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Have you ever cooked a 3-course meal from a recipe? That generally works out pretty well, even if you're not much of a cook. What does this have to do with mathematics? Well, you can solve a lot of math problems recipe-wise, too: Need to solve a Riccati's differential equation or the singular value decomposition of a matrix? Look it up in this book, you'll find a recipe for it here. Recipes are available for problems in the following topics: Calculus in one and more variables, linear algebra, vector analysis, theory on differential equations, ordinary and partial, and complex analysis. We have tried to summarize these recipes as good and also as understandable as possible in this book. It is often said that one must understand higher mathematics in order to be able to apply it. We show in this book that understanding also comes naturally by doing: no one learns the grammar of a language from cover to cover if he wants to learn a language. You learn a language by reading up a bit on the grammar and then getting going; you have to speak, make mistakes, have mistakes pointed out to you, know example sentences and recipes, work out topics in tidbits, then it works. In higher mathematics it is no different. Other features of this book include: The division of calculus and linear algebra into approximately 100 chapters of roughly equal length. Each chapter covers approximately the material of a 90-minute lecture. Numerous examples. Many tasks, the solutions to which can be found in the accompanying workbook. Many problems in calculus and linear algebra can be solved with computers. We always indicate how it works with MATLAB®. Due to the clear presentation, the book can also be used as an annotated collection of formulas with numerous examples. Prof. Dr. Christian Karpfinger teaches at the Technical University of Munich; in 2004 he received the State Teaching Award of the Free State of Bavaria. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com).

Algebra --- Mathematical analysis --- Mathematics --- algebra --- lineaire algebra --- analyse (wiskunde) --- wiskunde --- Algebras, Linear. --- Calculus. --- Differential equations. --- Àlgebra lineal --- Càlcul --- Equacions diferencials

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Building materials. Building technology --- Building design --- Tall buildings --- Architecture --- Building --- Structural design --- Immeubles de grande hauteur --- Constructions --- Design and construction --- Conception et construction --- Calcul --- Engineering --- Civil Engineering

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This book presents new computation schemes for the sensitivity of options using the binomial tree and introduces readers to the discrete Malliavin calculus. It also shows that applications of the discrete Malliavin calculus approach to the binomial tree model offer fundamental tools for computing Greeks. The binomial tree approach is one of the most popular methods in option pricing. Although it is a fairly traditional model for option pricing, it is still widely used in financial institutions since it is tractable and easy to understand. However, the book shows that the tree approach also offers a powerful tool for deriving the Greeks for options. Greeks are quantities that represent the sensitivities of the price of derivative securities with respect to changes in the underlying asset price or parameters. The Malliavin calculus, the stochastic methods of variations, is one of the most popular tools used to derive Greeks. However, it is also very difficult to understand for most students and practitioners because it is based on complex mathematics. To help readers more easily understand the Malliavin calculus, the book introduces the discrete Malliavin calculus, a theory of the functional for the Bernoulli random walk. The discrete Malliavin calculus is significantly easier to understand, because the functional space of the Bernoulli random walk is realized in a finite dimensional space. As such, it makes this valuable tool far more accessible for a broad readership.

Statistical science --- Finance --- Mathematics --- financieel management --- toegepaste wiskunde --- statistiek --- wiskunde --- statistisch onderzoek --- Derivative securities --- Malliavin calculus. --- Càlcul de Malliavin --- Actius financers derivats --- Mathematics.

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Control theory --- Mathematical optimization --- Calculus of variations --- Théorie de la commande --- Optimisation mathématique --- Calcul des variations --- Periodicals. --- Périodiques --- System analysis --- Mathematical analysis --- Analyse de systèmes. --- Calcul des variations. --- Analyse mathématique. --- Calculus of variations. --- Mathematical analysis. --- System analysis. --- Mathematical Sciences --- Physics --- Applied Mathematics --- Geometry --- Mathematical Analysis & Logic --- Mathematical Physics --- Mechanics --- Control theory - Periodicals --- Mathematical optimization - Periodicals --- Calculus of variations - Periodicals

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This textbook, now in its second edition, results from lectures, practical problems, and workshops on Optimal Control, given by the authors at Irkutsk State University, Far Eastern Federal University (both in Vladivostok, Russia), and Kwangwoon University (Seoul, South Korea). In this work, the authors cover the theory of linear and nonlinear systems, touching on the basic problem of establishing the necessary and sufficient conditions of optimal processes. Readers will find two new chapters, with results of potential interest to researchers with a focus on the theory of optimal control, as well as to those interested in applications in Engineering and related sciences. In addition, several improvements have been made through the text. This book is structured in three parts. Part I starts with a gentle introduction to the basic concepts in Optimal Control. In Part II, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of reachability set in the class of piecewise continuous controls and touch on the problems of controllability, observability, identification, performance, and terminal control. Part III, in its turn, is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for problems with mobile ends of trajectories. Problem sets at the end of chapters and a list of additional tasks, provided in the appendix, are offered for students seeking to master the subject. The exercises have been chosen not only as a way to assimilate the theory but also as to induct the application of such knowledge in more advanced problems.

Functional analysis --- Numerical methods of optimisation --- Operational research. Game theory --- analyse (wiskunde) --- systeemtheorie --- wiskunde --- kansrekening --- optimalisatie --- Mathematical optimization. --- Calculus of variations. --- System theory. --- Optimització matemàtica --- Càlcul de variacions --- Teoria de sistemes