"Version: 202108"--Title page verso.Includes bibliographical references.part I. Introduction. 1. What this book is about -- 1.1. Unpredictability -- 1.2. Domain structured dynamics -- 1.3. Random processes -- 1.4. Abstract fractals -- 1.5. Differential equations -- 1.6. Neural networkspart II. Chaos and fractals. 2. Unpredictability implies chaos -- 2.1. Unpredictability in dynamics -- 2.2. Unp…
"Version: 20210205"--Title page verso.Includes bibliographical references and index.1. Lorentz group and its representations -- 1.1. Generators of the Lorentz group -- 1.2. Two-by-two representation of the Lorentz group -- 1.3. Conformal representation of the Lorentz group -- 1.4. Representations of the Poincar?e group -- 1.5. Representations of the Lorentz group based on harmonic oscillators -…
"Version: 202112"--Title page verso.Includes bibliographical references.8. Continuum forces -- 8.1. The basic concepts of fluid mechanics -- 8.2. Drag forces -- 8.3. Bubbles in fizzy drinks -- 8.4. Magnetic-braking : the terminal velocity of a magnet falling in a tube of a non-magnetic metal9. Why is the sky blue? -- 9.1. Quantifying light intensity : subjectively and in absolute terms -- 9.2. …
"Version: 202110"--Title page verso.Includes bibliographical references.7. Toda's lattice of correlation potentials -- 7.1. The Toda soliton lattice -- 7.2. Developing nonlinearity -- 7.3. Conversion to Korteweg-deVries' lattice potential8. Scattering theory of the soliton lattice -- 8.1. Elemental waves -- 8.2. Scattering theory : dissipation, reflection, and transmission -- 8.3. Method of inv…
"Version: 202203"--Title page verso.Includes bibliographical references.10. Partial differential equations -- 10.1. Partial differential equations in physics -- 10.2. Finite difference method for solving ordinary differential equations -- 10.3. Finite difference method for solving PDEs -- 10.4. A finite difference method for PDEs involving both spatial and temporal derivatives11. Nonlinear dyna…
"Version: 202111"--Title page verso.Includes bibliographical references.1. Path integral approach -- 1.1. Path integral -- 1.2. Path integral in quantum field theory -- 1.3. Spin -- 1.4. Path integral and statistical mechanics -- 1.5. Fermion path integral2. Topology and vector spaces -- 2.1. Topological spaces -- 2.2. Group theory -- 2.3. Cocycle -- 2.4. Vector spaces -- 2.5. Linear maps -- 2.…
"Version: 20240201"--Title page verso.Includes bibliographical references.1. Manifolds -- 1.1. What is a manifold? -- 1.2. Curves and surfaces in a manifold -- 1.3. Coordinate transformations and summation convention -- 1.4. The local geometry of a manifold -- 1.5. Length, area, and volume -- 1.6. Local Cartesian coordinates and tangent space -- 1.7. The signature of a manifold -- 1.8. N-dimens…
"Version: 20240101"--Title page verso.Includes bibliographical references.1. Introduction -- 1.1. Singularity -- 1.2. Singularities in science and engineering -- 1.3. Acoustic vortex -- 1.4. Singularities in optics -- 1.5. Amplitude, phase and polarization -- 1.6. Brief historical account of optical phase singularities2. Topological features -- 2.1. Introduction -- 2.2. Wavefront shape -- 2.3. …
"Version: 20221201"--Title page verso.Includes bibliographical references.1. Formulas for the sums of the series of reciprocals of the cubic polynomials with integer roots, at least one zero / Radovan Pot?euc?eek -- 2. Polynomials for meshless methods in finding solutions in gradient elasticity problems / N. Fantuzzi, S. Saitta, F. Fabbrocino, R. Vescovini and R. Luciano -- 3. Numerical solutio…
"Version: 20230801"--Title page verso.Includes bibliographical references.1. The static behavior of functionally graded beams / Sahmani Saeid and Safaei Babak -- 2. The static behavior of functionally graded sandwich beams / Akgo?z Bekir and Civalek ?Omer -- 3. The static behavior of functionally graded plates / Shahriar Dastjerdi and Bekir Akgo?z -- 4. The static bending analysis of porous fun…