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Modeling with Differential Equations: Real-World Applications

Differential Equations: Master Advanced Math Concepts

Introduction to Differential Equations

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Introduction to differential equations

Order and solutions to differential equations

First Order Differential Equations

Separable differential equations

Separable Equations

Separable equations

Modeling with differential equations

Slope fields

Understanding Slope Fields

Exact differential equations

Integrating factor technique

Bernoulli equations

Interval of validity

Equilibrium solutions

Euler's method

Euler's Method

Euler"s Method

Euler"s method

Second Order Differential Equations

Method of undetermined coefficients

Applications of second order differential equations

Homogeneous linear second order differential equations

Characteristic equation with real distinct roots

Characteristic equation with complex roots

Characteristic equation with repeated roots

Reduction of order

Wronskian

Laplace Transforms

Introduction to the laplace transform

Calculating laplace transforms

Inverse laplace transforms

Solving differential equations with the laplace transform

Step functions

Solving differential equations with step functions

Dirac delta function

Convolution integral

We&apos;ve got you covered with our complete help for any Ordinary Differential Equations (ODE) courses, whether you are a math major, engineering major or in any fields that are related to math and sciences.

Our comprehensive lessons on differential equations cover help on topics like First order differential equation, Second order differential equation, Separable differential equations, Laplace transforms, and a lot more. Learn the concepts with our video tutorials made by our differential equations tutors that show you step-by-step solutions to even the hardest differential equations problems. Then, strengthen your understanding with tons of differential equations practice.

All our lessons are taught by experienced Differential Equations teachers. Let&apos;s finish your homework in no time, and ACE that final.

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Ex.1

Spherical balloon: deriving volume from surface area using separation of variables

Ex.2

Factory liquid conversion word problem with cubic rate differential equation

Ex.3

Solving a study-time differential equation and interpreting results

Ex.4

Logistic growth model for Facebook friends with limit analysis

Intro

Ex.5

Modeling nudibranch population doubling with exponential growth

Ex.6

Logistic growth model for nudibranch population with carrying capacity

Ex.7

Using Newton's Law of Cooling to estimate time of death

Overview of real-world applications of differential equations

Deriving the exponential population growth model using separation of variables

Deriving the logistic growth model from the carrying capacity concept

Newton's law of cooling and deriving its general solution

In this section, we will try to apply differential equations to real life situations. For each question we will look how to set up the differential equation. Afterwards, we will find the general solution and use the initial condition to find the particular solution. Depending on the question, we will even look at behaviours of the differential equation and see if it is applicable to real life situations. For example, one can notice that integrating the area of a sphere actually gives the volume of a sphere!

Modeling Real-World Systems with Differential Equations

What You'll Learn

Translate real-world scenarios into differential equations using rate of change language

Apply separation of variables to solve modeling differential equations

Use initial conditions to find particular solutions for applied problems

Model exponential population growth and decay with differential equations

Apply Newton's Law of Cooling to temperature change problems

Use the logistic growth model to represent populations with carrying capacity

What You'll Practice

Setting up differential equations from word problems about rates of change

Solving separable differential equations for spherical balloons and geometric applications

Finding particular solutions using given initial population or temperature data

Modeling populations with exponential growth and logistic growth equations

Applying Newton's Law of Cooling to forensic and temperature problems

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

11 Video lessons

Practice exercises

Learning resources

Skills

Differential Equations

Modeling

Separation of Variables

Initial Conditions

Exponential Growth

Logistic Growth

Newton's Law of Cooling

Applied Problem Solving