Lectures related to Complexity of Algorithms: Advanced Big-O Facts

Complexity of Algorithms: Advanced Big-O Facts

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

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.

Functions in Python

Introduces functions in Python, covering predefined and user-defined functions, formal and effective parameters, and the importance of docstrings.

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.

Binary Search: Logarithm Function

Explains binary search, the logarithm function, and recursive algorithms for factorial and Fibonacci sequences.

Power Functions: Properties and Derivatives

Covers properties of logarithms, power functions, and their derivatives, with examples illustrating key concepts.

Generalized Powers: Derivatives and Exponentials

Covers properties of logarithms, derivatives, exponentials, and sine-cosine functions.

Python Crash Course

Provides a Python crash course covering basic arithmetics, complex numbers, strings, lists, dictionaries, and more.

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Derivatives and Continuity

Explores derivatives, reciprocal functions, and continuity of functions with examples and formulas.

Logarithmic Functions: Properties and Applications

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

Comparison Series and Integrals

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.