4.6 The (surprisingly) difficult definition of exponentials and logarithms скачать в хорошем качестве

4.6 The (surprisingly) difficult definition of exponentials and logarithms

You know how to define 2^3, 2^(-3), and 2^(0.5), but what does 2^PI even mean? Related videos: Derivatives of other exponentials:    • 4.8 Derivative of other exponentials   Logarithmic differentiation:    • 4.9 Logarithmic Differentiation   Proof of the power rule for all exponents:    • 4.10 Proof of the power rule (for all expo...   Playlist - Derivatives of exponentials and logarithms:    • Derivatives of exponentials and logarithms   0:00 Introduction 0:22 Review of the Definition of Logarithm 1:03 Review of the Definition of Exponentials with Rational Exponents and Positive Bases 3:24 The Classical Analysis Solution for Defining Exponentials with Irrational Exponents 4:33 The Modern Analysis Solution for Defining Exponentials with Irrational Exponents 5:43 Modern Analysis Solution Step 1 Using Differential Equations 6:29 Modern Analysis Solution Step 1 Using Power Series 7:01 Modern Analysis Solution Step 1 Using Integrals