Search
- Filter Results
- Location
- Classification
- Include attachments
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/07%3A_Vector_Spaces/7.07%3A_Sums_and_IntersectionsIn this section we discuss sum and intersection of two subspaces.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.11%3A_Exact_EquationsThis page discusses exact differential equations, their solutions, and the concept of potential functions in physics, emphasizing the total derivative's role. It illustrates the Poincaré Lemma, which ...This page discusses exact differential equations, their solutions, and the concept of potential functions in physics, emphasizing the total derivative's role. It illustrates the Poincaré Lemma, which connects local potential functions to exact equations, and addresses the use of integrating factors to solve non-exact equations.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/05%3A_The_Laplace_Transform/5.03%3A_ConvolutionThis page discusses the use of inverse Laplace transforms and convolution in solving ordinary differential and Volterra integral equations. It highlights the simplification of computations through the...This page discusses the use of inverse Laplace transforms and convolution in solving ordinary differential and Volterra integral equations. It highlights the simplification of computations through these methods. An example is provided where a differential equation involving an integral is transformed into the frequency domain, resulting in the expression X(s)=s−1s2−2. The final solution is obtained as x(t)=cosh(√2t)−1√2sinh(√2t).
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/03%3A_Higher_order_linear_ODEs/3.08%3A_Mechanical_VibrationsLet us look at some applications of linear second order constant coefficient equations.
- 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/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/05%3A_Eigenvalues_and_Eigenvectors/5.3%3A_SimilarityThis page explores similar matrices defined by the relation A=CBC−1, focusing on their geometric interpretations, eigenvalues, eigenvectors, and properties as an equivalence relation. It expl...This page explores similar matrices defined by the relation A=CBC−1, focusing on their geometric interpretations, eigenvalues, eigenvectors, and properties as an equivalence relation. It explains how to compute matrix powers, emphasizing transformations and changes of coordinates between different systems. The relationship between matrices A and B is examined, highlighting how they share characteristics like trace and determinant but may differ in eigenvectors.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/03%3A_Linear_Transformations_and_Matrix_Algebra/3.04%3A_Matrix_MultiplicationThis page explores the interplay between compositions of transformations and matrix multiplication in linear algebra. It defines the composition of transformations, illustrates their properties, inclu...This page explores the interplay between compositions of transformations and matrix multiplication in linear algebra. It defines the composition of transformations, illustrates their properties, including non-commutativity and associativity, and connects these concepts to matrix operations. The Row-Column Rule for matrix multiplication is explained, alongside the implications of this non-commutative nature.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/01%3A_Systems_of_Equations/1.06%3A_Application_to_Polynomial_InterpolationGiven n points in R2, we solve a linear system to find an appropriate degree polynomial that passes through them.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/04%3A_R/4.04%3A_Spanning_Sets_in_RBy generating all linear combinations of a set of vectors one can obtain various subsets of Rn which we call subspaces. For example what set of vectors in R3 generate t...By generating all linear combinations of a set of vectors one can obtain various subsets of Rn which we call subspaces. For example what set of vectors in R3 generate the XY-plane? What is the smallest such set of vectors can you find? The tools of spanning, linear independence and basis are exactly what is needed to answer these and similar questions and are the focus of this section.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/04%3A_R/4.07%3A_Row_Column_and_Null_SpacesThis section discusses the Row, Column, and Null Spaces of a matrix, focusing on their definitions, properties, and computational methods.
- 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.
