ME 526: ENGINEERING ANALYTICAL METHODS
TEXTBOOK: ADVANCED ENGINEERING MATHEMATICS - BY O'NEIL
INSTRUCTOR: F.N. EGOLFOPOULOS
OHE 400B, (213) 740-0480, egolfopo@rcf.usc.edu
OFFICE HOURS: T, Th 11:00-1:00
COURSE OUTLINE - SUMMER 1999
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LECTURE NO. |
TOPICS |
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1, 2 |
Review of Ordinary Differential Equations. Solution of homogeneous equations. Solution of nonhomogeneous equations by the method of undetermined coefficients and the method of variation of parameters.
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3 |
Problems with variable coefficients. The method of Frobenius. Bessel functions and Legendre polynomials. |
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4 |
Introduction to Fourier series. Representation of piecewise continuous functions as sine and/or cosine series. Double Fourier series. |
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5 |
Fourier integrals and Fourier transforms. Laplace transform. Inverse integral, convolution integral. Application to Ordinary Differential Equations. |
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6 |
Introduction to Partial Differential Equations. Classification of Partial Differential Equations - parabolic, elliptic and hyperbolic equations. Boundary conditions. |
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Mid-term Examination (open book and notes) |
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7 |
Wave equation, D'Alembert's solution. The method of characteristics. |
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8 |
The method of separation of variables. The diffusion equation. Application of Fourier series to Partial Differential Equations. |
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9 |
Sturm-Liouville theory. Orthogonal eigenfunctions. |
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10 |
Partial Differential Equations in cylindrical coordinates. Fourier-Bessel series. Steady-state and time-dependent problems involving cylinders. |
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11 |
Problems in spherical geometry. Fourier-Legendre series. Spherical Bessel functions for time-dependent problems. |
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12 |
Non-homogeneous Partial Differential Equations. Poisson's equation. |
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13 |
Green's functions for partial differential equations. |
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FINAL EXAMINATION (open book and notes) |
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Grading: |
Homework |
10% |
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Mid-term Examination |
40% |
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Final Examination |
50% |