Many of the results presented here are the corresponding generalizations of some known formulas on calculus vol 1 apostol pdf classical Bernoulli poly
Many of the results presented here are the corresponding generalizations of some known formulas on calculus vol 1 apostol pdf classical Bernoulli polynomials and the classical Genocchi polynomials. Check if you have access through your login credentials or your institution. I have mentioned that you should google the words libgen and mirtitles.
A mathematical gift vol 1, 2 and 3. If you have started with Real analysis, you have started a long beautiful drive. Along the drive you begin to see clearly through ODEs and PDEs and that is engineering. How does Elias Stein take his students on this drive at Princeton?
The answer lies in his four volume set. Lang too has a set of books that cover all the basic important topics. Sorry, i was taken of track. I wanted to discuss what could follow your Linal and Calculus. Many things I suppose, but my vote goes to Calculus of Variations. When I first learnt the basics, I was well into my Phd and I was shocked that i was ignorant of such a basic subject for so long. I wondered why it is not on Undergraduate Curriculum.
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I was right for a change. You will now find this in MIT OCW as an Undergraduate Course. I used Gelfand and Fomin. MIR publishers problem book by Krasnov Makarenko et al have great coverage of illustrative problems. I found the notes by Professor Tim Healey at Cornell University extremely useful. The principle of least action, lecture 19 Volume 2 on this topic. Multivariable Calculus, one picks up Linear Algebra.
A friend of mine used to say that one should do Linear algebra atleast 3 times, once as an Undergraduate, once as a Graduate and once as a TA. Too many good books in Linear Algebra around. Most people have their own favourite. Prof Gilbert Strang name is the most popular when one mentions LA, and for good reason, lot of applications are dealt with in the basic course material. Numerical Linear Algebra: Ciarlet’s book is for the industrious, while the more recent book by Gregoire Allaire seems be to more easily palatable. Trefethen’s website for his course is scholarly.
I have heard from friends that Horn and Johnson’s books are a must have for all researchers. In my last post i shied away from recommending any book on Real Analysis. I will mention here the most popular books, Bartle, Rudin, Apostol. Royden as a second course. It is vital to get a feel for and master the basic theorems and move onto a bit more advanced stuff along the way. Feynman’s introduction in Lecture 2 and Lecture 3 in Volume 2 is a superb start. You could use many well known texts to master the basic stuff mentioned here, eg GB Thomas, Ervin Kreyzig.
Once you have a good start, it is time to build start on the exciting edifice on the foundations. It is a small book but gives a wealth of foundations. It is interesting to note that this book inspired Professor James Munkres to write his more uptodate version of the topics covered by Spivak. Most Real Analysis text books will also cover all the main theorems in a fast paced way, your real analysis study will then be a great revision of all the multivariable calculus that you have mastered before that. A nice book from the publishers MIR, that has both theory and a list of illustrated problems for engineering, tying it up with all the theorems of basic vector calculus: Vector and Tensor Analysis by Borisenko and Tarapov. Here we will definitely get a feel for the common features of the most standard equations in Engineering and this is precisely the value in investing in revisits in mathematics.
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I am keen on interacting with our students to aim for a long list of enviable GATE 2014 scores. My belief that Math Works. We should always invest in getting the foundations of our math on firm footings. An inspiring example is Feynman.