Read online Razvan A. Mezei - An Introduction to SAGE Programming : With Applications to Sage Interacts for Numerical Methods DJV, MOBI
9781119122784 English 1119122783 Features a simplified presentation of numerical methods by introducing and implementing SAGE programs "An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods" emphasizes how to implement numerical methods using SAGE Math and SAGE Interacts and also addresses the fundamentals of computer programming, including if statements, loops, functions, and interacts. The book also provides a unique introduction to SAGE and its computer algebra system capabilities, discusses second and higher order equations and estimate limits, and determines derivatives, integrals, and summations. Providing critical resources for developing successful interactive SAGE numerical computations, the book is accessible without delving into the mathematical rigor of numerical methods. The author illustrates the benefits of utilizing the SAGE language for calculus and the numerical analysis of various methods such as bisection methods, numerical integration, Taylor's expansions, and Newton's iterations. Providing an introduction to the terminology and concepts involved, "An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods" features: An introduction to computer programming using SAGE Many practical examples throughout to illustrate the application of SAGE Interacts for various numerical methods Discussions on how to use SAGE Interacts and SAGE Cloud in order to create mathematical demonstrations Numerous homework problems and exercises that allow readers to practice their programming skillset A companion website that includes related SAGE programming code and select solutions to the homework problems and exercises "An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods" is an ideal reference for applied mathematicians who need to employ SAGE for the study of numerical methods and analysis. The book is also an appropriate supplemental textbook for upper-undergraduate and graduate-level courses in numerical methods., This book provides an introduction to programming in SAGE, with an emphasis on how to create SAGE Interacts, for those who are studying numerical analysis. The author does not delve into the mathematical aspects of numerical methods, but rather provides readers with a resource on learning SAGE for their numerical computations and analysis. No prior knowledge of programming languages is needed to learn the benefits of utilizing the SAGE language for calculus and the numerical analysis of various methods, including bisection methods, numerical integration, Taylor's expansions, and Newton's iterations. The author provides an introduction to both the programming language and the terminology involved. Homework exercises and problems are included after each section to allow readers to practice their computational skillset, and all related SAGE codes can be found online for reader convenience. Topical coverage includes: Introduction to SAGE; Using SAGE as a Calculator; Programming in SAGE; and SAGE Interacts for Numerical Analysis. Specific concepts discussed include: Boolean expressions; nonlinear equations such as bisection algorithms, Newton-Raphson algorithms, and combined; numerical differentiation using Taylor series and interpolating polynomials; numerical integration with the Trapezoidal rule, Simpson's rule, and Romberg method; numerical methods for differential equations; and linear and cubic spline interpolation.
9781119122784 English 1119122783 Features a simplified presentation of numerical methods by introducing and implementing SAGE programs "An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods" emphasizes how to implement numerical methods using SAGE Math and SAGE Interacts and also addresses the fundamentals of computer programming, including if statements, loops, functions, and interacts. The book also provides a unique introduction to SAGE and its computer algebra system capabilities, discusses second and higher order equations and estimate limits, and determines derivatives, integrals, and summations. Providing critical resources for developing successful interactive SAGE numerical computations, the book is accessible without delving into the mathematical rigor of numerical methods. The author illustrates the benefits of utilizing the SAGE language for calculus and the numerical analysis of various methods such as bisection methods, numerical integration, Taylor's expansions, and Newton's iterations. Providing an introduction to the terminology and concepts involved, "An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods" features: An introduction to computer programming using SAGE Many practical examples throughout to illustrate the application of SAGE Interacts for various numerical methods Discussions on how to use SAGE Interacts and SAGE Cloud in order to create mathematical demonstrations Numerous homework problems and exercises that allow readers to practice their programming skillset A companion website that includes related SAGE programming code and select solutions to the homework problems and exercises "An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods" is an ideal reference for applied mathematicians who need to employ SAGE for the study of numerical methods and analysis. The book is also an appropriate supplemental textbook for upper-undergraduate and graduate-level courses in numerical methods., This book provides an introduction to programming in SAGE, with an emphasis on how to create SAGE Interacts, for those who are studying numerical analysis. The author does not delve into the mathematical aspects of numerical methods, but rather provides readers with a resource on learning SAGE for their numerical computations and analysis. No prior knowledge of programming languages is needed to learn the benefits of utilizing the SAGE language for calculus and the numerical analysis of various methods, including bisection methods, numerical integration, Taylor's expansions, and Newton's iterations. The author provides an introduction to both the programming language and the terminology involved. Homework exercises and problems are included after each section to allow readers to practice their computational skillset, and all related SAGE codes can be found online for reader convenience. Topical coverage includes: Introduction to SAGE; Using SAGE as a Calculator; Programming in SAGE; and SAGE Interacts for Numerical Analysis. Specific concepts discussed include: Boolean expressions; nonlinear equations such as bisection algorithms, Newton-Raphson algorithms, and combined; numerical differentiation using Taylor series and interpolating polynomials; numerical integration with the Trapezoidal rule, Simpson's rule, and Romberg method; numerical methods for differential equations; and linear and cubic spline interpolation.