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- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/06%3A_Systems_of_ODEs/6.04%3A_Matrices_and_linear_systems/6.4E%3A_Exercises_for_Section_6.4This page features an exercise set focused on matrix operations, including solving systems of equations with matrix inverses, computing determinants, and exploring matrix invertibility conditions. It ...This page features an exercise set focused on matrix operations, including solving systems of equations with matrix inverses, computing determinants, and exploring matrix invertibility conditions. It includes tasks like determining invertibility for matrices with variables, verifying matrix relationships, and provides solutions for all exercises. Key examples focus on determinant calculation and identifying nonzero matrices that meet specific multiplication criteria.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/05%3A_The_Laplace_Transform/5.01%3A_The_Laplace_Transform/5.1E%3A_Exercises_for_Section_5.1This page outlines exercises on finding Laplace transforms and their inverses for various functions, including polynomials, trigonometric, and piecewise functions. It provides examples and answers for...This page outlines exercises on finding Laplace transforms and their inverses for various functions, including polynomials, trigonometric, and piecewise functions. It provides examples and answers for certain problems, illustrating the application of Laplace transform rules. The exercises emphasize techniques such as integration by parts and the use of properties related to exponential and trigonometric functions within the context of Laplace transforms.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_Theory/6.08%3A_Singular_Value_Decomposition/6.8E%3A_Exercises_for_Section_6.8This page contains exercises on finding the Singular Value Decomposition (SVD) of various matrices, outlining the computation of matrices U, Σ, and V. Two detailed examples are provid...This page contains exercises on finding the Singular Value Decomposition (SVD) of various matrices, outlining the computation of matrices U, Σ, and V. Two detailed examples are provided, along with a fifth exercise concerning the determinant of an n×n matrix and its singular values.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.03%3A_Trigonometric_Substitution/3.3E%3A_Exercises_for_Section_3.3This page presents mathematical exercises focused on simplifying trigonometric and hyperbolic expressions, completing the square for trinomials, and performing integrals using trigonometric substituti...This page presents mathematical exercises focused on simplifying trigonometric and hyperbolic expressions, completing the square for trinomials, and performing integrals using trigonometric substitution. It includes notable results like simplifying 9\sec^2θ−9 to 9\tan^2θ and evaluating various integrals.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/01%3A_Systems_of_Equations/1.04%3A_Balancing_Chemical_Reactions/1.4E%3A_Exercises_for_Section_1.4This page contains various exercises on balancing chemical reactions, featuring unbalanced equations with some providing answers. The goal is to equalize the number of atoms for each element on both s...This page contains various exercises on balancing chemical reactions, featuring unbalanced equations with some providing answers. The goal is to equalize the number of atoms for each element on both sides of the equation. Key examples include the balancing of propane with oxygen and phosphorus pentoxide with water. Some exercises are unsolved, indicating they require completion.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/03%3A_DeterminantsThis page explains the importance of determinants in square matrices, covering their properties, applications, and geometric interpretations. It discusses their relation to matrix inverses and Cramer'...This page explains the importance of determinants in square matrices, covering their properties, applications, and geometric interpretations. It discusses their relation to matrix inverses and Cramer's Rule, emphasizes the effects of row operations on determinants, and includes examples for clarity. Furthermore, it highlights the geometric interpretation of determinants as volumes, enhancing comprehension of their defining properties and relevance in multivariable calculus.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/03%3A_Higher_order_linear_ODEs/3.04%3A_Constant_coefficient_second_order_linear_ODEs/3.4E%3A_Exercises_for_Section_3.4This page provides a variety of exercises focused on solving second-order and one first-order differential equations. It includes challenges to find general or particular solutions, often with initial...This page provides a variety of exercises focused on solving second-order and one first-order differential equations. It includes challenges to find general or particular solutions, often with initial conditions, and requires different solving methods. Some tasks involve constructing equations from provided solutions, covering a range from basic to moderately complex scenarios.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.06%3A_Linear_Equations_and_the_Integrating_Factor/1.6E%3A_Exercises_for_the_section_1.6These are homework exercises to accompany Libl's "Differential Equations for Engineering" Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engin...These are homework exercises to accompany Libl's "Differential Equations for Engineering" Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(Guichard)/02%3A_Instantaneous_Rate_of_Change-_The_Derivative/2.E%3A_Instantaneous_Rate_of_Change-_The_Derivative_(Exercises)These are homework exercises to accompany David Guichard's "General Calculus" Textmap.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(Guichard)/01%3A_Analytic_Geometry/1.E%3A_Analytic_Geometry_(Exercises)These are homework exercises to accompany David Guichard's "General Calculus" Textmap.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/01%3A_Integration/1.08%3A_Chapter_1_Review_ExercisesThis page features calculus exercises on definite integrals, Riemann sums, and antiderivatives. It includes exercises on evaluating mathematical truths and real-world applications, such as calculating...This page features calculus exercises on definite integrals, Riemann sums, and antiderivatives. It includes exercises on evaluating mathematical truths and real-world applications, such as calculating average costs and velocities. The content ranges from theoretical proofs to practical scenarios, emphasizing the continuity of functions and derivatives. Specific calculations and their answers are provided, demonstrating the connections between theory and application.
