Natural Logarithm: Definition and Properties

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Page 2 of 3

Explores exponential and logarithmic functions, their properties, relations, and graphs, including different bases and commonly used logarithms.

Taylor Polynomials: Approximating Functions with Taylor Polynomials

Delves into Taylor polynomials, showcasing how higher orders improve function approximations and how they can be used to calculate limits.

Analyse I: Summary

Covers real numbers, complex numbers, numerical sequences, series, real functions, function limits, derivatives, Taylor series, integrals, and growth rates of functions.

Exponential Functions: Properties and Logarithms

Covers the properties of exponential and logarithmic functions.

Natural Logarithm: Properties and Inequalities

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

Properties of Real Numbers

Covers countability and bijections between sets, demonstrating the uncountability of real numbers.

Geometric Series: Properties and Applications

Explores the properties and applications of geometric series, including logarithmic functions and theorems related to area under curves.

Derivatives and Jacobian Matrix

Introduces functions with real values, derivatives, and the Jacobian matrix, along with compound functions and variable change applications.

Taylor Polynomials: Examples and Convergence

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

Complex Numbers: Operations and Polar Form

Explores complex numbers, operations, absolute value, and polar form, along with the analysis and graphic representation of complex numbers.