Engineering Analysis: Advanced Mathematical Methods for Engineers introduces graduate engineering students to the fundamental but advanced mathematics tools used in engineering application, especially in mechanical, aerospace, and civil engineering. Most engineering problems are described by differential equations, particularly partial differential equations (PDEs). Deformation and failure in solid structures, fluid flow, heat transfer, and mass diffusion are all governed by PDEs in general. Many physical quantities in engineering are tensors, including deformation gradient, strain rates, stresses, elastic stiffness, and thermal conductivity of composite materials. This book helps engineering graduate students develop the skills to establish the mathematical models of engineering problems and to solve the problems described by the mathematical models.
PART I ORDINARY DIFFERENTIAL EQUATIONS – ADVANCED TOPICS 1. Ordinary Differential Equations and Power Series Solutions 2. The Frobenius Method 3. The Laplace Transform Method 4. Numerical Solutions of Ordinary Differential Equations PART II FOURIER ANALYSIS 5. Fourier Series 6. Fourier Transforms PART III PARTIAL DIFFERENTIAL EQUATIONS 7. Partial Differential Equations in Engineering 8. Separation of Variables Method 9. Separation of Variables Method – Circular and Spherical Regions 10. Integral Transform Methods 11. The Finite Difference Method PART IV TENSOR ANALYSIS 12. Cartesian Tensors 13. Tensor Analysis
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