Introduction to Special Functions
- Interactive Course
- Advanced
- 2 Certifications
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.
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.
Level 1 Certification
Pass the auto-graded quizzes and final exam to certify your proficiency in special functions.
About This Interactive Course
It's free and easy to get started with open interactive courses using the Wolfram Cloud—sign in with your Wolfram ID or create one. No plan is required. This interactive course includes video lessons, exercises, quizzes, a final exam and a scratch notebook, all in an easy-to-use interface. From the interactive course, click Track My Progress to chart your certification progress as you go. Recommended best practice for completing this interactive course is to start with Lesson 1 and progress through the video lessons and exercises, taking each quiz in the order it appears in the table of contents.
