Book containing taylor series expansions

In summary, a Taylor series expansion is a representation of a function as an infinite sum of terms based on its derivatives at a single point. It is useful for approximating complicated functions with simpler ones for easier calculations and analysis. The expansion is calculated by substituting the derivatives into a formula. A Maclaurin series is a special case of a Taylor series when the center is at 0. The accuracy of a Taylor series expansion depends on the number of terms included, but it is only an approximation and may not be exact for all values of the function.
  • #1
elarson89
20
0
Hello,

I am looking for a resource (preferably a textbook) to help me with nonlinear, multivariable functions and working through taylor series expansions of them. My calculus book only covers single variable expansions unfortunately.

Thanks
 
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  • #2
Schaum Series calculus maybe -- more as an exercise book for solved and unsolved problems.

How about Thomas and Finney? They do give some examples of multivariable Taylor Series -- at least in 2 variables.
 
  • #3
for reaching out! Taylor series expansions are an important tool in studying nonlinear, multivariable functions. I would recommend checking out "Multivariable Calculus" by James Stewart or "Calculus: Early Transcendentals" by Howard Anton and Irl Bivens. Both of these textbooks cover taylor series expansions for multivariable functions. Additionally, "Advanced Engineering Mathematics" by Erwin Kreyszig also has a section on taylor series expansions for multivariable functions, which may be helpful for more specific applications in engineering. I hope this helps and happy studying!
 

1. What is a Taylor series expansion?

A Taylor series expansion is a mathematical representation of a function as an infinite sum of terms that are calculated using the function's derivatives at a single point.

2. Why is a Taylor series expansion useful?

A Taylor series expansion is useful because it allows us to approximate a more complicated function with a simpler one, making it easier to perform calculations or analyze the behavior of the function.

3. How is a Taylor series expansion calculated?

A Taylor series expansion is calculated using the derivatives of a function at a specific point, which are then substituted into the Taylor series formula.

4. What is the difference between a Taylor series and a Maclaurin series?

A Taylor series expansion is centered around a specific point, while a Maclaurin series is centered around the point 0. In other words, a Maclaurin series is a special case of a Taylor series when the center is at 0.

5. How accurate is a Taylor series expansion?

The accuracy of a Taylor series expansion depends on the number of terms included in the series. As more terms are included, the approximation becomes more accurate. However, it is only an approximation and may not be exact for all values of the function.

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