# TEW - Linear Algebra & Multivariable Calculus(2019)

## Speakers and Syllabus

This Teachers’ Enrichment Workshop (TEW) is aimed primarily at mathematics teachers at the undergraduate and postgraduate levels. While research scholars in mathematics may also apply, they will have lower preference in selection. The sessions will be geared towards improving the understanding of the fundamental concepts and results in Linear Algebra and Multivariable Calculus, two subjects that are basic to mathematics and science. The workshop will be an intensive one and only those who are willing to actively participate and get their hands dirty by solving problems need apply.

 Speaker Affiliation Topic(s) Number of lecture hours Number of tutorial hours Details Anirban Mukhopadhyay IMSc, Chennai Linear Algebra and MVC 10.5 2 (conduct) + 2 (assist) The aim will be to highlight the unifying theme behind the fundamental theorem of calculus, Green’s theorem, and Guass’ divergence theorem. Stokes’ theorem (for Rn )will be presented as a culminating point of this string of results. Will  take the shortest possible path to give a self contained proof of Stokes’ theorem largely following Principles of Mathematical analysis by W. Rudin. K.N. Raghavan IMSc, Chennai Linear Algebra 10.5 2 (conduct) + 2 (assist) The emphasis will be on matrices,not on the more abstract notion of linear transformations. Should the situation demand it, some of the topics shall be partially or fully skipped. I will follow the notes on the web page https://www.imsc.res.in/~knr/past/linalg_ed.pdf,  which themselves are based on Gilbert Strang’s book Introduction to Linear Algebra. Why is row rank equal to column rank? RREF (row reduced echelon form) of a matrix, its properties. Solving linear equations: geometry of the solution space. Notion of orthogonal projection: application to the line of best fit (approximate solution to an overdetermined system). Determinant and volume; Eigenvalues and eigenvectors; characteristic and minimal polynomials; Cayley-Hamilton theorem (possibly without proof) Spectral theorem for a real symmetric matrix: applications Singular value decomposition: applications S Sundar IMSc, Chennai Multivariable Calculus 6 2 (conduct) + 2 (assist) Derivative as a linear map; examples; computing the derivative in terms of partial derivatives. Taylor’s theorem up to second order and applications to maxima-minima. Inverse function theorem with proof. Lagrange multiplier method with some examples.

## Time Table

 Time 09:30 to 11:00 11:15 to 12:45 14:00 to 15:30 15:45 to 16:45 Mon 13th KNR SS L AM Tutorials(KNR & SS) S Tue 14th AM T SS U KNR T Tutorials(AM & SS) N Wed 15th KNR E AM N SS E Tutorials(KNR & SS) A Thur 16th SS A KNR C AM A Tutorials(SS & AM) C Fri 17th KNR AM H KNR Tutorials(KNR & AM) K Sat 18th AM KNR AM Tutorials(AM & KNR) S

KNR = K.N.Raghavan, AM = Anirban Mukhopadhyay, SS = S.Sundar

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