Lecture Notes for Advanced Calculus - supermath.info
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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Lecture Notes for Linear Algebra
www.supermath.info3 Xmatrix of linear transformation Xchange of basis on vector space Xgeometry of Euclidean Space Xorthogonal bases and the Gram-Schmidt algorthim
Lecture Notes for Advanced Calculus - supermath.info
www.supermath.infoThe format of these notes is similar to that of my calculus and linear algebra and advanced calculus notes from 2009-2011. However, I will make a number of de nitions in the body of the text.
11. SEQUENCES AND SERIES - supermath.info
www.supermath.infoto arrive at a logically consistent treatment of sequences and series. The better part of ... new sequences from old sequences in many of the same ways as we did for functions. If ... When we study the geometric series this limit will help us stay out of trouble.
Lecture Notes for Abstract Algebra I
www.supermath.infoGalois insight was to identify the patterns in Lagrange’s work which involved permutations of the roots of the equation. In retrospect, this was the birth of Group Theory. In short, Galois said there was a nice solution to a quintic if the Galois group is solvable. If a group is simple5 then it cannot be broken down further, they’re sort of ...
5. APPLICATIONS OF DERIVATIVES
www.supermath.infoLinearization of a function is the process of approximating a function by a line near some point. The tangent line is the graph of the linearization. ... The shape of a graph can be ciphered through analyzing how the ... always word problems pose extra troubles as …
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