Learn Calculus with Python (A Hands-On Introduction to Real-World Modeling and Simulation)

See calculus in action with Python, visualization, and real-world applications.

The world around us is being designed and built using calculus. It’s a beautiful subject that makes more sense when you can see what it does.

Learn Calculus with Python turns calculus into something you can experiment with. You’ll begin by programming a virtual turtle, and as you shrink its steps you’ll arrive at limits, derivatives, integrals, and finally the fundamental theorem of calculus. Along the way, you’ll write a graphing calculator, watch integrals accumulate area, and move objects through space using differential equations. The code lets you see the math at work.

You’ll use calculus and the book’s interactive Jupyter Notebook coding environment to:

• Measure income inequality with an integral
• Simulate gravity and send two bodies into orbit
• Plot the Lorenz system to watch chaos emerge in the atmosphere
• Train a neuron using backpropagation and gradient descent
• Break an audio signal into its frequencies with the fast Fourier transform

More than 200 exercises take the ideas further. You’ll create ecosystems, simulate urban air pollution, explore supply and demand, predict wind turbine output, and model disease outbreaks and swarming behavior. You’ll derive solutions by hand, create mathematical models, and build simulations of your own.

By the end, you’ll understand the math needed to model systems that change over time and be able to write code to see what happens next.

REQUIREMENTS: Algebra and geometry, but no previous programming experience. You’ll find all the Python you need in the book. The notebooks run in your browser at https://calculus.dev with no installations required.