Teaching

Univariate Calculus: Function of one variable, Limit, Continuity and Differentiability of functions, Rolle’s theorem, Mean value theorem, maxima, minima, Riemann integral, Fundamental theorem of calculus, applications to length, area, volume, surface area of revolution.
Infinite Sequences and Series: Sequences, Infinite series, The Integral test, Comparison tests, The Ratio and Root tests, alternating series, absolute and conditional convergence, Power series. Taylor and Maclaurin series, Convergence of Taylor Series, Error Estimates, applications of Power series.
Multivariate Calculus: Functions of several variables, Limit, Continuity and Partial derivatives, Chain rule, Gradient, Directional derivative, and Differentiation, Tangent planes and normals. maxima, minima, saddle points, Lagrange multipliers, Double and Triple integrals, change of variables.
Calculus on Vector Field: Vector fields, Gradient, Curl and Divergence, Curves, Line integrals and their applications, Green’s theorem and applications, Divergence theorem, Stokes’ theorem and applications.

T. M. Apostol, Calculus, Vol. 1, Wiley.
T. M. Apostol, Calculus, Vol. 2, Wiley.
Ajit Kumar and S. Kumaresan, A Basic Course in Real Analysis, CRC Press, Taylor & Francis Group.

The Real Number System: Problem Set 01
Convergence of Sequences, Monotone Sequences: Problem Set 02
Cauchy criterion, Subsequence: Problem Set 03
Continuity and Limits: Problem Set 04
IVP, Existence of maxima/minima: Problem Set 05
Differentiability, Rolle’s theorem: Problem Set 06
Mean Value Theorem: Problem Set 07
Fixed point iteration method, Newton’s method: Problem Set 08
Maxima/minima, Curve tracing: Problem Set 09
Taylor's Theorem: Problem Set 10
Series: Definition of convergence, Necessary and sufficient conditions for convergence: Problem Set 11

Convex Analysis: convex sets, convex functions, calculus of convex functions.
Optimality of Convex Programs: 1st order necessary and sufficient conditions, KKT conditions.
Duality: Lagrange and conic duality.
Linear and Quadratic Programs.
Conic Programs: QCQPs, SOCPs, SDPs.
Smooth Problems: gradient descent, Nesterov's accelerated method, Newton's methods.
Non-smooth Problems: sub-gradient descent.
Special topics: active set and cutting planes methods, proximal point method.

S. Boyd and L.Vandenberghe, Convex Optimization. Cambridge University Press, 2004.

R. T. Rockafellar. Convex Analysis. Princeton University Press, 1996.
G. C. Calafiore and L. El Ghaoui, Optimization Models, Cambridge University Press, 2014.