Introduction to Partial Differential Equations
- Interactive Course
- Advanced
- 2 Certifications
Course Level: Advanced
Requirements: This course requires knowledge of multivariable calculus and ordinary differential equations and a basic working knowledge of Wolfram Language.
Certification Levels: CompletionLevel 1
Summary
This course introduces partial differential equations (PDEs) from scratch and covers the most important types of PDEs and their solution methods. The study of partial differential equations is a vital, dynamic and essential area of mathematics, with applications across physics, engineering and beyond. PDEs are used to describe many physical phenomena in fields such as fluid dynamics, electromagnetism, mechanics, classical optics and heat flow. Many fundamental laws of physics, including Maxwell's equations, the Navier–Stokes equations, the heat equation, the wave equation and Schrödinger's equation in quantum mechanics, are expressed in terms of PDEs. The course is designed to provide a user-friendly introduction to the theory and applications of PDEs, with interactive examples using Wolfram Language's powerful built-in solving methods.
Featured Products & Technologies: Wolfram Language (available in Mathematica and Wolfram|One)
You'll Learn To
- Classify partial differential equations
- Solve linear, quasilinear and nonlinear first-order PDEs
- Understand the method of separation of variables, the Fourier transform and the Laplace transform
- Solve well-known linear second-order PDEs, such as the heat equation, the wave equation and the Laplace equation
- Apply four famous PDEs: the Black–Scholes equation, the Schrödinger equation, the Maxwell equations and the Navier–Stokes equations
Certifications Available
Completion Certificate
Certify your completion of this course by watching course videos and passing the auto-graded quizzes.
Level 1 Certification
Pass the auto-graded quizzes and graded final exam to certify your proficiency in Introduction to Partial Differential Equations
New! Wolfram AI Course Assistant
This interactive course includes video lessons, quizzes, practice problems, a final exam and our new chat-based Course Assistant powered by Wolfram LLM Kit. Ask Course Assistant anything about the lesson, and it will provide you with contextually aware answers and even relevant code. Get started with our free courses by signing in to the Wolfram Cloud with your Wolfram ID—or create one; it's free! Our recommended best practice for completing this interactive course is to start with Lesson 1 and progress through the video lessons, taking each quiz in the order it appears in the table of contents. You can click Track My Progress to chart your certification progress as you go. Wolfram AI Course Assistant is included with a Wolfram Notebook Assistant + LLM Kit subscription.
