Chapter 8. Linear Algebra : Matrix Eigenvalue Problems
1
8.1 Eigenvalues, Eigenvectors
Denition Eigenvalues, Eigenvectors
Let A = [ajk ] be an n n matrix. Consider
Ax = x.
(1)
Clearly, x = 0 is a solu
Chapter 6. Laplace Transforms
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6.1 Laplace transform. Linearity.
First Shifting Theorem(s-Shifting)
Denition Laplace transform
Laplace transform
f (t) (t 0) 7 F (s)
F (s) = L(f ) =
estf (t)dt.
0
In
Chapter 5. Series Solutions of ODEs
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5.1 Power Series Method
Power series (in powers of x x0)
am(x x0)m = a0 + a1(x x0) + a2(x x0)2 + .
m=0
Examples(Maclaurin series)
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1x
= 1 + x + x2 + x3 +
x2
(|x
Chapter 4. Systems of ODEs. Phase Plane
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4.1 Systems of ODEs as Models
Example 1. (Mixing Problem Involving Two Tanks)
Initially, tank T1: 100 gal of pure water,
tank T2: 100 gal of water dissolved 1