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Product No. 99774 Supplementary Print Price: FREE with membership
 

Elliptic Integrals and Elliptic Functions in Calculus Beyond (UMAP)

Yves Nievergelt, Jacqueline Coomes


Mathematics Topic:
Calculus
Application Areas:
Engineering and physics
Prerequisites:
For elliptic integrals of the first kind: the concepts of limit, derivative, and integral; mathematical induction; Rolle's Theorem, the Mean-Value Theorem for Derivatives, the Fundamental Theorem of Calculus, the Inverse-Function Theorem with one variable; algebraic and trigonometric changes of variables in integrals. For elliptic integrals of the second kind: also infinite series.

| ©1999 by COMAP, Inc. | Tools for Teaching 1998 | 59 pages |


This module demonstrates the use of the main concepts and theorems from calculus in the solution of real problems, here the computation of the arc length of an ellipse and the swinging time of a pendulum.

Table of Contents:

INTRODCUTION

PHYSICAL ORIGINS OF ELLIPTIC INTEGRALS
Elliptic Integral of the Second Kind for Ellipses
Elliptic Integrals of the First Kind for the Circular Pendulum

ELLIPTIC INTEGRALS OF THE FIRST AND SECOND KINDS
Definition and Features of Elliptic Integrals of the First Kind
Definition and Features of Elliptic Integrals of the Second Kind

THE ARITHMETIC-GEOMETRIC MEAN ALGORITHM

LANDEN'S TRANSFORMATION
Landen's Transformation on [0, Pi/2]
Landen's Transformation on R

ALGORITHM TO COMPUTE ELLIPTIC INTEGRALS OF THE FIRST KIND

ALGORITHM TO COMPUTE ELLIPTIC INTEGRALS OF THE SECOND KIND

ALGORITHM TO COMPUTE JACOBI'S ELLIPTIC FUNCTIONS

RATE OF CONVERGENCE FOR NUMERICAL COMPUTATIONS

CONCLUSION

SOLUTIONS TO THE EXERCISES