Linear Algebra Systems Of Linear Equations
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Ordinary Differential Equations and Linear Algebra
Ordinary differential equations (ODEs) and linear algebra are foundational postcalculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course. Linear algebra is developed first, with an eye toward solving linear systems of ODEs. A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system. Ordinary Differential Equations and Linear Algebra: A Systems Approach systematically develops the linear algebra needed to solve systems of ODEs and includes over 15 distinct applications of the theory, many of which are not typically seen in a textbook at this level (e.g., lead poisoning, SIR models, digital filters). It emphasizes mathematical modeling and contains group projects at the end of each chapter that allow students to more fully explore the interaction between the modeling of a system, the solution of the model, and the resulting physical description.
Iterative Methods for Linear Systems
Iterative Methods for Linear Systems offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.
Linear Algebra: Systems of Linear Equations
"Linear Algebra: Systems of Linear Equations" is an introductory textbook designed for absolute beginners seeking to grasp the fundamental concepts of linear algebra. Through clear explanations, practical examples, and step-by-step guidance, this book demystifies the principles of systems of linear equations, equipping readers with essential skills to analyze and solve real-world problems using matrix operations, vector spaces, and foundational algebraic techniques. Ideal for students and self-learners alike, it aims to foster a deep understanding of linear algebra's relevance and applicability across various disciplines.