About This Chapter
Differential equations have derivatives of variables in the equations. You may recognize it when you see d/dx before a variable. In these equations there can be either ordinary or partial derivatives.
Discover how differential equations may be used in physics through notation. These can be found in many areas of science and math, including algebra. Then you can learn how to solve system differential equations. These can be solved by separating variables in equations in a divide-and-conquer method.
These engaging videos cover some of the unique problems that are often seen in math. You may have heard the two-trains-leave-a-station word problem many times. Watch these lessons to find out how to solve this type of problem, specifically by using the distance-between-moving-points equations. Also, learn how to solve population dynamics problems. Finally, learn how to handle everyday equations, such as the draining-tank and painting-surface-area problems.
Many of these problems can be found in common situations during your daily life. By studying these principles, you'll grasp a basic understanding of calculus, physics, algebra and other types of math and science, looking at the roles they play in real life.
1. Differential Notation in Physics
Stop. Look around. Everything is changing. In this lesson, you'll learn what a differential equation is and how these equations can describe the world around you.
2. Separation of Variables to Solve System Differential Equations
In this lesson, we discuss how to solve some types of differential equations using the separation of variables technique. We'll ponder the dastardly deeds of a mad scientist, using his chemical concoction as an example for how to use separation of variables.
3. Calculating Rate and Exponential Growth: The Population Dynamics Problem
You know how the world population keeps increasing? It's increasing faster now than it was 100 or 1,000 years ago. In this lesson, learn how differential equations predict this type of exponential growth.
4. Related Rates: The Draining Tank Problem
Grab an empty cup and pour some water into it. In this lesson we will watch how the height of the water changes as we learn about related rates of change and learn how to solve the draining tank problem.
5. Related Rates: The Distance Between Moving Points Problem
Remember the classic problem of math horror stories everywhere? You know, where one train leaves Kentucky at 2 p.m. and another leaves Sacramento at 4 p. m.? In this lesson, tame the horror and learn how to solve these problems using differentiation and related rates.
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Other chapters within the Math 104: Calculus course
- Graphing and Functions
- Vectors in Calculus
- Geometry and Trigonometry
- How to Use a Scientific Calculator
- Rate of Change
- Calculating Derivatives and Derivative Rules
- Graphing Derivatives and L'Hopital's Rule
- Applications of Derivatives
- Area Under the Curve and Integrals
- Integration and Integration Techniques
- Integration Applications
- Studying for Math 104