The Sphere and Ellipsoids

The sphere is what might be called a perfect shape. Unfortunately, nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years.

Scope and Content

This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences, and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry, and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure.

Additional Resources

Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding.

Intended Audience

The book serves as a comprehensive reference for applied mathematicians, physicists, engineers, and for anyone who needs to know the current state of the art in this fascinating subject.