Calculus 3 Books: Jordan Measure & More

In summary, the Jordan measure is a mathematical concept used in calculus to assign numerical values to sets of points. Calculus 3 expands upon the concepts of calculus 1 and 2, allowing for the analysis of functions with multiple variables. Recommended textbooks for learning calculus 3 include "Multivariable Calculus" by James Stewart, "Calculus: Early Transcendentals" by James Stewart, and "Vector Calculus" by Jerrold E. Marsden and Anthony J. Tromba. Calculus 3 has various real-world applications, such as predicting the trajectory of a rocket or modeling fluid flow. While it is possible to study calculus 3 without a strong understanding of calculus 1 and 2, it is recommended
  • #1
hellbike
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I'm looking for book about Jordan measure and stuff like that.
 
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  • #2
the only calculus book i know of treating "jordan measure" i.e. "jordan content", is loomis and sternberg, available free on sternberg's website i believe.

Jordan content is the higher dimensional version of riemann integration, and since it takes a lot of work to develop it, which has to be done over again to get the stronger theory of lebesgue measure, most books skip it. Still it seems useful as an exercise.
 

FAQ: Calculus 3 Books: Jordan Measure & More

What is the Jordan measure and why is it important in calculus?

The Jordan measure is a concept in mathematics that is used to assign a numerical value to a set of points in a given space. It is particularly useful in calculus as it allows for the calculation of the area under a curve or the volume of a solid object, both of which are important in many real-world applications.

How does calculus 3 differ from calculus 1 and 2?

Calculus 3, also known as multivariable calculus, extends the concepts learned in calculus 1 and 2 to functions with multiple independent variables. This includes topics such as partial derivatives, multiple integrals, and vector calculus. It is used to solve problems in physics, engineering, and other fields where multiple variables are present.

What are some recommended textbooks for learning calculus 3?

Some highly recommended textbooks for learning calculus 3 include "Multivariable Calculus" by James Stewart, "Calculus: Early Transcendentals" by James Stewart, and "Vector Calculus" by Jerrold E. Marsden and Anthony J. Tromba. These books cover topics such as vector calculus, partial derivatives, and multiple integration in a clear and comprehensive manner.

How can I use calculus 3 in real-life applications?

Calculus 3 has many real-world applications, including calculating the trajectory of a rocket, determining the optimal shape for an airplane wing, and modeling the flow of fluids. It is also used in economics, biology, and other fields to analyze complex systems and make predictions based on mathematical models.

Is it necessary to have a strong understanding of calculus 1 and 2 before studying calculus 3?

While it is possible to study calculus 3 without a strong understanding of calculus 1 and 2, it is highly recommended to have a solid foundation in these earlier topics. Many of the concepts in calculus 3 build upon those learned in previous courses, and a strong understanding of calculus 1 and 2 will make it easier to grasp the more advanced concepts in calculus 3.

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