Learn differential equations with online courses and programs

Differential equations are used in countless real-life scenarios, from financial projections to the movement within our solar system. Deepen your mathematical expertise and learn how to predict complex processes by enrolling in a differential equations class.

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Differential Equations | Introduction Image

What are differential equations?

Differential equations are mathematical equations that involve derivatives and describe relationships between an unknown function and its derivatives. They are used to represent dynamic systems and their behavior over time or in response to certain inputs.

When you solve differential equations, you can gain insights into how systems change and predict future behavior in disciplines such as physics, engineering, and biology. They play an important role in understanding and predicting complex processes and phenomena, ranging from the motion of celestial bodies to the spread of diseases and the behavior of electrical circuits.

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Differential equations course curriculum

Differential equations are considered intermediate mathematics and are usually taught after initial calculus courses. A course that covers differential equations could teach learners about:

Differential equations and their solutions.
Qualitative analysis via directional fields.
Separable equations.
Linear algebra and matrices

How to get started in differential equations

The best way to get started learning differential equations depends on your existing knowledge. For example, have you mastered the basics of linear algebra and intermediate calculus? Differential equations rely on these types of math, so you should feel comfortable with them first. Browse the following learning options for each level of differential equations knowledge:

Beginner: NYIF: Option Contracts, Participants, Strategies, and Pricing

https://www.edx.org/learn/economics/new-york-institute-of-finance-option-contracts-participants-strategies-and-pricing

One beginner-friendly option for learning differential equations is the New York Institute of Finance's Option Contracts, Participants, Strategies, and Pricing course. While you need some basic financial vocabulary knowledge, the course content only requires students to know the building blocks of differential equations, like algebra, percentages, interest, and binomial trees.

Intermediate: HarvardX Calculus Applied

https://www.edx.org/learn/calculus/harvard-university-calculus-applied

HarvardX's Calculus Applied course covers real-life examples of how calculus can be applied to your day-to-day. You'll learn how to analyze mathematical models like variables, constants, and parameters. You should be familiar with the basics of derivatives, integrals, polynomial functions, exponential functions, and logarithmic functions.

Explore jobs related to differential equations

A range of career fields use knowledge of differential equations for mathematical modeling, analysis, and problem-solving. Some examples of jobs that involve working with differential equations include:

Mathematical modeler: Creates mathematical models that simulate and predict real-world phenomena, such as population dynamics, climate change, and financial markets.
Research scientist: Conducts research and development in scientific fields, applying differential equations to study complex systems, analyze data, and develop mathematical models.
Data scientist: Utilizes differential equations in data analysis and machine learning to extract insights, build predictive models, and solve complex problems in various industries.
Financial analyst: Employs differential equations in financial modeling, risk assessment, and derivative pricing to support investment decisions and portfolio management.

Each of these roles requires different education and skills. Some employers may seek candidates with a degree in mathematics or computer science, depending on the role. Before deciding on a specific learning path, research the positions you hope to pursue and align your coursework with your career goals.

Frequently asked questions about differential equations

How long does it take to learn differential equations?

While it may take a year or more to completely master differential equations, you can learn the basics in just a few weeks. Most people can reach a college-level proficiency in about 3–4 months. How long it takes to learn differential equations depends on your chosen learning method, schedule, and level of dedication.

Which is harder, Calc 3 or differential equations?

Calculus Three (also known as multivariable calculus) is generally more challenging for learners who struggle to grasp spatial reasoning and three-dimensional concepts, while differential equations can be challenging for learners who require more time to understand abstract thinking and pattern recognition. Which type of math you find more difficult depends on the type of thinker you are and your existing level of proficiency for each.

What level of math is differential equations?

The topic of differential equations is typically a 200- or 300-level course at the undergraduate level, which is considered a mid-to-upper-level course that follows calculus one, two, and sometimes three. However, this may vary by institution.

Is differential equations a hard class?

Many learners find differential equations to be challenging — especially if they have historically struggled with highly conceptual types of math. Some students struggle to choose the right type of equation to use in different situations and understanding behavior-based concepts such as growth, decay, and oscillation. However, learners who struggle with calculus sometimes find learning differential equations easier.

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