About This Chapter
Who's it for?
Anyone who needs help understanding differential equations will benefit from taking this course. You will be able to grasp the subject matter faster, retain critical knowledge longer and earn better grades. You're in the right place if you:
- Have fallen behind in understanding differential notation or working with system differential equations.
- Need an efficient way to learn about consumer decision making.
- Learn best with engaging auditory and visual tools.
- Struggle with learning disabilities or learning differences, including autism and ADHD.
- Experience difficulty understanding your teachers.
- Missed class time and need to catch up.
- Can't access extra math learning resources at school.
How it works:
- Start at the beginning, or identify the topics that you need help with.
- Watch and learn from fun videos, reviewing as needed.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Submit questions to one of our instructors for personalized support if you need extra help.
- Verify you're ready by completing the Differential Equations chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Differential Equations chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any relevant question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
In this chapter, you'll learn the answers to questions including:
- How is differential notation used in physics?
- Why do I have to separate variables to solve system differential equations?
- What steps are involved when calculating rates?
- How do I calculate exponential growth?
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.
6. Differential Calculus: Definition & Applications
This lesson is an introduction to differential calculus, the branch of mathematics that is concerned with rates of change. If you ever wanted to know how things change over time, then this is the place to start!
7. Newton-Raphson Method for Nonlinear Systems of Equations
Solving a system of nonlinear equations might sound complicated! But anyone who can multiply and add can get a solution by following the Newton-Raphson method. In this lesson, we will explain step-by-step just how this is done.
8. Solving Systems of Linear Differential Equations
In this lesson, we will look at two methods for solving systems of linear differential equations: the eigenvalue method and the Laplace transform method.
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Other chapters within the Calculus: Help and Review course
- Graphing and Functions: Help and Review
- Continuity in Calculus: Help and Review
- Geometry and Trigonometry in Calculus: Help and Review
- Using Scientific Calculators in Calculus: Help and Review
- Limits in Calculus: Help and Review
- Rate of Change in Calculus: Help and Review
- Calculating Derivatives and Derivative Rules: Help and Review
- Graphing Derivatives and L'Hopital's Rule: Help and Review
- Applications of Derivatives: Help and Review
- Area Under the Curve and Integrals: Help and Review
- Integration and Integration Techniques: Help and Review
- Integration Applications: Help and Review