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Lecture
Stirling's formula: Euler's integral and Gaussian integral
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Related lectures (31)
Complexity of Algorithms: Advanced Big-O Facts
Covers big-O estimates for factorial function and combinations of functions.
Natural Logarithm: Graph
MOOC: Trigonometric, Logarithmic and Exponential Functions
Explores the properties and graph of the natural logarithm function, emphasizing its bijectivity and the Euler's number 'e'.
Natural Logarithm: Definition and Properties
Explores the definition, properties, and limits of the natural logarithm function.
Limit Properties: Exponential and Logarithmic Functions
Covers the properties of limits related to exponential and logarithmic functions.
Complexity of Algorithms: Advanced Big-O Facts
Explores advanced big-O facts for powers, logarithms, factorials, and function combinations.
Generalized Powers: Derivatives and Exponentials
Covers properties of logarithms, derivatives, exponentials, and sine-cosine functions.
Power Functions: Properties and Derivatives
Covers properties of logarithms, power functions, and their derivatives, with examples illustrating key concepts.
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.
Algebraic Identities and Trigonometry
Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.
Logarithmic Functions: Properties and Applications
MOOC: Trigonometric, Logarithmic and Exponential Functions
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
Introduces combinatorics and counting methods for determining possible outcomes in various scenarios, illustrated with examples.
Enumeration: Counting Subsets
Covers the concept of enumeration and counting subsets of a finite set with examples and factorial notation.
Exponential Functions and Logarithms
MOOC: Trigonometric, Logarithmic and Exponential Functions
Explores exponential and logarithmic functions, their properties, relations, and graphs, including different bases and commonly used logarithms.
Dynamics on homogeneous spaces and interactions with number theory
Explores dynamics on homogeneous spaces, Khintchine theorem, Sullivan's logarithm law, and interactions with number theory.
Exponential Functions: Properties and Logarithms
Explores exponential functions, their properties, and the relationship with logarithmic functions.
Limits and Exponential Functions
Explores limits, exponential functions, and logarithms properties.
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