 Problem Set #3 Sample Solution Set (due 20 February 2007) Chapter 2: Review Problem For x(y), we have dx/dy + x = y, with integrating factor exp(y). Integrating both sides and using integration by parts once on the right-hand side gives x(y

APMA 2101 Problem Set #2 Sample Solution Set (due 6 February 2007) Section 2.2
Section 2.5
Section 2.5, #8 (continued)
Historical Research (a) In 1754, the year that King's College was founded on Wall Street, Daniel Bernoulli was teaching physics

APMA 2101 Problem Set #5 Sample Solution Set (due 27 March 2007) Section 8.1: Matrix Algebra
Section 8.2: Systems of Linear Algebraic Equations
Section 8.3: Rank
Section 8.4: Determinants
Section 8.5: Properties of Determinants
Section 8.6: Matr

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Error function - Wikipedia, the free encyclopedia
http:/en.wikipedia.org/wiki/Error_function
Error function
From Wikipedia, the free encyclopedia
In mathematics, the error function (also called the Gauss error function) is a special function (non-elementa

The Number e and the Exponential Function
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The Number e and the Exponential Function
Michael Fowler, UVa Disclaimer: these notes are not mathematically rigorous. Instead, they present quick, and, I hope, plausible, deriv

Applied Mathematics 2101 Supplement on identities relevant to harmonic oscillators The behavior of forced harmonic oscillator systems (whether L-R-C electronic circuits, spring dashpot mechanisms like shock-absorbers in automobiles, or instruments to dete

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9:09 AM
Page 1
Second Printing Errata for Advanced Engineering Mathematics, by Dennis G. Zill and Michael R. Cullen
(Yellow highlighting indicates corrected material)
Page 47
The second equation in (5) is the result of

The method of undetermined coefficients: "inspired guessing" for the particular solution of inhomogeneous linear constant coefficient ordinary differential equations of arbitrary order.
Steps: (1) Determine the homogeneous solution.
(2) If g(x) has severa

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2.5 Exact Equations 39
In order to determine hey) from Eq. (11) it is essential that, despite its appearance,
Theorem 2.3. Let the functions M, N, M1I, and N", be continuous in the rectandifferentiate the qua