**Linear Algebra II** (MAT224)

Fields, complex numbers, vector spaces over a field, linear transformations, matrix of a linear transformation, kernel, range, dimension theorem, isomorphisms, change of basis, eigenvalues, eigenvectors, diagonalizability, real and complex inner products, spectral theorem, adjoint/self-adjoint/normal linear operators, triangular form, nilpotent mappings, Jordan canonical form.

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**Real analysis** (MAT337)

Construction of Real Numbers. Metric spaces; compactness and connectedness. Sequences and series of functions, power series; modes of convergence. Interchange of limiting processes; differentiation of integrals. Function spaces; Weierstrass approximation; Fourier series. Contraction mappings; existence and uniqueness of solutions of ordinary differential equations. Countability; Cantor set; Hausdorff dimension.

**Real analysis**

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**Complex analysis and ODEs**

## This is a course designed to prepare students for use of essential

mathematical concepts and techniques for Electrical and Computer

Engineering applications. It includes basics of Complex Analysis, Differential Equations and Laplace Transforms.

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**Nonlinear-optimization** (APM462)

An introduction to first and second order conditions for finite and infinite dimensional optimization problems with mention of available software. Topics include Lagrange multipliers, Kuhn-Tucker conditions, convexity and calculus of variations. Basic numerical search methods and software packages which implement them will be discussed.

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