Calculus Lectures Pdf

[Heberto Calderon]

Thesevideo lectures of Professor David Jerison teaching 18.01 were recorded live in the Fall of 2007 and do not correspond precisely to the lectures taught in the Fall of 2006 (e.g., the lecture notes).

As well, here are some hard to find videos corresponding to the 11th edition of Thomas Calculus that I enjoyed a long time ago. While the book links all appear to be dead, and not all of the videos work, most of the videos do work, and the deliverers are outstanding: Thomas.

You may find Adrian Banner's Calculus Lifesaver course useful. The series of 24+ videos are available at and are also provided on the iTunes Store as Podcasts. The quality of the videos is variable, but the exposition is thorough, and his style is engaging.

NOTE: In Video lecture for Multi-variable Calculus by Edward Frenkel of UC berkeley, in the first lecture he is referring to an equation (function y=f(x)) and he says that there are 2 "independent" variables and 1 equation, so number of independent variables minus number of equations gives us the dimension.

The video lectures at the "best" schools tend to be less systematic and orderly. All are useful, but if you are using videos to self-teach I would suggest the UMKC calculus 1 lectures by Delaware. There is no live audience, and thus no stammering, no showing up and teaching off the top of one's head. More progressive and orderly.

I highly recommend learning Calculus from the ground up with Professor Leonard. His video lectures are comprehensive, comprehensible, and help the math stick long after you've watched his videos. I completed his Calc 1 and Calc 2 courses. I am halfway through his Calc 3 videos. I suggest starting here: =PLF797E961509B4EB5

I am in a particular situation that I am doing Master's in a Computer Science related degree, and I would like to take the course on Convex Optimisation which is taught by the Machine Learning department of our University. I did my undegrad almost 10 years ago and my memories of maths courses are quite sparse. The pre-requirements for this course are Linear Algebra and Multivariable Calculus. As for the former, I have already been going through Gilbert Strang's OCW lectures and working the problems from his book. The latter is what my question is about - I've got some disjoint knowledge of Calculus already, and also I have been going through the Spivak's Calculus book. I have considered 2 options so far:

My question is what would be the most optimal way to get up to speed with Multivariable Calculus. In particular professor mentioned things we need to understand such as Vector spaces, Taylor theorem for multivariable case, level sets. I already have a fairly good understanding of Taylor expansion in single variable case, and I can imagine how it could be generalised to many variables, but I still need to do my homework. I am not necesserily looking to cherry pick certain topics and be done with it, I would like to learn everything properly, but maybe you can advice me something considering the time constraints that I have. Thank you.

Update: Subsequently I found Massively Multivariable Open Online Calculus Course by Ohio State University at Coursera and I am really liking it. It is reach in examples, builds up intuition, but also provides formal proofs where necessary. It is largely a text based course, without any video lectures, but it does not bother me, as long as it guides me through. As suggested by others I will also go through the lectures at OCW.

I would honestly take the classes again if possible. If not possible, then I would definitely study the OCW from Denis Auroux because I think it's the best. Find out what concepts are most widely used and then concentrate your studying on those things as well.

I think MITOCW would be best recommended. Also, edx.org and coursera.org are a good recommendation. I say this due to the fact that the websites provide one-on-one assistance and lots of other information to you would find intrest in looking into. This should give you a general idea of what to expect. However looking at the websites yourself is the true test to you potential needs.

If you want a purely theoretical approach to multivariable calculus you can look intoTom Apostol's Calculus Volume 2.Other than that if you want an application based course with enough foundational concepts explained, then go with MITOCW lectures by Professor Dennis Auroux.

Spivak's Calculus is considered a good resource because it is highly regarded for its clear and concise explanations, as well as its challenging problem sets which help students develop a deeper understanding of the subject.

Yes, there are several online resources available for studying Spivak's Calculus, such as lecture notes, video lectures, and practice problems. Some universities also have online courses that use Spivak's Calculus as the main textbook.

To use Spivak's Calculus to improve your understanding of calculus, it is recommended to read through the text carefully, complete the challenging problem sets, and seek additional resources or help from a teacher or tutor if needed.

The author opens with the study of three classical problems whose solutions led to the theory of calculus of variations. They are the problem of geodesics, the brachistochrone, and the minimal surface of revolution. He gives a detailed discussion of the Hamilton-Jacobi theory, both in the parametric and nonparametric forms. This leads to the development of sufficiency theories describing properties of minimizing extremal arcs.

In the second part of the book, the author discusses optimal control problems. He notes that originally these problems were formulated as problems of Lagrange and Mayer in terms of differential constraints. In the control formulation, these constraints are expressed in a more convenient form in terms of control functions. After pointing out the new phenomenon that may arise, namely, the lack of controllability, the author develops the maximum principle and illustrates this principle by standard examples that show the switching phenomena that may occur. He extends the theory of geodesic coverings to optimal control problems. Finally, he extends the problem to generalized optimal control problems and obtains the corresponding existence theorems.

The appearance of this book is one of the most exciting events for friends of the Calculus of Variations since the publication of Carathodory's classic in 1935 on the calculus of variations and partial differential equations of first order. The author ... gives here a very lively, greatly stimulating, and highly personalized account of the calculus of variations and optimal control theory ... In his many refreshing asides, the author not only puts ideas and techniques into their historic perspective, but also succeeds in making men, who for many of us are merely revered names, come alive through skillful selection of quotes and descriptions of their interaction with each other and the subject matter at hand ... A beautiful book ... that is bound to stimulate many mathematicians and students of mathematics.

A considerable number of heretofore unpublished results developed by the author are found ... The book is an important contribution to the calculus of variations and optimal control theory. It is most appropriate that the theory of generalized curves should be presented ... by its founder. The book is well written with an unusual and lively style. It is filled with historical remarks and with comments which enlarge one's outlook on the role of mathematics and mathematicians in our society ... This book should be mastered by anyone who wishes to become an expert in this field.

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