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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.01%3A_Integration_by_PartsThis page provides an overview of integration by parts, a technique used to simplify the integration of products of functions. It includes the formula derived from the product rule, guidance on choosi...This page provides an overview of integration by parts, a technique used to simplify the integration of products of functions. It includes the formula derived from the product rule, guidance on choosing functions with the LIATE mnemonic, and multiple examples ranging from logarithmic to trigonometric integrals. The text also discusses evaluating both definite and indefinite integrals and emphasizes validating results through differentiation.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/00%3A_Front_Matter/01%3A_TitlePageCalculus II: Integral Calculus ( CC BY-SA; Via Wikimedia)
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.08%3A_Exponential_Growth_and_Decay/2.8E%3A_Exercises_for_Section_2.8This page features true or false exercises focused on exponential functions, including growth and decay, along with financial calculations. It offers solutions and explanations for problems related to...This page features true or false exercises focused on exponential functions, including growth and decay, along with financial calculations. It offers solutions and explanations for problems related to population growth models, radioactive decay, interest rates, and more. Specific topics include calculating doubling times, analyzing population changes, and understanding temperature dynamics.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.01%3A_Related_RatesIf two related quantities are changing over time, the rates at which the quantities change are related. For example, if a balloon is being filled with air, both the radius of the balloon and the volum...If two related quantities are changing over time, the rates at which the quantities change are related. For example, if a balloon is being filled with air, both the radius of the balloon and the volume of the balloon are increasing. In this section, we consider several problems in which two or more related quantities are changing and we study how to determine the relationship between the rates of change of these quantities.
- 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/Math_1D%3A_De_Anza/02%3A_Multiple_Integration/2.05%3A_Cylindrical_and_Spherical_CoordinatesIn this section, we look at two different ways of describing the location of points in space, both of them based on extensions of polar coordinates. As the name suggests, cylindrical coordinates are u...In this section, we look at two different ways of describing the location of points in space, both of them based on extensions of polar coordinates. As the name suggests, cylindrical coordinates are useful for dealing with problems involving cylinders, such as calculating the volume of a round water tank or the amount of oil flowing through a pipe. Similarly, spherical coordinates are useful for dealing with problems involving spheres, such as finding the volume of domed structures.
- 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/Introductory_Differential_Equations/02%3A_Applications_of_First_Order_Equations/2.01%3A_Growth_and_DecayThis section begins with a discussion of exponential growth and decay, which you have probably already seen in calculus. We consider applications to radioactive decay, carbon dating, and compound inte...This section begins with a discussion of exponential growth and decay, which you have probably already seen in calculus. We consider applications to radioactive decay, carbon dating, and compound interest. We also consider more complicated problems where the rate of change of a quantity is in part proportional to the magnitude of the quantity, but is also influenced by other other factors for example, a radioactive susbstance is manufactured at a certain rate, but decays at a rate proportional
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/00%3A_Front_Matter/06%3A_About_the_AuthorsHe is especially grateful to his wife for her unwavering support in caring for their child, allowing him the time to focus on completing his Open Educational Resources (OER) textbook to benefit studen...He is especially grateful to his wife for her unwavering support in caring for their child, allowing him the time to focus on completing his Open Educational Resources (OER) textbook to benefit students and educators alike. She believes that math is not just a subject, but a language, a tool for understanding the world, and she is committed to helping every student unlock its power.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_Theory/6.02%3A_Eigenvalues_and_Eigenvectors_for_Special_MatricesIn this section we consider three kinds of matrices where we can simplify the process of finding eigenvalues and eigenvectors.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/07%3A_Vector_Spaces/7.04%3A_Linear_IndependenceIn this section, we will again explore concepts introduced earlier in terms of Rn and extend them to apply to abstract vector spaces.
