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- https://math.libretexts.org/Courses/Coastline_College/Math_C285%3A_Linear_Algebra_and_Diffrential_Equations_(Tran)/15%3A_Fourier_series_and_PDEs/15.01%3A_Boundary_value_problemsBefore we tackle the Fourier series, we need to study the so-called boundary value problems (or endpoint problems).
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/MAT-204%3A_Differential_Equations_for_Science_(Lebl_and_Trench)/06%3A_Fourier_series_and_PDEs/6.01%3A_Boundary_value_problemsBefore we tackle the Fourier series, we need to study the so-called boundary value problems (or endpoint problems).
- https://math.libretexts.org/Bookshelves/Differential_Equations/A_First_Course_in_Differential_Equations_for_Scientists_and_Engineers_(Herman)/06%3A_Linear_Systems/6.04%3A_Eigenvalue_ProblemsWe seek nontrivial solutions to the eigenvalue problem
- https://math.libretexts.org/Courses/Mission_College/Math_4B%3A_Differential_Equations_(Kravets)/08%3A_Boundary_Value_Problems_and_Fourier_Expansions/8.01%3A_Eigenvalue_Problems_for_y''__y__0This section deals with five boundary value problems for the differential equation y'' + λy = 0. They are related to problems in partial differential equations that will be discussed in Chapter 9. We ...This section deals with five boundary value problems for the differential equation y'' + λy = 0. They are related to problems in partial differential equations that will be discussed in Chapter 9. We define what is meant by eigenvalues and eigenfunctions of the boundary value problems, and show that the eigenfunctions have a property called orthogonality.
- https://math.libretexts.org/Courses/Mission_College/Math_4B%3A_Differential_Equations_(Reed)/08%3A_Boundary_Value_Problems_and_Fourier_Expansions/8.01%3A_Eigenvalue_Problems_for_y''__y__0This section deals with five boundary value problems for the differential equation y'' + λy = 0. They are related to problems in partial differential equations that will be discussed in Chapter 9. We ...This section deals with five boundary value problems for the differential equation y'' + λy = 0. They are related to problems in partial differential equations that will be discussed in Chapter 9. We define what is meant by eigenvalues and eigenfunctions of the boundary value problems, and show that the eigenfunctions have a property called orthogonality.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/4%3A_Fourier_series_and_PDEs/4.01%3A_Boundary_value_problemsBefore we tackle the Fourier series, we need to study the so-called boundary value problems (or endpoint problems).
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Numerical_Methods_(Chasnov)/07%3A_Ordinary_Differential_Equations/7.01%3A_Examples_of_Analytical_SolutionsThe differential equation (7.1) is separable, and separating and integrating from time t=0 to t yields ∫qq0dqq=−1RC∫t0dt which can b...The differential equation (7.1) is separable, and separating and integrating from time t=0 to t yields ∫qq0dqq=−1RC∫t0dt which can be integrated and solved for q=q(t) : q(t)=q0e−t/RC. The classic second-order initial value problem is the RLC circuit, with differential equation Ld2qdt2+Rdqdt+qC=0. Here, a charged capacitor is connected to …
- https://math.libretexts.org/Bookshelves/Differential_Equations/Applied_Linear_Algebra_and_Differential_Equations_(Chasnov)/02%3A_II._Linear_Algebra/05%3A_Eigenvalues_and_Eigenvectors/5.01%3A_The_Eigenvalue_ProblemWe can demonstrate how to find the eigenvalues of a general 2-by-2 matrix given by A=(abcd). We have \[\begin{aligned} 0 &=\...We can demonstrate how to find the eigenvalues of a general 2-by-2 matrix given by A=(abcd). We have 0=det(A−λI)=|a−λbcd−λ|=(a−λ)(d−λ)−bc=λ2−(a+d)λ+(ad−bc), which can be more generally written as \[\lambda^{2}-\operatorname{Tr}…
- https://math.libretexts.org/Bookshelves/Differential_Equations/Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)/11%3A_Boundary_Value_Problems_and_Fourier_Expansions/11.01%3A_Eigenvalue_Problems_for_y''__y__0This section deals with five boundary value problems for the differential equation y'' + λy = 0. They are related to problems in partial differential equations that will be discussed in Chapter 12. We...This section deals with five boundary value problems for the differential equation y'' + λy = 0. They are related to problems in partial differential equations that will be discussed in Chapter 12. We define what is meant by eigenvalues and eigenfunctions of the boundary value problems, and show that the eigenfunctions have a property called orthogonality.