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- 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/Calculus_I%3A_Differential_Calculus/03%3A_DerivativesCalculating velocity and changes in velocity are important uses of calculus, but it is far more widespread than that. Calculus is important in all branches of mathematics, science, and engineering, an...Calculating velocity and changes in velocity are important uses of calculus, but it is far more widespread than that. Calculus is important in all branches of mathematics, science, and engineering, and it is critical to analysis in business and health as well. In this chapter, we explore one of the main tools of calculus, the derivative, and show convenient ways to calculate derivatives. We apply these rules to a variety of functions in this chapter.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/05%3A_Introduction_to_Differential_Equations/5.03%3A_Separable_EquationsWe now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of discipli...We now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of disciplines, including physics, chemistry, and engineering. We illustrate a few applications at the end of the section.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.05%3A_Physical_Applications_of_Integration/2.5E%3A_Exercises_for_Section_2.5This page offers a series of exercises on calculating work done in various scenarios, including lifting objects, applying forces, and determining masses. It covers spring constant calculations and wor...This page offers a series of exercises on calculating work done in various scenarios, including lifting objects, applying forces, and determining masses. It covers spring constant calculations and work related to pumping fluids, featuring problems on constant and variable forces, density functions, and hydrostatic calculations. Answers for these exercises are included, reinforcing fundamental principles of physics and calculus associated with work and mass.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/02%3A_Limits/2.02%3A_The_Limit_of_a_Function/2.2E%3A_Exercises_for_Section_2.2This page covers various mathematical limits, including those of functions and piecewise functions, through exercises that require constructing tables for approximation and evaluating left-hand and ri...This page covers various mathematical limits, including those of functions and piecewise functions, through exercises that require constructing tables for approximation and evaluating left-hand and right-hand limits. It highlights cases where limits do not exist, explores trigonometric limits, and examines graphical representations to estimate limits as variables approach specific points.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/00%3A_Front_Matter/05%3A_About_the_BookFrom understanding the rate of change to calculating areas and volumes of irregular shapes, this book encourages learners to explore the richness of Calculus in various fields, including physics, econ...From understanding the rate of change to calculating areas and volumes of irregular shapes, this book encourages learners to explore the richness of Calculus in various fields, including physics, economics, and engineering. The online version of the textbook includes 3D figures which gives a three-dimensional visual experience to the learner to understand the concept.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/02%3A_Applications_of_First_Order_Equations/2.03%3A_Elementary_MechanicsThis section discusses applications to elementary mechanics involving Newton's second law of motion. The problems considered include motion under the influence of gravity in a resistive medium, and de...This section discusses applications to elementary mechanics involving Newton's second law of motion. The problems considered include motion under the influence of gravity in a resistive medium, and determining the initial velocity required to launch a satellite.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.06%3A_Moments_and_Centers_of_Mass/2.6E%3A_Exercises_for_Section_2.6This page presents exercises aimed at calculating the center of mass for various mass configurations, including point masses and continuous distributions. It evaluates different geometric figures, suc...This page presents exercises aimed at calculating the center of mass for various mass configurations, including point masses and continuous distributions. It evaluates different geometric figures, such as triangles and circles, for their centroids. Each problem includes solutions that specify the center of mass coordinates and other relevant quantities, employing principles of symmetry and calculus.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/03%3A_Derivatives/3.02%3A_The_Derivative_as_a_Function/3.2E%3A_Exercises_for_Section_3.2This page covers calculus exercises centered on derivatives, continuity, and piecewise functions. It includes finding derivatives using definitions, graph analysis, and continuity conditions. Real-lif...This page covers calculus exercises centered on derivatives, continuity, and piecewise functions. It includes finding derivatives using definitions, graph analysis, and continuity conditions. Real-life applications of derivatives, such as rates of change in population and temperature, are discussed.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.05%3A_Physical_Applications_of_IntegrationIn this section, we examine some physical applications of integration. Several physical applications of the definite integral are common in engineering and physics. Definite integrals can be used to d...In this section, we examine some physical applications of integration. Several physical applications of the definite integral are common in engineering and physics. Definite integrals can be used to determine the mass of an object if its density function is known. Work can also be calculated from integrating a force function, or when counteracting the force of gravity, as in a pumping problem. Definite integrals can also be used to calculate the force exerted on an object submerged in a liquid.
- 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.
