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- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_Theory/6.05%3A_Markov_MatricesIn this section we look at a particular kind of matrix, called a Markov matrix, and consider some its applications.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_TheoryThis page discusses Eigenvalues and Eigenvectors in Spectral Theory, covering special matrices, diagonalization, applications, Markov matrices, dynamical systems, orthogonal diagonalization, singular ...This page discusses Eigenvalues and Eigenvectors in Spectral Theory, covering special matrices, diagonalization, applications, Markov matrices, dynamical systems, orthogonal diagonalization, singular value decomposition, special factorizations, and quadratic forms. It includes exercises for practice to enhance understanding of both theoretical and practical aspects of these concepts.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.09%3A_Calculus_of_the_Hyperbolic_FunctionsThis page discusses differentiation and integration of hyperbolic functions and their inverses, emphasizing their calculus applications, particularly in modeling catenary curves. Key objectives includ...This page discusses differentiation and integration of hyperbolic functions and their inverses, emphasizing their calculus applications, particularly in modeling catenary curves. Key objectives include understanding derivatives, integrals, and their respective formulas for hyperbolic functions, as well as domain considerations for inverse functions. The text provides examples, exercises, and instructions for evaluating integrals using \(u\)-substitution.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/00%3A_Front_Matter/05%3A_About_the_BookFrom understanding the rate of change to calculating areas and volumes of irregular shapes, this book encourages learners to explore the richness of Calculus in various fields, including physics, econ...From understanding the rate of change to calculating areas and volumes of irregular shapes, this book encourages learners to explore the richness of Calculus in various fields, including physics, economics, and engineering. The online version of the textbook includes 3D figures which gives a three-dimensional visual experience to the learner to understand the concept.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.03%3A_Integrals_as_SolutionsThis page discusses solving first-order ordinary differential equations (ODEs) using integration, detailing the standard form and methods for general solutions. It differentiates between indefinite an...This page discusses solving first-order ordinary differential equations (ODEs) using integration, detailing the standard form and methods for general solutions. It differentiates between indefinite and definite integrals, supplemented by examples illustrating ODE applications in mechanics. Additionally, it provides two calculus problems involving a car's speed and acceleration, showcasing how to calculate distance through integration over specified time intervals.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.09%3A_Autonomous_EquationsThis page analyzes autonomous differential equations focusing on dependent variable dynamics, using examples like Newton's law of cooling and the logistic equation to discuss critical points and their...This page analyzes autonomous differential equations focusing on dependent variable dynamics, using examples like Newton's law of cooling and the logistic equation to discuss critical points and their stability. It emphasizes the importance of critical points in population dynamics, illustrating how parameter variations affect outcomes, including extinction or stabilization.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/00%3A_Front_Matter/04%3A_About_the_BookThe study of the slope of the tangent lines is not limited to functions, but also includes implicitly and parametrically defined curves. From understanding the essence of differential and integral cal...The study of the slope of the tangent lines is not limited to functions, but also includes implicitly and parametrically defined curves. From understanding the essence of differential and integral calculus in one variable, to constructing and using Taylor series, to studying vector calculus and its applications, this textbook series encourages learners to explore the richness of Calculus in various fields, including physics, economics, and engineering.
- https://math.libretexts.org/Courses/Stanford_Online_High_School/Logic_for_All%3A_An_Introduction_to_Logical_Reasoning/03%3A_Propositional_LogicThis page discusses propositional logic, emphasizing its importance in structuring reasoning through propositions with defined truth values. It covers logical connectives, including negation, conjunct...This page discusses propositional logic, emphasizing its importance in structuring reasoning through propositions with defined truth values. It covers logical connectives, including negation, conjunction, and disjunction, and introduces the exclusive or (XOR), discussing the role of parentheses and precedence. The text highlights practical applications in fields like computer science and law, addresses common misconceptions, and provides exercises for better understanding.
