Math and Computing Courses

Review of single variable calculus, Functions of several variables: limits, continuity, partial derivatives, tangent plane,
directional derivatives, differentiation, the chain rule, maxima and minima, Double and triple integrals: area and volume, change of
variables, Curves: parametrization, arc-length and its invariance, curl and divergence, line integrals, conservative vector fields and
Green's theorem, surface integrals and Stokes' theorem, Gauss divergence theorem, First-order differential equations: geometrical
meaning of a first-order differential equation, variable separable equations, exact equations, integrating factors, linear and Bernoulli
equations, orthogonal trajectories, existence and uniqueness of solutions for initial value problems, Second-order differential equations:
homogeneous linear equations with constant coefficients, Euler-Cauchy equations, linear independence of solutions and Wronskian,
solution of non-homogeneous equations, Power series method, Legendre's equation, Legendre polynomials, Frobenius method,
Bessel's equation, Sturm-Liouville problems.

 Basics: C++ environment, variables, arrays, selection and repetition structure, functions, pointers, file handling,
OOPS: class, memory allocation, operator overloading, inheritance, templates, Algorithm: singular value decomposition, sorting,
searching, Euler project problems, Matlab: introduction, algebra of matrices, linear solvers, singular value decomposition, tensor
classes, tensor toolbox. 

Python: datatypes, list, tuple, dictionary, sets, branching, loops, recursion, functions,
arguments, class, numpy, scipy, matplotlib, pandas, R: default data-sets, import, colors, charts,
frequencies, data handling, hypothesis testing, regression, correlation, T-test, chi-square test, ANOVA.