Mathematics II
4 Series and Limits
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Notes
1
Complex Numbers
2
Second Order Linear Differential Equations
3
Functions of more than one variable
4
Series and Limits
5
Two–by–Two Matrices
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Chapter 4
Series and Limits
4.1
Finite and Infinite Series
4.1.1
Finite Series of Natural Numbers (Gauß)
4.1.2
Finite Geometric Progression
4.1.3
Binomial
4.1.4
Infinite Series
4.2
Taylor–Series
4.2.1
The Exponential Function
4.2.2
Power Series for
sin
(
x
)
and
cos
(
x
)
4.2.3
General Case
4.2.4
Example: The Exponential Function
exp
(
x
)
4.3
Taylor–Expansion of Functions
4.3.1
Convergence: Expansion of
f
(
x
)
=
ln
(
1
+
x
)
4.3.2
Alternative way to generate a Taylor Series
4.3.3
Taylor expansion of
f
(
x
)
around an arbitrary
x
=
a
4.4
Further Examples for Series and Limits
4.4.1
Newtonian Limit of Relativistic Energy
4.4.2
Limits
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