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- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/02%3A_Applications_of_First_Order_EquationsThis page covers applications of first-order differential equations, focusing on exponential growth and decay, including radioactive decay, carbon dating, and compound interest. It discusses complex g...This page covers applications of first-order differential equations, focusing on exponential growth and decay, including radioactive decay, carbon dating, and compound interest. It discusses complex growth scenarios, Newton's law of cooling, motion in resistive media, and mixing problems. Additionally, it introduces orthogonal trajectories and pursuit curves, alongside exercises for practical comprehension.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/03%3A_Higher_order_linear_ODEsIn this chapter, we go a little further and look at second-order equations, which are equations containing second derivatives of the dependent variable. The solution methods we examine are different f...In this chapter, we go a little further and look at second-order equations, which are equations containing second derivatives of the dependent variable. The solution methods we examine are different from those discussed earlier, and the solutions tend to involve trigonometric functions as well as exponential functions. Here we concentrate primarily on second-order equations with constant coefficients.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEsThis page presents a curriculum on differential equations, addressing classification, integrals, slope fields, and both linear and nonlinear equations. It highlights solution existence and uniqueness,...This page presents a curriculum on differential equations, addressing classification, integrals, slope fields, and both linear and nonlinear equations. It highlights solution existence and uniqueness, along with first-order linear equations methods. Topics include separable and autonomous equations, numerical methods like Euler’s, and transforming nonlinear equations for easier manipulation. Each section is supported by exercises to enhance understanding.
