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Introduction to SAGE Programming : With Applications to SAGE Interacts for Numerical Methods (Hardcover)
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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.