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CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Electrical Engineering
Instruction in: English
Course Code: 18308
Transcript Source: Partner Institution
Course Details: Level 200
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Calculus II, Differential Equations
DESCRIPTION
1. Complex functions Complex numbers. Complex functions. Limits. Continuous functions. Derivatives and Cauchy-Riemann equations. Armonic functions. 2. Elementary functions Polynomials. Exponential function. Trigonometric functions. Hyperbolic functions. Logarithm. Complex exponents. Inverses of trigonometric and hyperbolic functions. 3. Integrals in the complex domain. Contour integrales. Cauchy-Goursat theorem. Cauchy formula. Morera theorem. Bounds for analytic functions. The fundamental theorem of algebra. 4. Series Sequences and convergence criteria. Power series. radius of convergence. Taylor series. Laurent series. Analytic continuation. Power series and differential equations. Frobenius theory. Special functions of Mathematical Physics 5. Residues and poles Zeros of a function. Singularities. Poles. Residue formula. Residue theorem. Real integrals of trigonometric functions. Real improper integrals. Integrals on branch cuts. Summations of series by using residue theorem. 6. Fourier series Fourier series and their application to periodic signals. Square integrable functions. Pointwise convergence. Uniform convergence. Application to differential and partial differential equations. 7. Fourier transform. Definition and properties. Inverse Fourier transform. Representation of aperiodic signals. Discrete time Fourier transform. 8. Laplace transform Definition, properties and convergence. Inverse Laplace transform. Derivatives, integrals, and convolution. Applications to systems of linear differential equations. Transfer function. 9. z-Transform Convergence region and other properties. Inverse z-transform. Transforms between continuous and discrete time signals. Applications to linear difference equations. 10. Linear invariant-time systems Linear time-invariant (LTI) systems. Analysis of LTI systems with transforms.
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