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Analysis

Related lectures (25)

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Holomorphic Functions: Taylor Series Expansion

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

Explicit Stabilised Methods: Applications to Bayesian Inverse Problems

Explores explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems, covering optimization, sampling, and numerical experiments.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Calculus Foundations: Taylor Series and Integrals

Introduces calculus concepts, focusing on Taylor series and integrals, including their applications and significance in mathematical analysis.

Numerical Analysis: Introduction to Computational Methods

Covers the basics of numerical analysis and computational methods using Python, focusing on algorithms and practical applications in mathematics.

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.

Algebraic Identities and Trigonometry

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

Distributions and Derivatives Log in to Mediaspace to watch this video

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Normed Spaces Log in to Mediaspace to watch this video

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Differential Calculation: Trigonometric Derivatives Log in to Mediaspace to watch this video

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

Applications of Residue Theorem in Complex Analysis Log in to Mediaspace to watch this video

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

Functions: Differentials, Taylor Expansions, Integrals Log in to Mediaspace to watch this video

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Laplacian in Polar and Spherical Coordinates: Derivatives Log in to Mediaspace to watch this video

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Mechanics: Introduction and Calculus Log in to Mediaspace to watch this video

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Differentiable Functions and Lagrange Multipliers Log in to Mediaspace to watch this video

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Numerical Methods: Euler and Crank-Nicolson Log in to Mediaspace to watch this video

Covers Euler and Crank-Nicolson methods for solving differential equations.

Riemann Sums and Definite Integrals Log in to Mediaspace to watch this video

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Numerical Integration Methods Log in to Mediaspace to watch this video

Explores numerical integration methods and their application in solving differential equations and simulating physical systems.