Complexity of Algorithms: Advanced Big-O Facts

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Complexity of Algorithms: Advanced Big-O Facts

Explores advanced big-O facts for powers, logarithms, factorials, and function combinations.

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Power Series Functions: Logarithm and Exponential

Explores power series functions, particularly the logarithm and exponential functions, discussing convergence, extension, and roots of entire functions.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Holomorphic Functions: Cauchy-Riemann Equations and Applications

Discusses holomorphic functions, focusing on the Cauchy-Riemann equations and their applications in complex analysis.

Limit Properties: Exponential and Logarithmic Functions

Covers the properties of limits related to exponential and logarithmic functions.

Real Numbers and Functions

Introduces Real Analysis I, covering real numbers, functions, limits, derivatives, and integrals.

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

Explores Stirling's formula, Euler's integral, and the Gaussian integral for estimating n factorial.

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.