"Version: 20190601"--Title page verso.Includes bibliographical references and index.1. Forms of quantum mechanics -- 1.1. The Schr?odinger and Heisenberg pictures -- 1.2. Interaction picture -- 1.3. Density-matrix formulation of quantum mechanics -- 1.4. Further contents of Heisenberg's commutation relations2. Lorentz group and its representations -- 2.1. Lie algebra of the Lorentz group -- 2.2…
"Version: 20181101"--Title page verso.Includes bibliographical references.1. Linear and perturbed equations -- 1.1. Stability analysis -- 1.2. Lyapunov regularity2. Nonlinear differential equations -- 2.1. Continuous dependence and stability of solutions -- 2.2. Orbital Hausdorff dependence of the solutions -- 2.3. Differentiability of solutions3. Semilinear evolution equations -- 3.1. First-or…
"Version: 20181201"--Title page verso.Includes bibliographical references.1. Synopsis of general relativity -- 2. Curves and surfaces in E3 -- 3. Elements of topology -- 4. Differentiable manifolds -- 5. Tangent vectors and tangent spaces -- 6. Tensor algebra -- 7. Tensor fields and commutators -- 8. Differential forms and exterior calculus -- 9. Maps between manifolds -- 10. Integration on man…
"Version: 20191101"--Title page verso.Includes bibliographical references.1. Introduction -- 2. Fundamental nonlinear Schr?odinger equation -- 2.1. NLSE with cubic nonlinearity -- 2.2. Summary of subsection 2.1.1 -- 2.3. Summary of subsection 2.2.13. Nonlinear Schr?odinger equation with power law and dual power law nonlinearities -- 3.1. NLSE with power law nonlinearity -- 3.2. Summary of secti…
"Version: 20200901"--Title page verso.Includes bibliographical references.1. What is computation? -- 1.1. Defining computation -- 1.2. The roles of computation in scientific research -- 1.3. Analog computing -- 1.4. Further reading2. Computation in science -- 2.1. Traditional science : celestial mechanics -- 2.2. Scientific models and computation -- 2.3. Computation at the interface between obs…
"Version: 20151201"--Title page verso.Includes bibliographical references.Preface -- 1. Introduction -- 1.1. A brief history of embedding -- 1.2. Overview -- 1.3. A note on Green functions -- 1.4. Units2. The variational embedding method -- 2.1. The variational principle -- 2.2. The embedded Schr?odinger equation -- 2.3. A first application -- 2.4. The embedded Green function -- 2.5. Applicatio…
"Version: 20161201"--Title page verso.Includes bibliographical references.Preface -- 1. Introduction -- part I. Mathematical theory of composite materials2. Material properties and governing equations -- 2.1. Introduction -- 2.2. Conductivity and elasticity -- 2.3. Abstract Hilbert space framework -- 2.4. Boundary value problems -- 2.5. Geometry of local spaces3. Composite materials -- 3.1. Mat…
"Version: 20150101"--Title page verso.Includes bibliographical references.Preface -- Author biography -- Introduction : bringing together Darwinian evolution and games -- Transmission, development, selection : the Price equation and the role of games -- Extensive-form games : from genomes to genes -- Symmetry and collective fluctuations : large deviations and scaling in population processes -- …
"Version: 20180501"--Title page verso.Includes bibliographical references.1. Introduction -- 2. Background and definitions -- 2.1. Classical mechanics -- 2.2. Quantum mechanics -- 2.3. Integrability and superintegrability3. Separation of variables -- 3.1. Some approaches to separability -- 3.2. The Levi-Civita procedure -- 3.3. Nonorthogonal separation : examples -- 3.4. Intrinsic characterizat…