This book (plus free online edition) provides comprehensive, realistic exam practice in the style of the Higher Level Edexcel A & B GCSE Maths papers. There's a wide range of questions covering the whole course, with grades to indicate the difficulty level and helpful tips and guidance throughout. Detailed worked solutions are printed at the back of the book, with a complete mark scheme that makes it easy to check your progress. At the end of the book, there are two complete practice exams - and if you're stuck, you can watch online videos of CGP's Maths experts working through these exams. Last but not least, a free online digital edition of the entire book is also included - just use the unique code printed in the book to access it.
This book focuses on the nonlinear behaviour of thin-wall shells (single- and multilayered with delamination areas) under various uniform and non-uniform loadings.
This book is devoted to new methods of control for complex dynamical systems and deals with nonlinear control systems having several degrees of freedom, subjected to unknown disturbances, and containing uncertain parameters. Various constraints are imposed on control inputs and state variables or their combinations. The book contains an introduction to the theory of optimal control and the theory of stability of motion, and also a description of some known methods based on these theories. Major attention is given to new methods of control developed by the authors over the last 15 years. Mechanical and electromechanical systems described by nonlinear Lagrange's equations are considered. General methods are proposed for an effective construction of the required control, often in an explicit form. The book contains various techniques including the decomposition of nonlinear control systems with many degrees of freedom, piecewise linear feedback control based on Lyapunov's functions, methods which elaborate and extend the approaches of the conventional control theory, optimal control, differential games, and the theory of stability. The distinctive feature of the methods developed in the book is that the c- trols obtained satisfy the imposed constraints and steer the dynamical system to a prescribed terminal state in ?nite time. Explicit upper estimates for the time of the process are given. In all cases, the control algorithms and the estimates obtained are strictly proven.