Introduction to Special Functions
- Interactive Course
- 6 h 30 min
- Advanced
- 2 Certifications
Estimated Time: 6 h 30 min
Course Level: Advanced
Requirements: This course requires knowledge of calculus, differential equations, complex analysis and Wolfram Language.
Certification Levels: CompletionLevel 1
Summary
This course offers a comprehensive introduction to special functions, their properties and their wide-ranging applications through the powerful lens of Wolfram Language. The course begins with the historical development of special functions and foundational methods for working with them, including symbolic evaluation, analytic continuation and high-precision numerical computation. Various exercises help you deepen your knowledge and fundamental understanding of the topic. As the lessons progress, you'll explore major classes of special functions, including the gamma and zeta families, special integrals, Bessel and Airy functions, orthogonal polynomials and hypergeometric functions. Advanced topics include elliptic and Heun-related functions, multivariate generalizations like the Appell functions and superfunctions such as Meijer G and Fox H. These topics, though essential in many areas of mathematics, physics and engineering, are often underrepresented in traditional university curricula. This course was designed to fill that gap with practical computation, visualization and theory. Wolfram AI Course Assistant is available for this interactive course.
Featured Products & Technologies: Wolfram Language (available in Mathematica and Wolfram|One)
You'll Learn To
- Make connections between differential equations and special functions as data structures
- Perform asymptotic analysis and derive series expansions with mathematical rigor
- Visualize special functions and their singularities in the complex plane
- Analyze and apply gamma, Bessel, Airy, hypergeometric, elliptic, Heun, Meijer G, Fox H and many more functions
- Solve physical and engineering problems using exact symbolic solutions (e.g. via DSolve)
- Leverage orthogonal polynomials and special integrals in approximation theory and quantum mechanics
Certifications Available
Completion Certificate
Certify your completion of this course by watching course videos and passing the auto-graded quizzes.
Track My Progress
Level 1 Certification
Pass the auto-graded quizzes and final exam to certify your proficiency in special functions.
Track My Progress
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.
