B. Tech. Courses

Univariate and Multivariate Calculus

Linear Algebra

Probability & Statistics

SMAT430C: Convex Optimization

  • Announcements

  • Course Outline
    • 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.

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

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

  • Question Papers and Answer Keys
  • Marks (Formula for Total Marks = Q1 + MS + 0.8*Q2 + ES)

SMAT330: Complex Analysis and Integral Transformations

  • Course Outline
    • Laplace Transforms: Definition and properties, Sufficient condition of Existence, Transforms of derivatives and integrals, Derivatives and integrals of transforms, Inverse Laplace Transforms, Exponential shifts, Convolutions, Applications: Differential and Integral Equations.
    • Fourier Series: Periodic functions, fundamental period, Trigonometric series, Fourier series, Bessel's inequality, Orthonormal and orthogonal set, Euler formulas, Functions with arbitrary periods, Even and odd functions , Half range expansions, Fourier coefficients without integration, Approximation by trigonometric polynomials, Application to differential equation.
    • Fourier Transforms: Fourier integral theorem, Sine and Cosine Integrals, Inverse Transforms, Transforms of Elementary Functions, Properties, Convolution, Parsevals relation, Transform of Dirac Delta Function, Multiple Fourier transform, Finite Fourier transform.
    • Z Transforms: Z-transforms, properties, Inverse Z- transforms, relationship with Fourier transforms.
    • Complex Analysis: Complex numbers, Modulus, Argument, Curves and regions in complex plane, Functions, Limits, Derivatives, Analytic functions, Cauchy-Riemann equations, Complex exponential logarithms and trigonometric function, General powers, Line integrals, Cauchy's theorem, Cauchys integral theorem, Cauchys integral formula, Taylor and Laurent series , Zeros and singularities, Residues, Residues theorem, Evaluation of real improper integrals.

  • Text Book
    • E. Kreyszig, Advanced Engineering Mathematics, Wiley.

  • Reference Books
    • M. Braun, Differential Equations and Their Applications, Springer-Verlag, New York.
    • W. Trench, Elementary Differential Equations.
    • J. Schiff, The Laplace Transform: Theory and Applications, Springer.
    • J. Brown and R. Churchill, Complex Variables and Application, McGraw-Hill.
    • G. F. Simmons, Differential Equations, Tata Mcgraw Hill.
    • R. Jain and S. Iyenger, Advanced Engineering Mathematics, Narosa.
  • Questions and Keys

Minor in Mathematical Analysis

    I introduced a Minor in Mathematical Analysis for B.Tech. (IT, ECE & BI) students which will be opted by them from 3rd till the 7th semester. The list of the courses in this minor is: 1) Real Analysis 2) Introduction to Topology 3) Differential Geometry of Curves and Surfaces 4) Measure Theory 5) Functional Analysis.

PhD Courses

    I taught the following courses to PhD students: 1) Mathematical Analysis (Calculus of Seevral Variables, Measure Theory & Fourier Series) 2) Functional Analysis 3) Fundamentals of Discrete Mathematics.