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Mathematics Semester 1 (AUG) UM 101: Analysis and Linear Algebra I (3:0) One-variable calculus: Real and complex numbers; Convergence of sequences and series; Continuity, intermediate value theorem, existence of maxima and minima; Differentiation, mean value theorem, Taylor series; Integration, fundamental theorem of Calculus, improper integrals. Linear Algebra: Vector spaces (over real and complex numbers), basis and dimension; Linear transformations and matrices. Instructor: A. Ayyer Suggested books: 1. T M Apostol, Calculus, Volume I, 2nd. Edition, Wiley, India, 2007.

continuity, Cauchy sequences and completeness. Review of total derivatives, inverse and implicit function theorems. Review of Green’s theorem and Stokes’ theorem. Complex linearity, the Cauchy-Riemann equations and complex-analytic functions. Möbius transformations, the

  Equations, Functions, Complex, Cauchy, Riemann, Riemann equations

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  Sciences, Of science

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