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ADVANCED CALCULUS QUESTIONS SERIES

Chapter 13 is on Hodge duality ( part of this ).

Chapter 12 is on the Generalized Stokes Theorem ( part of this ).

Chapter 11 is on exterior algebra of forms on Rn ( part of this ).

Chapter 10 on basics of abstract manifold theory.

Chapter 9 on generalized Newton's method and how it justifies the implicit and inverse function and mapping theorems (wow).

Chapter 8 on manifolds as level sets and Lagrange multipliers.

Chapter 7 on local extrema from lense of multivariate Taylor and the joy of quadratic forms.

Chapter 6 with what was said in lecture more or less.

Coriolis effect adjoined to end of chapter.

Chapter 4 with what was said in lecture more or less.

Chapter 3 with what was said in lecture more or less.

Chapter 2 (version 2) with what was said in lecture more or less.

Notice the blank spots are filled in in the pdfs below.

the first version of my Math 332 course notes.

They are partly based on my Math 430 notes and in Chapter 14 my notes from a Junior level classical mechanics course I took at NCSU as an undergraduate. What is posted below are the notes I provided during that semester. I partly used Hildebrand for the variational calculus portion of the course as well. In my first run through this course we used C.H.

the second version of my Math 332 course notes.

Instead, I sketch the proofs and refer the reader to Edwards. In particular, I no longerĭelay proof of the implicit and inverse function theorem. This was a fairly major revision of the first version. I post below my second version of Math 332 notes.

the third version of my Math 332 course notes.

Also, I makeĪn effort to be more inuitive and less formal in the introduction of manifolds. This updates the 2011 version to include more on normed linear spaces. I post below my third version of Math 332 notes.

(2010)advanced calculus with some analysis.

From a focused hybrid 332/422 course with a student who went on to graduate school:

Based on Rosenlicht's Introduction to Analysis text.

push-forward example on matrix manifold (from Fall 2011).

(2013)advanced calculus, DEqns, manifolds.

ADVANCED CALCULUS QUESTIONS SERIES

a series of discussions with several students over the summer "break"(these conversations partly inspired the 2013 revision of the Advanced Calculus course.

$advanced calculus questions$

best hits of advanced calculus a condensed remix.a picture gallery of an intensive 2hr lecture I once gave to a certain student who never followed up on the work.I sometimes foolishly try to teach students outside the framework of formal courses. Here I collect a few conversations I've had with students on the topic of advanced calculus and associated real analysis. Problem Set III: Multivariate Extrema and the solution.Problem Set II: Geometry of Curves and Surfaces and the solution.Problem Set I: Euclidean space and Analysis and the solution.homework, exams and some solutions from Spring 2010:.Problems and Exams with some Solutions from past years:

In any event, you can follow along at Advanced Calculus You Tube Playlist (Lectures from Fall 2015). Lee's "Manifolds and Differential Geometry" (Graduate Studies in Mathematics). I'm also hopeful to implement the musical morphisms and coordinate change partly from a few sections in Jeffrey M. In particular, I'm looking at Renteln's "Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists" for some interesting new homework ideas. However, I am influenced by many other sources. We are mostly following my Lecture Notes (2015) which are based on "Advanced Calculus of Several Variables," by C.H.Edwards, Jr. this and this form the first version of my Math 332 course notes (Spring 2010).the second version of my Math 332 course notes (2011).the third version of my Math 332 course notes (2013).the fourth version of my Math 332 course notes (2015).My Lecture Notes for Advanced Calculus:.Advanced Calculus You Tube Playlist (Lectures from Fall 2015).Lecture Notes and Videos from past offerings of Math 332: Notice, I only follow these the first bit of the course then we transfer control over to McInerney, although, I'll probably add a fair amount about differential forms which can be found in my old versions of this course's notes. the fifth version of my Math 332 course notes (2017).Advanced Calculus You Tube Playlist (Lectures from Fall 2017).Enjoy.Ĭourse Materials for Fall 2017 Advanced Calculus: Welcome, I include here the most recent and the most ancient materials on this course.