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- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/2%3A_Higher_order_linear_ODEs/2.6%3A_Forced_Oscillations_and_ResonanceLet us consider to the example of a mass on a spring. We now examine the case of forced oscillations, which we did not yet handle.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/Appendix_A%3A_Linear_Algebra/A.2%3A_Matrix_AlgebraThis page provides a comprehensive overview of matrices, covering one-by-one matrices, matrix addition, scalar multiplication, matrix multiplication, and properties of matrices. It explains the operat...This page provides a comprehensive overview of matrices, covering one-by-one matrices, matrix addition, scalar multiplication, matrix multiplication, and properties of matrices. It explains the operations related to matrices such as adding and multiplying matrices and scalars, including special cases like identity matrices and inverse matrices. The concept of transpose is also introduced, with examples demonstrating how swapping rows and columns affects matrix multiplication.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/4%3A_Fourier_series_and_PDEs/4.02%3A_The_trigonometric_seriesThe document discusses the concept of periodic functions, focusing on Fourier series as a method to solve differential equations with periodic inputs. It provides a step-by-step explanation of how to ...The document discusses the concept of periodic functions, focusing on Fourier series as a method to solve differential equations with periodic inputs. It provides a step-by-step explanation of how to decompose a periodic function into a sum of sine and cosine terms, leveraging the orthogonality of trigonometric functions to determine expansion coefficients. Examples illustrate how functions like the sawtooth and square wave can be expressed as Fourier series.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/5%3A_Eigenvalue_problemsThe page covers topics related to differential equations, specifically focusing on Sturm-Liouville problems, the application of eigenfunction series, and steady periodic solutions. It is part of a tex...The page covers topics related to differential equations, specifically focusing on Sturm-Liouville problems, the application of eigenfunction series, and steady periodic solutions. It is part of a textbook aimed at engineering students for a one-semester introductory course on differential equations. It includes exercises to supplement learning.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/1%3A_First_order_ODEs/1.8%3A_Exact_EquationsThis page discusses the concept of exact equations in physics and engineering, focusing on the identification and usage of potential functions related to conservation laws, such as the conservation of...This page discusses the concept of exact equations in physics and engineering, focusing on the identification and usage of potential functions related to conservation laws, such as the conservation of energy. It provides a detailed explanation of how to derive exact differential equations from potential functions, solve them, and interpret these solutions in terms of path independence and conservative vector fields.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/1%3A_First_order_ODEs/1.1%3A_Integrals_as_solutionsThis document provides an overview of solving first-order ordinary differential equations (ODEs), particularly when the function f depends only on the variable x. The process involves integrat...This document provides an overview of solving first-order ordinary differential equations (ODEs), particularly when the function f depends only on the variable x. The process involves integrating f(x) to find the general solution, represented as y(x)=∫f(x)dx+C. It discusses the relationship between definite and indefinite integrals and includes methods to solve equations of the form y′=f(y).
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/2%3A_Higher_order_linear_ODEs/2.1%3A_Second_order_linear_ODEsThis page discusses second-order linear differential equations, focusing on the homogeneous case where the written form is y″. Key theorems include the superposition theorem,...This page discusses second-order linear differential equations, focusing on the homogeneous case where the written form is y'' + p(x)y' + q(x)y = 0. Key theorems include the superposition theorem, which allows solutions to be combined linearly, and the existence and uniqueness theorem ensuring a unique solution for given initial conditions.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/zz%3A_Back_Matter/10%3A_Index
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/1%3A_First_order_ODEs/1.9%3A_First_Order_Linear_PDEThe page delves into solving linear first-order partial differential equations (PDEs), focusing on the transport equation where u_t + \alpha u_x = 0. It discusses the use of characteristic curves ...The page delves into solving linear first-order partial differential equations (PDEs), focusing on the transport equation where u_t + \alpha u_x = 0. It discusses the use of characteristic curves to transform PDEs into ordinary differential equations (ODEs), simplifying them for solutions.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/0%3A_IntroductionThis page includes sections on notes, an introduction to differential equations, and their classification, along with related exercises. 'CDATA' blocks seem to contain settings and configuration data ...This page includes sections on notes, an introduction to differential equations, and their classification, along with related exercises. 'CDATA' blocks seem to contain settings and configuration data for a MindTouch platform, which may deal with character count and path removal messages.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/Appendix_A%3A_Linear_Algebra/A.E%3A_Linear_Algebra_(Exercises)This page contains a series of linear algebra exercises, covering topics such as vectors, matrices, linear mappings, and determinants. It provides practice problems on drawing vectors, computing magni...This page contains a series of linear algebra exercises, covering topics such as vectors, matrices, linear mappings, and determinants. It provides practice problems on drawing vectors, computing magnitudes, matrix operations, row reduction, and finding bases for subspaces. It also includes applications of the Gram-Schmidt process for orthogonalization and explores inner product spaces along with projections.
