Differential Equations Application Example: Population Growth with Harvesting скачать в хорошем качестве

Differential Equations Application Example: Population Growth with Harvesting

In this example problem video, we model population growth with harvesting using differential equations. We set up a differential equation that accounts for both natural population growth and a constant harvesting rate. After solving the equation, we analyze the long-term behavior of the population to determine what happens over time. In this video, you’ll see examples involving: • Setting up a population model with harvesting • Writing and solving a linear differential equation • Applying an initial condition • Finding equilibrium solutions • Interpreting the long-term behavior of the population These worked examples show how differential equations are used to model real-world population dynamics. This video is part of my Differential Equations application examples series. Differential Equations playlists:    / @understandthemath   Guided notes and additional resources: https://www.understandthemath.com ODE Videos    • Ordinary Differential Equations Free Cours...      • Classification of Differential Equations |...      • Slope Fields for First-Order Differential ...      • Autonomous Differential Equations | Critic...      • Separable Differential Equations | Definit...      • Linear Differential Equations | Integratin...      • Exact Differential Equations | Definition,...      • Homogeneous Differential Equations | Defin...      • Bernoulli Differential Equations | Method,...      • Applications of First-Order Linear Differe...      • Euler’s Method | Numerical Approximation f...      • Differential Equations Midterm Exam Review...   In this example problem video, we model population growth with harvesting using differential equations. We set up a differential equation that accounts for both natural population growth and a constant harvesting rate. After solving the equation, we analyze the long-term behavior of the population to determine what happens over time. In this video, you’ll see examples involving: • Setting up a population model with harvesting • Writing and solving a linear differential equation • Applying an initial condition • Finding equilibrium solutions • Interpreting the long-term behavior of the population These worked examples show how differential equations are used to model real-world population dynamics. This video is part of my Differential Equations application examples series. Differential Equations playlists:    / @understandthemath   Guided notes and additional resources: https://www.understandthemath.com ODE Videos    • Ordinary Differential Equations Free Cours...      • Classification of Differential Equations |...      • Slope Fields for First-Order Differential ...      • Autonomous Differential Equations | Critic...      • Separable Differential Equations | Definit...      • Linear Differential Equations | Integratin...      • Exact Differential Equations | Definition,...      • Homogeneous Differential Equations | Defin...      • Bernoulli Differential Equations | Method,...      • Applications of First-Order Linear Differe...      • Euler’s Method | Numerical Approximation f...      • Differential Equations Midterm Exam Review...   Connect & Support TikTok:   / understandthemath   Instagram:   / understandthemath   Facebook: https://www.facebook.com/profile.php?... Support: https://buymeacoffee.com/understandth... More About Understand The Math Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples. Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective. #DifferentialEquations #PopulationGrowth #Harvesting #ApplicationsOfDifferentialEquations #ODEs #MathExamples #EngineeringMath #AppliedMath #CollegeMath #UnderstandTheMath