Exponential Function: Theory and Applications

This lecture covers the theory behind the exponential function, starting with a brief recap of logarithmic functions. The instructor explains the properties of the exponential function, its relationship with the natural logarithm, and how to write exponential expressions in standard form. Through mathematical derivations, the lecture demonstrates the calculation of exponential values for natural numbers and real numbers. The lecture also delves into the properties of the exponential function, including its objectivity, growth rate, and its role in defining generalized power functions and logarithms. The session concludes with practical exercises on solving equations involving exponential and hyperbolic functions, emphasizing the importance of understanding the properties of logarithms and exponentials.