Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Mathematics majors at Michigan State University take a “Capstone” course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basicwavelettheoryisanaturaltopicforsuchacourse. Byname, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are suf?ciently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity. These are introduced in the ?rst two sections of chapter 1. In the remainder of chapter 1 we review linear algebra. Students should be familiar with the basic de?nitions in sections 1. 3 and 1. 4. From our viewpoint, linear transformations are the primary object of study; v Preface vi a matrix arises as a realization of a linear transformation. Many students may have been exposed to the material on change of basis in section 1. 4, but may bene?t from seeing it again. In section 1.

Algebras, Linear --- Wavelets (Mathematics) --- Algebras, Linear. --- Wavelets (Mathematics). --- 517.518.8 --- 519.65 --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Approximation of functions by polynomials and their generalizations --- Wavelet analysis --- Harmonic analysis --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- 519.65 Approximation. Interpolation --- Approximation. Interpolation --- EPUB-LIV-FT SPRINGER-B --- Global analysis (Mathematics). --- Algebra. --- Numerical analysis. --- Analysis. --- Numerical Analysis. --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematics --- 517.1 Mathematical analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is a book for people interested in solving optimization problems. Because of the wide (and growing) use of optimization in science, engineering, economics, and industry, it is essential for students and practitioners alike to develop an understanding of optimization algorithms. Knowledge of the capabilities and limitations of these algorithms leads to a better understanding of their impact on various applications, and points the way to future research on improving and extending optimization algorithms and software. Our goal in this book is to give a comprehensive description of the most powerful, state-of-the-art, techniques for solving continuous optimization problems. By presenting the motivating ideas for each algorithm, we try to stimulate the reader’s intuition and make the technical details easier to follow. Formal mathematical requirements are kept to a minimum. Because of our focus on continuous problems, we have omitted discussion of important optimization topics such as discrete and stochastic optimization.

519.853 --- 519.65 --- Mathematical optimization --- #TELE:SISTA --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- 519.65 Approximation. Interpolation --- Approximation. Interpolation --- 519.853 Nonlinear programming. Relaxation methods --- Nonlinear programming. Relaxation methods --- Mathematical optimization. --- Numerical methods of optimisation --- Mathematics. --- Operations research. --- Decision making. --- System theory. --- Calculus of variations. --- Calculus of Variations and Optimal Control; Optimization. --- Systems Theory, Control. --- Operation Research/Decision Theory. --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Systems theory. --- Operations Research/Decision Theory. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Systems, Theory of --- Systems science --- Science --- Isoperimetrical problems --- Variations, Calculus of --- Decision making --- Philosophy