The courses specified subsequently are indicative of the courses we offer tution for. Tuition is offered both for individual notions within each course and for the whole course.
Multivariable Differential Calculus
Differential calculus for functions of two or more variables. Topics: vectors and vector-valued functions in 2-space and 3-space, tangent and normal vectors, curvature, functions of two or more variables, partial derivatives and differentiability, directional derivatives and gradients, maxima and minima, optimization using Lagrange multipliers.
Multivariable Integral Calculus
Integral calculus for functions of two or more variables. Topics: double and triple integrals, change of variables and the Jacobian, vector fields, line integrals, independence of path and the fundamental theorem of line integrals, Green’s theorem, divergence theorem, and Stokes’ theorem.
An introductory course in Linear Algebra. Topics: matrices, linear equations, vector spaces, bases, coordinates, linear transformations, eigenvectors, eigenvalues, and diagonalization.
Theory of abstract algebra, with particular emphasis on applications involving symmetry. Topics: groups, rings, fields, matrix and crystallographic groups, and constructibility.
Theory of functions of a real variable. Topics: sequences, series, limits, continuity, differentiation, integration, and basic point-set topology.
Basic techniques and methods for solving ordinary differential equations. Topics: linear, separable, and exact equations, existence and uniqueness theorems, difference equations, basic theory of higher order equations, variation of parameters, undetermined coefficients, series solutions, Laplace transform, systems of equations.
Theory of differentiation and integration of complex functions. Topics: algebra of complex numbers, complex functions, multi-valued functions, exponentials, logarithms, analyticity, integrals, power series, Laurent series, residues, isolated singularities, poles and zeros.
Partial Differential Equations
Theory of differential equations involving functions of more than one variable. Topics: first order equations, classification of second order equations, initial-boundary value problems for heat equation, wave and related equations, separation of variables, eigenvalue problems, Fourier series, existence and uniqueness questions.
In all cases we take into account the mathematical background of our students and design programs of studies tailored to their needs.