Lecture Notes for Advanced Calculus - supermath.info

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Lecture Notes for Advanced CalculusJames S. CookLiberty UniversityDepartment of MathematicsFall 20132introduction and motivations for these notesThere are many excellent texts on portions of this subject. However, the particular path I choosethis semester is not quite in line with any particular text. I required the text on Advanced Cal-culus by Edwards because it contains all the major theorems that traditionally are covered in anAdvanced Calculus algebra is not a prerequisite for this course. However, I will use linear algebra. Matrices,linear transformations and vector spaces are necessary ingredients for a proper discussion of ad-vanced Calculus .

previous experience with calculus. Towards that end, I am including a section or two on series and sequences and a discussion of pointwise verses uniform convergence. These discussions set-up the technique of exchanging derivatives and integrals which is a powerful technique seldom discussed in current calculus courses.

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