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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.03%3A_Trigonometric_SubstitutionThe technique of trigonometric substitution comes in very handy when evaluating integrals of certain forms. This technique uses substitution to rewrite these integrals as trigonometric integrals.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.09%3A_Calculus_of_the_Hyperbolic_FunctionsThis page discusses differentiation and integration of hyperbolic functions and their inverses, emphasizing their calculus applications, particularly in modeling catenary curves. Key objectives includ...This page discusses differentiation and integration of hyperbolic functions and their inverses, emphasizing their calculus applications, particularly in modeling catenary curves. Key objectives include understanding derivatives, integrals, and their respective formulas for hyperbolic functions, as well as domain considerations for inverse functions. The text provides examples, exercises, and instructions for evaluating integrals using u-substitution.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.04%3A_The_Mean_Value_Theorem/4.4E%3A_Exercises_for_Section_4.4This page contains exercises on the Mean Value Theorem (MVT) in calculus, highlighting the importance of closed intervals and continuity. It includes counterexamples and specific functions to demonstr...This page contains exercises on the Mean Value Theorem (MVT) in calculus, highlighting the importance of closed intervals and continuity. It includes counterexamples and specific functions to demonstrate where the MVT applies and where it does not. The exercises cover graphing functions, estimating derivatives, and identifying conditions for roots, while also proving aspects of the MVT in relation to differentiability and continuity.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.08%3A_Implicit_DifferentiationWe use implicit differentiation to find derivatives of implicitly defined functions (functions defined by equations). By using implicit differentiation, we can find the equation of a tangent line to t...We use implicit differentiation to find derivatives of implicitly defined functions (functions defined by equations). By using implicit differentiation, we can find the equation of a tangent line to the graph of a curve.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus_II__Integral_Calculus_._Lockman_Spring_2024/01%3A_Fast_Review_of_Important_Calc_I_Stuff/1.02%3A_Derivatives_ReviewA condensed review of the definition of the derivative of a function, the rules of differentiation, and the derivatives of basic functions.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/05%3A_The_Laplace_Transform/5.03%3A_Convolution/5.3E%3A_Exercises_for_Section_5.3This page covers exercises on convolution computations relevant to differential equations and integral solutions. It includes tasks like finding convolutions, solving linear differential equations wit...This page covers exercises on convolution computations relevant to differential equations and integral solutions. It includes tasks like finding convolutions, solving linear differential equations with initial conditions, and using convolution to derive answers with specific functions. The findings are presented through integrals or function forms, emphasizing the application of convolution in addressing differential equations and Laplace transforms.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/06%3A_Systems_of_ODEs/6.02%3A_Linear_systems_of_ODEsThis page summarizes concepts related to homogeneous and nonhomogeneous systems of ordinary differential equations (ODEs). It explains differentiation rules for matrix and vector-valued functions, sol...This page summarizes concepts related to homogeneous and nonhomogeneous systems of ordinary differential equations (ODEs). It explains differentiation rules for matrix and vector-valued functions, solving first-order linear systems, superposition principles, and linear independence.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.07%3A_Integrals_Exponential_Functions_and_LogarithmsWe already examined exponential functions and logarithms in earlier chapters. However, we glossed over some key details in the previous discussions. For example, we did not study how to treat exponent...We already examined exponential functions and logarithms in earlier chapters. However, we glossed over some key details in the previous discussions. For example, we did not study how to treat exponential functions with exponents that are irrational. The definition of the number e is another area where the previous development was somewhat incomplete. We now have the tools to deal with these concepts in a more mathematically rigorous way, and we do so in this section.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.01%3A_Defining_the_Derivative/3.1E%3A_Exercises_for_Section_3.1This page encompasses exercises focused on calculating secant and tangent slopes for various functions using defined formulas. It covers average and instantaneous velocities, analyzing motion models, ...This page encompasses exercises focused on calculating secant and tangent slopes for various functions using defined formulas. It covers average and instantaneous velocities, analyzing motion models, and understanding costs linked to production through different function types.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/00%3A_Front_Matter/04%3A_About_the_BookThe study of the slope of the tangent lines is not limited to functions, but also includes implicitly and parametrically defined curves. From understanding the essence of differential and integral cal...The study of the slope of the tangent lines is not limited to functions, but also includes implicitly and parametrically defined curves. From understanding the essence of differential and integral calculus in one variable, to constructing and using Taylor series, to studying vector calculus and its applications, this textbook series encourages learners to explore the richness of Calculus in various fields, including physics, economics, and engineering.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/06%3A_AppendicesContributors and Attributions Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download fo...Contributors and Attributions Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org.
