This subject builds on the student’s ability to use calculus, to introduce more advancedtechniques of integration and their application to separable differential equations, and to analogue signals via Laplace transformsand digital signals via Fourier coefficients. The subject also introduces the basic conceptsof differential equations and uses the techniques of calculus and Laplace Transforms tosolve first and second order differential equations. The subject also introduces Transferfunctions, writing them in standard form, calculating poles and zeros, applying the Routh Criterion for stability to the transfer function in second and third order stability problems in Electronic Engineering. Convergence of sequences and series are introduced. Matrices are used to determine stability in first and second order stability problems in Electronic Engineering via the Hurwiz Criterion.
Techniques of Integration
Basic rules; integration by substitution; integration by parts. The method of partial fractions, including the use of Maclaurin series and Taylor series, and including integrals involving Sinusoidal Oscillations, Piecewise linear signals and odd and even signals, and applied to solving separable differential equations.
Introduction. Transforms of standard functions. Inverse transforms. Table ofinverse transforms. Transfer functions, writing them in standard form, findingpoles and zeros. RouthCriterion for stability. Differential equations for RC, LC and LRC circuits withDC and AC sources. Solution of first order linear ODEs with constant coefficientsby Laplace transform method. The Laplace transform of a second order linearODE with constant coefficients.
Algebra of matrices, including matrices with complex entries. Inverse of amatrix. Determinants. Simultaneous linear equations Gaussian eliminationUniqueness of solutions. Applications to second and third order stabilityproblems in Electronic Engineering via the Hurwiz criterion.
Sequences and Series
Definitions. Geometric progressions. Summing series,limits and convergence. Ratio test for convergence.
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