Concept

Mathematical analysis

Related lectures (25)

Mathematical Equation Rule

Covers the process of converting handwritten entries into text and sharing mathematical equation rules.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Uniform Convergence: Series of Functions

Explores uniform convergence of series of functions and its significance in complex analysis.

End of Semester Contact Session

Covers the transition to a blended format, student performance, and mathematical analysis methods.

Sequences, Convergence

Introduces sequences, convergence, limits, bounded and monotonic sequences, divergence, and convergence criteria.

Derivability and Continuity

Explores continuity, derivability, and linear approximation in mathematical analysis.

Convergence Criteria

Covers convergence criteria for sequences and explores monotone sequences and the two policemen criterion.

Proof of Delta Function Properties

Explores the proof of properties related to the delta function in mathematical analysis.

SGD and Mean Field Analysis

Explores Stochastic Gradient Descent and Mean Field Analysis in two-layer neural networks, emphasizing their iterative processes and mathematical foundations.

The Analytic Determination of Sheath Trace

Covers the analytic determination of the trace of a sheath, shedding light on a crucial aspect of modern analysis.

Stationary Points in Analytical Functions

Explores stationary points in analytical functions and their significance in mathematical analysis.

Cauchy and Laurent Series

Covers Cauchy and Laurent series in complex analysis.

Fourier Series: Convergence and Coefficients

Explores Fourier series convergence and coefficient calculations through examples and derivations.

Analyzing Limits: Indeterminate Forms

Explores handling indeterminate forms in limits through simplification and extracting dominant terms for effective evaluation.

Introduction to Real Numbers and Their Properties

Introduces real numbers, their properties, and their significance in analysis.

Uniform Convergence of Fourier Series

Covers the concept of uniform convergence of Fourier series and Dirichlet's theorem application.

Injectivity: Sufficient Conditions

Explores the conditions for injectivity in mathematical functions, with detailed examples and proofs.

Riemann Zeta Function

Covers the definition and properties of the Riemann Zeta function, including convergence and singularities.

Geotechnical Foundations: Load Factors and Formulas

Discusses load factors, stress calculations, and limit analysis in geotechnical engineering.

Sequences: Convergence and Limits

Explores sequences, convergence, and limits, emphasizing the importance of understanding how sequences approach specific values.