Topics in Engineering Mathematics -

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Résumé :
A kaleidoscopic excursion into numerical calculations of differential equations.- 1. Introduction.- 2. Logistic equation.- 3. Harmonic oscillator.- 4. Wave equations.- 5. Epilogue.- An introduction to the Finite Element Method.- 1. Introduction.- 2. An elementary example.- 3. The 2-dimensional Poisson equation.- 4. Final remarks.- Coupling of sound and structural vibrations.- 1. Introduction.- 2. Governing equations and analysis.- 3. Numerical results and discussion.- Mathematical modeling and dimensional analysis.- 1. Introduction.- 2. Mathematical Modeling.- 3. Dimensional Analysis.- 4. Four-wheel steering.- About difference equations, algebras and discrete events.- 1. Difference equations.- 2. Changing the algebra.- 3 Example on production.- 4. Some graph theory and the spectral theory of matrices.- 5. A stochastic extension.- 6. Counter versus dater description.- 7. The Z-transform.- 8. Conclusions.- Acoustical detection of obstructions in a pipe with a temperature gradient.- 1. Introduction.- 2. The problem.- 3. The model.- 4. Solution.- 5. Results.- 6. Conclusions.- Interior point approach to linear programming: theory, algorithms and parametric analysis.- 1. Introduction.- 2. Central approach to the theory of LP.- 3. A polynomial-time path-following algorithm.- 4. Parametric analysis.- Some reflections on Newton's Method.- 1. Introduction and motivation.- 2. Rational Newton Flows.- 3. Structural Stability.- 4. Newton Graphs.- 5. Characterization of Newton Graphs.- 6. Open problems.- Recurrence and induction in Computer Science.- 1. Introduction.- 2. Strings of Symbols.- 3. Gray codes and recursiveness.- 4. Recursive algorithms....

Sommaire:
A kaleidoscopic excursion into numerical calculations of differential equations.- 1. Introduction.- 2. Logistic equation.- 3. Harmonic oscillator.- 4. Wave equations.- 5. Epilogue.- An introduction to the Finite Element Method.- 1. Introduction.- 2. An elementary example.- 3. The 2-dimensional Poisson equation.- 4. Final remarks.- Coupling of sound and structural vibrations.- 1. Introduction.- 2. Governing equations and analysis.- 3. Numerical results and discussion.- Mathematical modeling and dimensional analysis.- 1. Introduction.- 2. Mathematical Modeling.- 3. Dimensional Analysis.- 4. Four-wheel steering.- About difference equations, algebras and discrete events.- 1. Difference equations.- 2. Changing the algebra.- 3 Example on production.- 4. Some graph theory and the spectral theory of matrices.- 5. A stochastic extension.- 6. Counter versus dater description.- 7. The Z-transform.- 8. Conclusions.- Acoustical detection of obstructions in a pipe with a temperature gradient.- 1. Introduction.- 2. The problem.- 3. The model.- 4. Solution.- 5. Results.- 6. Conclusions.- Interior point approach to linear programming: theory, algorithms and parametric analysis.- 1. Introduction.- 2. Central approach to the theory of LP.- 3. A polynomial-time path-following algorithm.- 4. Parametric analysis.- Some reflections on Newton's Method.- 1. Introduction and motivation.- 2. Rational Newton Flows.- 3. Structural Stability.- 4. Newton Graphs.- 5. Characterization of Newton Graphs.- 6. Open problems.- Recurrence and induction in Computer Science.- 1. Introduction.- 2. Strings of Symbols.- 3. Gray codes and recursiveness.- 4. Recursive algorithms.