About This Chapter
Differential Equations & Applications - Chapter Summary
Our instructors will define differential calculus and explain its varied applications. The concepts of separation of variables and how to calculate exponential growth are discussed. You will also learn how to solve seemingly complicated problems involving the distance between two moving points by using differentiation.
As you move through the lessons, several methods you can use to solve systems of linear differential equations are also covered. This chapter will teach you to:
- Describe how differential equations describe what is happening in the world around you
- Use the separation of variables technique to solve equations
- Understand how differential equations predict exponential growth
- Solve the draining tank problem
- Define the Newton-Raphson method
- Outline several ways to solve linear differential equations
Our instructors are available to help you as you move through the lessons. Simply contact one of them if you need additional help. You can access these study materials at any time, 24 hours a day, seven days a week. Use the quizzes and tests to measure how well you've retained the information that you've learned.
1. 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!
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
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.
9. Solving Systems of Linear Differential Equations by Elimination
Solving linear differential equations may seem tough, but there's a tried and tested way to do it! We'll explore solving such equations and how this relates to the technique of elimination from algebra. We will also solve a population growth system problem using what we've learned.
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Other chapters within the NDA Exam Preparation & Study Guide course
- About the NDA Exam
- Algebra Concepts
- Advanced Algebra Concepts
- Solving Matrices & Determinants
- Trigonometry Concepts
- Geometry & Linear Equations
- Analytic Geometry
- Functions, Limits & Continuity
- Derivative Rules
- Calculations & Applications of Derivatives
- Integral Calculus
- Scalars & Vectors in Algebra
- Visualizing Statistics
- Probability Concepts in Math
- Grammar and Usage
- Improving Reading Comprehension
- Measurements in Physics
- Motion in Physics
- Basics of Work, Power & Energy
- Understanding Heat Transfer
- Sound Waves
- Light, Mirrors & Lenses
- Electric Currents & Power
- Scientific Technology, Machines & Tools
- The Atom & Structure of Elements
- Chemical Properties of Elements & Substances
- Chemical Symbols, Formulas & Reactions
- Qualities of Living Organisms
- Health Science Basics
- Solar System & Eclipses
- Achievements of Famous Scientists
- Indian History
- Overview of Major World History Events
- World Government Types
- The Earth
- Earth's Oceans, Atmosphere & Climate
- Regional Geography of South Asia
- Modern Day Events in India
- NDA Exam Preparation & Study Guide Flashcards