Computer Algebra Recipes: An Introductory Guide to the Mathematical Models of Science

Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models. Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry. The topics are organized into the Appetizers dealing with graphical aspects, the Entrees concentrating on symbolic computation, and the Desserts illustrating numerical simulation. The heart of the text is a large number of computer algebra recipes based on the Maple 10 software system. These have been designed not only to provide tools for problem solving, but also to stimulate the reader’s imagination. Associated with each recipe is a scientific model or method and an interesting or amusing story (accompanied with a thought-provoking quote) that leads the reader through the various steps of the recipe. The recipes are also included on the CD-ROM enclosed with the book. Each section of recipes is followed by a set of problems that readers can use to check their understanding or to develop the topic further. This text is the first of two volumes, the advanced guide, aimed at junior/senior/graduate level students, dealing with more advanced differential equation models. Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models.Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry. The topics are organized into the Appetizers dealing with graphical aspects, the Entrees concentrating on symbolic computation, and the Desserts illustrating numerical simulation.The heart of the text is a large number of computer algebra recipes based on the Maple 10 software system. These have been designed not only to provide tools for problem solving, but also to stimulate the reader's imagination. Associated with each recipe is a scientific model or method and an interesting or amusing story (accompanied with a thought-provoking quote) that leads the reader through the various steps of the recipe. The recipes are also included on the CD-ROM enclosed with the book. Each section of recipes is followed by a set of problems that readers can use to check their understanding or to develop the topic further.This text is the first of two volumes. The advanced guide, aimed at junior/senior/graduate level students, deals with more advanced differential equation models.

computer Algebra Systems Have The Potential To Revolutionize The Teaching Of And Learning Of Science. Not Only Can Students Work Thorough Mathematical Models Much More Efficiently And With Fewer Errors Than With Pencil And Paper, They Can Also Work With Much More Complex And Computationally Intensive Models. Thus, For Example, In Studying The Flight Of A Golf Ball, Students Can Begin With The Simple Parabolic Trajectory, But Then Add The Effects Of Lift And Drag, Of Winds, And Of Spin. Not Only Can The Program Provide Analytic Solutions In Some Cases, It Can Also Produce Numerical Solutions And Graphic Displays.
aimed At Undergraduates In Their Second Or Third Year, This Book Is Filled With Examples From A Wide Variety Of Disciplines, Including Biology, Economics, Medicine, Engineering, Game Theory, Physics, Chemistry. The Text Is Organized Along A Spiral, Revisiting General Topics Such As Graphics, Symbolic Computation, And Numerical Simulation In Greater Detail And More Depth At Each Turn Of The Spiral.
the Heart Of The Text Is A Large Number Of Computer Algebra Recipes. These Have Been Designed Not Only To Provide Tools For Problem Solving, But Also To Stimulate The Reader's Imagination. Associated With Each Recipe Is A Scientific Model Or Method And A Story That Leads The Reader Through Steps Of The Recipe. The Recipes Are Also Included On The Cd-rom Enclosed With The Book. Each Section Of Recipes Is Followed By A Set Of Problems That Readers Can Use To Check Their Understanding Or To Develop The Topic Further.

Computer algebra systems have the potential to revolutionize the teaching of and learning of science. Not only can students work thorough mathematical models much more efficiently and with fewer errors than with pencil and paper, they can also work with much more complex and computationally intensive models. Thus, for example, in studying the flight of a golf ball, students can begin with the simple parabolic trajectory, but then add the effects of lift and drag, of winds, and of spin. Not only can the program provide analytic solutions in some cases, it can also produce numerical solutions and graphic displays. Aimed at undergraduates in their second or third year, this book is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, physics, chemistry. The text is organized along a spiral, revisiting general topics such as graphics, symbolic computation, and numerical simulation in greater detail and more depth at each turn of the spiral. The heart of the text is a large number of computer algebra recipes. These have been designed not only to provide tools for problem solving, but also to stimulate the reader's imagination. Associated with each recipe is a scientific model or method and a story that leads the reader through steps of the recipe. Each section of recipes is followed by a set of problems that readers can use to check their understanding or to develop the topic further. Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models. Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry. The topics are organized into the Appetizers dealing with graphical aspects, the Entrees concentrating on symbolic computation, and the Desserts illustrating numerical simulation. The heart of the text is a large number of computer algebra recipes based on the Maple 10 software system. These have been designed not only to provide tools for problem solving, but also to stimulate the reader’s imagination. Associated with each recipe is a scientific model or method and an interesting or amusing story (accompanied with a thought-provoking quote) that leads the reader through the various steps of the recipe. This text is the first of two volumes. The advanced guide, aimed at junior/senior/graduate level students, deals with more advanced differential equation models. The heart of the text is a large number of computer algebra recipes based on the Maple 10 software system. These have been designed not only to provide tools for problem solving, but also to stimulate the reader7F 19s imagination. Associated with each recipe is a scientific model or method and an interesting or amusing story (accompanied with a thought-provoking quote) that leads the reader through the various steps of the recipe. The recipes are also included on the CD-ROM enclosed with the book. Each section of recipes is followed by a set of problems that readers can use to check their understanding or to develop the topic further. This text is the first of two volumes, the advanced guide, aimed at junior/senior/graduate level students, dealing with more advanced differential equation models."--Publisher's website Aimed at undergraduates in their second or third year, this book is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, physics, chemistry. The text is organized along a spiral, revisiting general topics such as graphics, symbolic computation, and numerical simulation in greater detail and more depth at each turn of the spiral. The heart of the text is a large number of computer algebra recipes. These have been designed not only to provide tools for problem solving, but also to stimulate the reader's imagination. Associated with each recipe is a scientific model or method and a story that leads the reader through steps of the recipe. The recipes are also included on the CD-ROM enclosed with the book Introduction....Pages 1-10 Front Matter....Pages 11-11 The Pictures of Science....Pages 13-64 Deriving Model Equations....Pages 65-117 Front Matter....Pages 119-119 Algebraic Models. Part I....Pages 121-172 Algebraic Models. Part II....Pages 173-212 Linear ODE Models....Pages 213-270 Difference Equation Models....Pages 271-316 Front Matter....Pages 317-317 Monte Carlo Methods....Pages 319-380 Fractal Patterns....Pages 381-416 Computer algebra systems allow students to work on mathematical models more efficiently than in the case of pencil and paper. Aimed at undergraduates in their second or third year, this book is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, physics, and chemistry. Although modern scientific models are usually not difficult to qualitatively understand, the task of deriving the relevant model equations and finding, visualizing, and interpreting the associated solutions may be too demanding or too tedious to realistically carry out without the aid of a computer.