MATH 332: Advanced Calculus
James Cook's Advanced Calculus Homepage

Welcome, I include here the most recent and the most ancient materials on this course. Enjoy.

Course Materials for Fall 2017 Advanced Calculus:

Lecture Notes and Videos from past offerings of Math 332:

Advanced Calculus of Fall 2015:
We are mostly following my Lecture Notes (2015) which are based on "Advanced Calculus of Several Variables," by C.H.Edwards, Jr. which is available from Dover. However, I am influenced by many other sources. In particular, I'm looking at Renteln's "Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists" for some interesting new homework ideas. I'm also hopeful to implement the musical morphisms and coordinate change partly from a few sections in Jeffrey M. Lee's "Manifolds and Differential Geometry" (Graduate Studies in Mathematics). In any event, you can follow along at Advanced Calculus You Tube Playlist (Lectures from Fall 2015).

Problems and Exams with some Solutions from past years:
Select Conversations:
Here I collect a few conversations I've had with students on the topic of advanced calculus and associated real analysis. I sometimes foolishly try to teach students outside the framework of formal courses.
Course Notes from Fall 2013:
I post below my third version of Math 332 notes. This updates the 2011 version to include more on normed linear spaces. Also, I make an effort to be more inuitive and less formal in the introduction of manifolds.
  • the third version of my Math 332 course notes

  • Course Notes from Fall 2011:
    I post below my second version of Math 332 notes. This was a fairly major revision of the first version. In particular, I no longer delay proof of the implicit and inverse function theorem. Instead, I sketch the proofs and refer the reader to Edwards.
  • the second version of my Math 332 course notes

  • Course Notes from Spring 2010:
    In my first run through this course we used C.H. Edward's Advanced Calculus text. I partly used Hildebrand for the variational calculus portion of the course as well. What is posted below are the notes I provided during that semester. 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.

  • the first version of my Math 332 course notes

  • Notice the blank spots are filled in in the pdfs below.
    1. Chapter 2 (version 2) with what was said in lecture more or less.
    2. Chapter 3 with what was said in lecture more or less.
    3. Chapter 4 with what was said in lecture more or less.
    4. Coriolis effect adjoined to end of chapter.
    5. Chapter 6 with what was said in lecture more or less.
    6. Chapter 6 with what was said in lecture more or less.
    7. Chapter 7 on local extrema from lense of multivariate Taylor and the joy of quadratic forms.
    8. Chapter 8 on manifolds as level sets and Lagrange multipliers
    9. Chapter 9 on generalized Newton's method and how it justifies the implicit and inverse function and mapping theorems (wow).
    10. Chapter 10 on basics of abstract manifold theory. Just the basics.
    11. Chapter 11 is on exterior algebra of forms on Rn ( part of this )
    12. Chapter 12 is on the Generalized Stokes Theorem ( part of this )
    13. Chapter 13 is on Hodge duality ( part of this )
    14. Chapter 14 is on Variational Calculus: the main chapter and some extra and the central force problem.
    Recommended Reading:
    Additional Examples:
    A few calculations which are advanced calculus we did not precisely cover:
    Last modified 9-4-2017

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