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Animating Calculus is designed to help you explore calculus and visualize concepts through the use of computation and animation. This collection of 22 labs, together with the computer algebra system Mathematica, can be used for self-study, demonstration, or as a laboratory supplement to an existing calculus sequence. Standard calculus topics as well as new and unusual extensions and applications are presented, including derivatives and rate of change, calculus and landing airplanes, population dynamics and iteration, the fundamental theorem, The Buffon needle problem, numerical and symbolic integration, rolling wheels (round and square), subtleties of the harmonic series, and more. Animating Calculus includes exercises and demonstrations that focus on important and fundamental ideas and applications rather than the everyday mechanics of a computer algebra system. Sophisticated animations are used to clarify geometric concepts in calculus. In addition, discussions of numerical and graphical pitfalls help the student to understand the importance of verifying results. Originally published by W. H. Freeman, this new TELOS edition of Animating Calculus includes the full set of labs for DOS/Windows as well as Macintosh platforms.
Applies the principles of process philosophy and Deleuzian film aesthetics to animation as a genre and medium.
This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Aristotle to today's million-dollar reward that awaits whoever cracks Reimann's hypothesis. Filled with idiosyncratic characters from Pythagoras to Euler, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilization, including science, politics, ethics, philosophy, and much besides.
- This updated version of Animation Maths is an accessible and practical guide to animation programming This updated version of Animation Maths is an accessible and practical guide to animation programming. It opens with arithmetic, solving systems and trigonometry fundamentals, then guides the reader through standard topics such as real functions, the relevant golden section, coordinate systems and vectors. All the subsequent topics are programming oriented and calculus-free and have been selected to add efficiency to your games and animations. In addition to programmable kinematics, Animation Maths offers collision detection, the parametric equations of lines and planes in 3D, and matrices, which are covered in great detail. On its extension to complex numbers, Animation Maths shows the abilities of quaternions as superior 3D rotators.
The internationally bestselling authors of The Cartoon Introduction to Economics return to make calculus fun The award-winning illustrator Grady Klein has teamed up once again with the world’s only stand-up economist, Yoram Bauman, Ph.D., to take on the daunting subject of calculus. A supplement to traditional textbooks, The Cartoon Introduction to Calculus focuses on the big ideas rather than all the formulas you have to memorize. With Klein and Bauman as our guides, we scale the dual peaks of Mount Derivative and Mount Integral, and from their summits, we see how calculus relates to the rest of mathematics. Beginning with the problems of speed and area, Klein and Bauman show how the discipline is unified by a fundamental theorem. We meet geniuses like Archimedes, Liu Hui, and Bonaventura Cavalieri, who survived the slopes on intuition but prepared us for the avalanche-like dangers posed by mathematical rigor. Then we trek onward and scramble through limits and extreme values, optimization and integration, and learn how calculus can be applied to economics, physics, and so much more. We discover that calculus isn’t the pinnacle of mathematics after all, but its tools are foundational to everything that follows. Klein and Bauman round out the book with a handy glossary of symbols and terms, so you don’t have to worry about mixing up constants and constraints. With a witty and engaging narrative full of jokes and insights, The Cartoon Introduction to Calculus is an essential primer for students or for anyone who is curious about math.
Physics for Flash Games, Animation, and Simulations teaches ActionScript programmers how to incorporate real physics into their Flash animations, games, user interfaces, and simulations. Introduces Flash physics in an accurate, but approachable way, covering what is required to produce physically realistic simulations (as opposed to animations that look roughly right) Packed full of practical examples of how physics can be applied to your own games and applications Addresses the diverse needs of game developers, animators, artists, and e-learning developers The book assumes a basic knowledge of ActionScript and Flash. However, no previous knowledge of physics is required—only some very basic math skills. The authors present everything from basic principles to advanced concepts, so you'll be able to follow the logic and easily adapt the principles to your own applications. The book builds on your physics knowledge, enabling you to create not only visual effects, but also more complex models and simulations.
A high-school mathematics teacher who learned how to sequence and present ideas during his 30-year career presents a bridge for beginning calculus students to study independently in preparation for a traditional calculus curriculum or as supplemental material for students who are currently in a calculus class.
A complete—and completely enjoyable—new illustrated guide to calculus Master cartoonist Larry Gonick has already given readers the history of the world in cartoon form. Now, Gonick, a Harvard-trained mathematician, offers a comprehensive and up-to-date illustrated course in first-year calculus that demystifies the world of functions, limits, derivatives, and integrals. Using clear and helpful graphics—and delightful humor to lighten what is frequently a tough subject—he teaches all of the essentials, with numerous examples and problem sets. For the curious and confused alike, The Cartoon Guide to Calculus is the perfect combination of entertainment and education—a valuable supplement for any student, teacher, parent, or professional.
John Funge introduces a new approach to creating autonomous characters. Cognitive modeling provides computer-animated characters with logic, reasoning, and planning skills. Individual chapters in the book provide concrete examples of advanced character animation, automated cinematography, and a real-time computer game. Source code, animations, imag
Have you ever wanted to include believable physical behaviors in your games and projects to give them that extra edge? Physics for JavaScript Games, Animation, and Simulations teaches you how to incorporate real physics, such as gravity, friction, and buoyancy, into your HTML5 games, animations, and simulations. It also includes more advanced topics, such as particle systems, which are essential for creating effects such as sparks or smoke. The book also addresses the key issue of balancing accuracy and simplicity in your games and simulations, and the final chapters provide you with the information and the code to make the right choice for your project. Physics for JavaScript Games, Animation, and Simulations assumes you have a basic knowledge of JavaScript and HTML5. However, no previous knowledge of physics is required—only some very basic math skills. The authors present everything from basic principles to advanced concepts in an approachable way, so you’ll be able to follow the logic and easily adapt the principles to your own applications. The book is packed full of practical examples of how you can apply physics to your own games and applications. Spring behaviors can be used for anything from tweaking lowrider suspension to creating cloth simulation; flotation mechanics enable the simulation of submersibles or dirigibles; you can even create your own solar system with accurate orbits and gravity. It doesn’t matter if you’re modeling the Lorentz force in an electromagnetic field or you’re modeling the lift force in a flight simulator, Physics for JavaScript Games, Animation, and Simulations enables you to fill your games and applications with accurate and realistic effects.