Stirling's formula: Euler's integral and Gaussian integral

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Explores the properties and applications of natural logarithmic functions, including area invariance and harmonic series divergence.

Natural Logarithm: Properties and Inequalities

Covers properties and inequalities of the natural logarithm function, including solving related inequalities.

Taylor Polynomials: Examples and Convergence

Covers examples of Taylor polynomials and discusses their convergence when approximating functions.

Integration Techniques: Change of Variable and Integration by Parts

Explores advanced integration techniques such as change of variable and integration by parts to simplify complex integrals and solve challenging integration problems.

Exponential Function: Properties and Definitions

Explores the properties and definitions of the exponential function and its relation to the natural logarithm.

Combinatorics: Counting Methods

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Enumeration: Counting Subsets

Covers the concept of enumeration and counting subsets of a finite set with examples and factorial notation.

Exponential Functions and Logarithms

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Dynamics on homogeneous spaces and interactions with number theory

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