Transcendental Functions And Initial Value Problems A Different Approach to Calculus II

Transcendental Functions and Initial Value Problems: A Different Approach to Calculus II

Author: Byungchul Cha

College Mathematics Journal, Vol. 38, No. 4 (Sep, 2007), pp. 288–296

Summary: This article develops many of the elementary functions such as sine, cosine, the natural logarithm, and the exponential function as solutions to initial value problems. The author states (without proof) the existence and uniqueness of solutions to first-order initial value problems and gives an explanation of the theorem using direction fields. He then develops the properties of each of the elementary functions directly from the initial value problems. Finally, the author explains how these ideas can be integrated into a second semester calculus course.

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