微積分-指數與對數篇 Calculus-Exponential and Logarithmic Functions

Master the fundamentals of exponential and logarithmic functions with this comprehensive course! We'll start by solidifying your understanding of their properties, then delve into the derivatives of these essential functions.

This unit covers key topics including:

• Definitions: A clear explanation of exponential functions and logarithmic functions.
• Exponentiation Identities: Learn and apply fundamental rules of exponents.
• Logarithmic Identities: Explore the properties of logarithms.
• Change of Base Formula: Understand how to convert logarithms between different bases.
• Common Logarithm: A detailed look at the base-10 logarithm.
• Compounded Interest: Discover the application of exponential functions in finance.
• Euler's Number (e): Explore the significance of e in mathematics.
• Derivatives of Exponential Functions: Learn how to differentiate exponential functions.
• Derivatives of Logarithmic Functions: Master the techniques for finding derivatives of logarithmic functions.
• Hyperbolic Functions: An introduction to hyperbolic sine, cosine, and related functions.

Prerequisites: A strong foundation in calculus, particularly understanding limits, is recommended before starting this unit.

Estimated Completion Time: Allow approximately two weeks to complete the materials.

Source: This course content is adapted from the Calculus I course (Unit 6: Exponential and Logarithmic Functions and Unit 7: Derivatives of Logarithmic Functions) at China University of Technology. The materials have been certified by the Ministry of Education, Taiwan, in the first cohort of digital learning materials in 2014.

Language: The entire course is taught in Traditional Chinese.

Important Note: This course is intended for self-study only and does not offer academic credit from China University of Technology.