| Description |
1 online resource (xvi, 624 pages) : illustrations |
| Contents |
Cover -- Contents -- Chapter 1. Mathematical Auxiliaries -- 1.1. Matrix Computations -- 1.2. Brief on Vector Analysis -- 1.3. Curves in R3 -- 1.4. Linear Differential Equations -- 1.5. Linear Differential Systems of First Order -- 1.6. The Flux Integral and its Vector Field -- 1.7. Vector Spaces -- 1.8. Derivatives -- 1.9. Mappings in Banach Spaces -- 1.10. Convex Sets and Functions -- 1.11. Quadratic Functionals -- Chapter 2. Numerical Methods -- 2.1. Interpolation and Approximation -- 2.2. Orthogonal Polynomials -- 2.3. Numerical Integration -- 2.4. Initial Value Problems -- 2.5. Boundary Value Problems -- 2.6. Periodic Problems -- 2.7. Differential Algebraic Problems -- 2.8. Hints to the MATLAB Programs -- Chapter 3. Optimization -- 3.1. Minimization of a Function -- 3.2. Extrema with Constraints -- 3.3. Linear Programming -- 3.4. Linear-Quadratic Problems -- 3.5. Nonlinear Optimization -- 3.6. A Brief on Lagrange Theory -- 3.7. Hints to the MATLAB Programs -- Chapter 4. Variation and Control -- 4.1. Variation -- 4.2. Control Problems without Constraints -- 4.3. Control Problems with Constraints -- 4.4. Examples -- 4.5. On the Re-Entry Problem -- 4.6. Hints to the MATLAB Programs -- Chapter 5. The Road as Goal -- 5.1. Bifurcation Problems -- 5.2. Scaling -- 5.3. Calculation of Singular Points -- 5.4. Ordinary Differential Systems -- 5.5. Hopf Bifurcation -- 5.6. Numerical Bifurcation -- 5.7. Continuation -- 5.8. Hints to the MATLAB Programs -- Chapter 6. Mass Points and Rigid Bodies -- 6.1. The Force and its Moment -- 6.2. Dynamics of a Mass Point -- 6.3. Mass Point in Central Field -- 6.4. Systems of Mass Points -- 6.5. The Three-Body Problem -- 6.6. Rotating Frames -- 6.7. Inertia Tensor and Top -- 6.8. On Multibody Problems -- 6.9. On Some Principles of Mechanics -- 6.10. Hints to the MATLAB Programs -- Chapter 7. Rods and Beams -- 7.1. Bending Beam -- 7.2. Eigenvalue Problems -- 7.3. Numerical Approximation -- 7.4. Frameworks of Rods -- 7.5. Frameworks of Beams -- 7.6. Hints to the MATLAB Programs -- Chapter 8. Continuum Theory -- 8.1. Deformations -- 8.2. The Three Transport Theorems -- 8.3. Conservation Laws -- 8.4. Material Forms -- 8.5. Linear Elasticity Theory -- 8.6. Discs -- 8.7. Kirchhoffs Plate -- 8.8. Von Karmans Plate and the Membrane -- 8.9. On Fluids and Gases -- 8.10. Navier-Stokes Equations -- Chapter 9. Finite Elements -- 9.1. Elliptic Boundary Value Problems -- 9.2. From Formula to Figure, Example -- 9.3. Constructing Finite Elements -- 9.4. Further Topics -- 9.5. On Singular Elements -- 9.6. Navier-Stokes Equations -- 9.7. Mixed Applications -- 9.8. Examples -- 9.9. Hints to the MATLAB Programs -- Chapter 10. A Survey on Tensor Calculus -- 10.1. Tensor Algebra -- 10.2. Algebra of Alternating Tensors -- 10.3. Differential Forms in Rn -- 10.4. Tensor Analysis -- 10.5. Examples -- 10.6. Transformation Groups -- Chapter 11. Case Studies -- 11.1. An Example of Gas Dynamics -- 11.2. The Reissner-Mindlin Plate -- 11.3. Examples of Multibody Problems -- 11.4. Dancing Discs -- 11.5. Buckling of a Circular Plate -- Chapter 12. Appendix -- 12.1. Notations and Tabl |
| Summary |
The interaction between mathematics and mechanics is a never ending source of new developments. This present textbook includes a wide a "ranging spectrum of topics from the three body problem and gyroscope theory to bifurcation theory, optimization, control and continuum mechanics of elastic bodies and fluids. For each of the covered topics the reader can practice mathematical experiments by using a large assortment of Matlab-programs which are available on the authora (TM)s homepage. The self-contained and clear presentation including Matlab is often useful to teach technical details by |
| Bibliography |
Includes bibliographical references (pages 599-609) and index |
| Notes |
Translated from the German |
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Print version record |
| In |
Springer eBooks |
| Subject |
Mechanics -- Mathematics
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Mathematics.
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Engineering.
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mathematics.
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applied mathematics.
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mechanics (physics)
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engineering.
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SCIENCE -- Mechanics -- General.
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SCIENCE -- Mechanics -- Solids.
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Mechanics -- Mathematics.
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Ingénierie.
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Mechanics -- Mathematics
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| Form |
Electronic book
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| LC no. |
2008929625 |
| ISBN |
9783540692799 |
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3540692797 |
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3540692789 |
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9783540692782 |
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3642088775 |
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9783642088773 |
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