Advanced Engineering Mathematics MATH 011 (TIP Reviewer)
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Transcript of Advanced Engineering Mathematics MATH 011 (TIP Reviewer)
Sum and Difference of Formulas
Relationships of Hyperbolic and Trigonometric
P - Euler's Theorem
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Laplace Transform:
*s = θ + jw*w = 2πf (angular frequency)
Time Domain h(t) Complex Frequency Domain H(s)
1
t
tn
cos wt
sin wt
cosh wt
sinh wt
Theorems on Laplace Transform1. Linearity Property:*Constants can be taken out before transforming to Laplace.
2. First Shifting Theorem:
3. Second Shifting Theorem:
4. General Heaviside Step Function:
F - List of Formulas
MATH 011 Page 3
Initial Value Theorem and Final Value Theorem
*magkabaliktad
Laplace Transforms of Derivative:
MATH 011 Page 4
)
)
= 1.587
P - Assignment Part 1
MATH 011 Page 5
P - Assignment Part 2
MATH 011 Page 6
MATH 011 Page 7
MATH 011 Page 8
MATH 011 Page 9
Laplace Transform:
*s = θ + jw*w = 2πf (angular frequency)
Time Domain h(t) Complex Frequency Domain H(s)
1
t
tn
\pppñqzsxqwpxsqa
cos wt
sin wt
cosh wt
sinh wt
Theorems on Laplace Transform1. Linearity Property:*Constants can be taken out before transforming to Laplace.
2. First Shifting Theorem:
3. Second Shifting Theorem:
M - Laplace and Inverse Laplace Transform
MATH 011 Page 10
4. General Heaviside Step Function:
Inverse Laplace Transform
H(s) h(t)
1
t
cos wt
sin wt
cosh wt
sinh wt
MATH 011 Page 11
M - Problems
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5.
Derivation #3
MATH 011 Page 14
Definition of Z-Transform:
The z-transform is the discrete-time counterpart of the Laplace transform.
the z-transform is defined as follows:
Z-Transform
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