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- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/03%3A_Higher_order_linear_ODEs/3.02%3A_The_Method_of_Undetermined_Coefficients_IThis section present the method of undetermined coefficients, which can be used to solve nonhomogeneous equations of the form ay''+by'+cy=F(x) where a, b, and c are constants and F(x) has a special ...This section present the method of undetermined coefficients, which can be used to solve nonhomogeneous equations of the form ay''+by'+cy=F(x) where a, b, and c are constants and F(x) has a special form that is still sufficiently general to occur in many applications. This sections makes extensive use of the idea of variation of parameters introduced previously.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Contemporary_Mathematics_(OpenStax)/05%3A__Algebra/5.01%3A__Algebraic_ExpressionsThis page focuses on algebraic expressions and equations, detailing how to translate between written and symbolic forms, and explaining operations such as addition, subtraction, multiplication, and di...This page focuses on algebraic expressions and equations, detailing how to translate between written and symbolic forms, and explaining operations such as addition, subtraction, multiplication, and division. It provides examples of expressions versus equations, demonstrates the importance of the order of operations (PEMDAS), and introduces historical context about the symbols used in algebra. Exercises are given for practice, both in translating expressions and performing algebraic operations.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/03%3A_Higher_order_linear_ODEs/3.06%3A_Reduction_of_OrderThis section deals with reduction of order, a technique based on the idea of variation of parameters, which enables us to find the general solution of a nonhomogeneous linear second order equation p...This section deals with reduction of order, a technique based on the idea of variation of parameters, which enables us to find the general solution of a nonhomogeneous linear second order equation provided that we know one nontrivial (not identically zero) solution of the associated homogeneous equation.
- 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.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/04%3A_Power_series_methodsThis page explores power series as solutions to differential equations, covering definitions and series solutions around ordinary points, as well as addressing singular points using the Frobenius meth...This page explores power series as solutions to differential equations, covering definitions and series solutions around ordinary points, as well as addressing singular points using the Frobenius method. It notes that certain singular points may allow power series solutions, while others may necessitate alternative methods. Exercises are provided for practice.
