# Ch 10: Differential Equations in AP Calculus: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other AP calculus work.
- Identify the differential equations concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our AP calculus tutoring solution will benefit any student who is trying to learn about differential equations for AP calculus and earn better grades. This resource can help students including those who:

- Struggle with understanding differential notation, separation of variables, rate and exponential growth calculations or any other differential equations in AP calculus topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their differential equations in AP calculus unit
- Cope with ADD or ADHD
- Want to get ahead in AP calculus
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning about differential equations for AP calculus simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live calculus tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about differential equations on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Explain how differential notation is used in physics.
- Solve system differential equations using separation of variables.
- Calculate rate and exponential growth.
- Find the rate at which a tank drains.
- Determine the distance between moving points.

### 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

Other chapters within the AP Calculus AB & BC: Tutoring Solution course

- Functions in AP Calculus: Tutoring Solution
- Graphing and Functions in AP Calculus: Tutoring Solution
- Sequences and Series in AP Calculus: Tutoring Solution
- Limits in AP Calculus: Tutoring Solution
- Continuity in AP Calculus: Tutoring Solution
- Exponentials and Logarithms in AP Calculus: Tutoring Solution
- Exponents and Polynomials in AP Calculus: Tutoring Solution
- Applications of Derivatives in AP Calculus: Tutoring Solution
- AP Calculus - Derivatives Calculations & Rules: Tutoring Solution
- Area Under the Curve and Integrals in AP Calculus: Tutoring Solution
- AP Calculus - Graphing Derivatives & L'Hopital's Rule: Tutoring Solution
- AP Calculus - Integration: Tutoring Solution
- Integration Applications in AP Calculus: Tutoring Solution
- Rate of Change in AP Calculus: Tutoring Solution
- Geometry and Trigonometry in AP Calculus: Tutoring Solution
- How to Use Scientific Calculators for AP Calculus: Tutoring Solution