Udacity

Differential Equations in Action (Udacity)

Offered by Udacity,
Differential Equations in Action (Udacity)

Making Math Matter. In this course, you'll hone your problem-solving skills through learning to find numerical solutions to systems of differential equations. You'll write code in Python to fight forest fires, rescue the Apollo 13 astronauts, stop the spread of epidemics, and resolve other real-world dilemmas.

Class Deals by MOOC List - Click here and see Udacity's Active Discounts, Deals, and Promo Codes.

By the end of this course, you'll develop an intuition for the use of differential equations in the applied sciences. You'll also learn how to build mathematical models for systems of differential equations using a variety of techniques. Along the way, you'll learn how to translate mathematical expressions into Python code and solve some really cool problems!

What You Will Learn

Lesson 1
Rescuing Apollo 13, Part 1

  • Introduction to the Forward Euler Method.

Lesson 2
Rescuing Apollo 13, Part 2

  • Comparing solvers
  • Heun's Method.
  • Symplectic Euler Method.

Lesson 3
Analyzing the Spread of Diseases

  • Implicit methods and stiffness.

Lesson 4
There's Plenty of Fish in the Sea?

  • Stability
  • sensitivity
  • and optimization.

Lesson 5
Antilock Brake Systems

  • Friction
  • equilibria
  • and control theory.

Lesson 6
The Path of a Forest Fire

  • Partial differential equations and heat conduction.

Lesson 7
Advanced Applications of Numerical Methods

  • Chaos
  • software
  • and predictive capability.

Prerequisites and Requirements
You'll need a basic knowledge of programming in Python for this course, around the level of Intro to Computer Science. An understanding of Python packages, as discussed in Programming Foundations with Python, will also be helpful.In addition, you'll need to feel comfortable with trigonometry at the high school level, as well as basic vector algebra. This class will primarily involve solving differential equations numerically rather than analytically, but some exposure to calculus and physics at the level of Intro to Physics wouldn't hurt.Most of all, bring with you a love of learning and problem solving!

Go to Class
MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Related Courses

Introduction to Complex Analysis (Coursera) Coursera
Wesleyan University

Introduction to Complex Analysis (Coursera)

Sci: Mathematics

This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. We will start by introducing the complex plane, along with the algebra and geometry of complex numbers, and then we will make our way via differentiation, integration, complex dynamics, power series representation and Laurent series into territories at the edge of what is known today.

Aug 17th 2026
5-12 Weeks
Algebra Geometry Compilers
Details
Computing for Data Analysis (edX) EdX
Georgia Institute of Technology,GTx

Computing for Data Analysis (edX)

CS: Software Engineering Statistics & Data Analysis

A hands-on introduction to basic programming principles and practice relevant to modern data analysis, data mining, and machine learning. The modern data analysis pipeline involves collection, preprocessing, storage, analysis, and interactive visualization of data. In the course, you’ll see how computing and mathematics come together.

Aug 24th 2026
13-24 Weeks
Programming Python Computing
Details
Matrix Methods (Coursera) Coursera
University of Minnesota

Matrix Methods (Coursera)

Sci: Mathematics

Mathematical Matrix Methods lie at the root of most methods of machine learning and data analysis of tabular data. Learn the basics of Matrix Methods, including matrix-matrix multiplication, solving linear equations, orthogonality, and best least squares approximation. Discover the Singular Value Decomposition that plays a fundamental role in dimensionality reduction, Principal Component Analysis, and noise reduction.

Aug 17th 2026
5-12 Weeks
Math Machine Learning Matrix
Details
Spark (Udacity) Udacity
Udacity,Insight

Spark (Udacity)

Data Science

Master how to work with big data and build machine learning models at scale using Spark! In this course, you’ll learn how to use Spark to work with big data and build machine learning models at scale, including how to wrangle and model massive datasets with PySpark, the Python library for interacting with Spark. In the first lesson, you will learn about big data and how Spark fits into the big data ecosystem. In lesson two, you will be practicing processing and cleaning datasets to get comfortable with Spark’s SQL and dataframe APIs. In the third lesson, you will debug and optimize your Spark code when running on a cluster. In lesson four, you will use Spark’s Machine Learning Library to train machine learning models at scale.

Self Paced
Self-Paced
Python Debugging Machine Learning
Details
Statistics (Udacity) Udacity
Udacity,San Jose State University

Statistics (Udacity)

Sci: Mathematics Statistics & Data Analysis

The Science of Decisions. We live in a time of unprecedented access to information...data. Whether researching the best school, job, or relationship, the Internet has thrown open the doors to vast pools of data. Statistics are simply objective and systematic methods for describing and interpreting information so that you may make the most informed decisions about life.

Self Paced
Self-Paced
Math Statistics Probability
Details