Confused about the various concepts on Differentiation Techniques taught in school or simply want more practice questions? This book on Differentiation Techniques seeks to offer a condensed version of what you need to know for your journey in IB Mathematics (SL), alongside with detailed worked examples and extra practice questions. Tips on certain question types are provided to aid in smoothing the working process when dealing with them.

Confused about the various concepts on Applications of Differentiation taught in school or simply want more practice questions? This book on Sequences and Series seeks to offer a condensed version of what you need to know for your journey in IB Mathematics (SL), alongside with detailed worked examples and extra practice questions. Tips on certain question types are provided to aid in smoothing the working process when dealing with them.

Confused about the various concepts on Integration Techniques taught in school or simply want more practice questions? This book on Integration Techniques seeks to offer a condensed version of what you need to know for your journey in IB Mathematics (SL), alongside with detailed worked examples and extra practice questions. Tips on certain question types are provided to aid in smoothing the working process when dealing with them.

Differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas. In general, the parameters, variables and initial conditions within a model are considered as being defined exactly. In reality there may be only vague, imprecise or incomplete information about the variables and parameters available. This can result from errors in measurement, observation, or experimental data; application of different operating conditions; or maintenance induced errors. To overcome uncertainties or lack of precision, one can use a fuzzy environment in parameters, variables and initial conditions in place of exact (fixed) ones, by turning general differential equations into Fuzzy Differential Equations ("FDEs"). In real applications it can be complicated to obtain exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic, creating the need for use of reliable and efficient numerical techniques in the solution of fuzzy differential equations. These include fuzzy ordinary and partial, fuzzy linear and nonlinear, and fuzzy arbitrary order differential equations. This unique work provides a new direction for the reader in the use of basic concepts of fuzzy differential equations, solutions and its applications. It can serve as an essential reference work for students, scholars, practitioners, researchers and academicians in engineering and science who need to model uncertain physical problems.

This book takes a fresh look at programs for advanced studies for high school students in the United States, with a particular focus on the Advanced Placement and the International Baccalaureate programs, and asks how advanced studies can be significantly improved in general. It also examines two of the core issues surrounding these programs: they can have a profound impact on other components of the education system and participation in the programs has become key to admission at selective institutions of higher education. By looking at what could enhance the quality of high school advanced study programs as well as what precedes and comes after these programs, this report provides teachers, parents, curriculum developers, administrators, college science and mathematics faculty, and the educational research community with a detailed assessment that can be used to guide change within advanced study programs.

Vols. for 1963- include as pt. 2 of the Jan. issue: Medical subject headings.

Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.