The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes, Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation, with an extensive treatment of local spline interpolation, and its application in quadrature. Exercises are provided at the end of each chapter

Prevalent in animation movies and interactive games, subdivision methods allow users to design and implement simple but efficient schemes for rendering curves and surfaces. Adding to the current subdivision toolbox, Wavelet Subdivision Methods: GEMS for Rendering Curves and Surfaces introduces geometry editing and manipulation schemes (GEMS) and covers both subdivision and wavelet analysis for generating and editing parametric curves and surfaces of desirable geometric shapes. The authors develop a complete constructive theory and effective algorithms to derive synthesis wavelets with minimum support and any desirable order of vanishing moments, along with decomposition filters. Through numerous examples, the book shows how to represent curves and construct convergent subdivision schemes. It comprehensively details subdivision schemes for parametric curve rendering, offering complete algorithms for implementation and theoretical development as well as detailed examples of the most commonly used schemes for rendering both open and closed curves. It also develops an existence and regularity theory for the interpolatory scaling function and extends cardinal B-splines to box splines for surface subdivision. Keeping mathematical derivations at an elementary level without sacrificing mathematical rigor, this book shows how to apply bottom-up wavelet algorithms to curve and surface editing. It offers an accessible approach to subdivision methods that integrates the techniques and algorithms of bottom-up wavelets.

 

What can a life-or-death adventure expedition teach you about leading a successful team or business? How does the act of navigating through Africa's untamed landscapes relate to steering your way through the boardrooms of today's corporate jungles? In this groundbreaking book by Johan de Villiers, you'll explore the astonishing parallels between adventurous escapades and business leadership.

In a captivating narrative that flits between crocodile-infested waters, treacherous treks in Nepal, scaling some of the world's highest mountains, and high-stakes corporate decision-making, Johan deftly explores key concepts like risk management, adaptability, and team dynamics. With wit, wisdom, and an adventurer's heart, he goes beyond traditional business manuals and travelogues, offering unique perspectives on leadership and personal development. Drawing on principles from Jeff Bezos' Day 1 philosophy to Sun Tzu's Art of War, from Stoicism to Ray Dalio's Radical Truth, and his own experiences as a helicopter pilot, Johan offers the reader a philosophical compass to navigate both the unpredictable wilderness and the complex corporate realm.

But this is more than a gripping collection of stories and invaluable business strategies - it's a comprehensive guidebook for life enriched with Johan's audacious experiences. Whether you're a thrill seeker, a solo entrepreneur or a seasoned executive in a large corporation, this book is an indispensable guide to mastering life's complexities through a lens of limitless possibilities.

Perfect for the adventurer in a suit or the CEO in hiking boots, Overlanding Through the Boardroom proves that the greatest risks often yield the most rewarding views. It's your essential toolkit for mastering the art of decision-making, resilience, and adaptability in any environment and a must-read for anyone who believes that life, like business, is the ultimate adventure.

 

Table of Contents:CHAPTER 1 The Principles of Overlanding and Their Application to Business SuccessCHAPTER 2 Lessons from A Heli Pilot and the Swiss Cheese EffectCHAPTER 3 The Dunning-Kruger EffectCHAPTER 4 Black Swan EventsCHAPTER 5 The Psychology of Sales and the Importance of Team SelectionCHAPTER 6 Importance vs UrgencyCHAPTER 7 The Age of Acceleration: How to Prepare for the Fourth Industrial RevolutionCHAPTER 8 Volume vs Value in BusinessCHAPTER 9 The Art of WarCHAPTER 10 Avoiding Day 2CHAPTER 11 Applying Stoicism in Your LifeCHAPTER 12 Ray Dalio's PrinciplesCHAPTER 13 The Power of AdaptationCHAPTER 14 Disruptive InnovationAPPENDIX Overlanding Techniques – In Case You Ever Need Them

The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula ; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter