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- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/01%3A_Basics/1.01%3A_TerminologyThis page discusses the structure of mathematics, emphasizing the importance of proofs and fundamental categories like undefined terms, defined terms, axioms, and theorems. Undefined terms prevent inf...This page discusses the structure of mathematics, emphasizing the importance of proofs and fundamental categories like undefined terms, defined terms, axioms, and theorems. Undefined terms prevent infinite definitions, while defined terms rely on these and established definitions. Axioms are unproven statements serving as a foundation for deriving new statements. Mastering these concepts is essential for solving mathematical problems.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.07%3A_Existence_and_Uniqueness_of_Solutions_of_Nonlinear_EquationsAlthough there are methods for solving some nonlinear equations, it is impossible to find useful formulas for the solutions of most. Whether we are looking for exact solutions or numerical approximati...Although there are methods for solving some nonlinear equations, it is impossible to find useful formulas for the solutions of most. Whether we are looking for exact solutions or numerical approximations, it is useful to know conditions that imply the existence and uniqueness of solutions of initial value problems for nonlinear equations. In this section we state such a condition and illustrate it with examples.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_IV%3A_Multivariable_Calculus/01%3A_Differentiation_of_Functions_of_Several_Variables/1.02%3A_Limits_and_ContinuityWe have now examined functions of more than one variable and seen how to graph them. In this section, we see how to take the limit of a function of more than one variable, and what it means for a func...We have now examined functions of more than one variable and seen how to graph them. In this section, we see how to take the limit of a function of more than one variable, and what it means for a function of more than one variable to be continuous at a point in its domain. It turns out these concepts have aspects that just don’t occur with functions of one variable.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/00%3A_Front_Matter/05%3A_8.1%3A_OverviewThis page is a textbook on linear algebra that integrates algebra and geometry, focusing on solving matrix equations and eigenvalue problems. It includes practical applications in various fields like ...This page is a textbook on linear algebra that integrates algebra and geometry, focusing on solving matrix equations and eigenvalue problems. It includes practical applications in various fields like engineering and biology, and discusses measurement errors in systems of equations. The text is structured for Math 1553 at Georgia Tech, featuring key concepts, algorithms, and interactive demos for enhanced learning.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/05%3A_Linear_Transformations/5.01%3A_Linear_TransformationsIn this section we will consider how matrix multiplication transforms vectors while preserving vector addition and scalar multiplication. Such transformations are called linear transformations.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/04%3A_R/4.05%3A_Linear_IndependenceThis section discusses the linear dependence and independence between vectors.
