Lectures related to Limits: Understanding the Concept

Cylindrical Coordinates and Fubini: Division of Domains

Covers the use of cylindrical coordinates and Fubini's theorem to calculate volumes of revolution bodies.

Integration by Parts: Taylor Series Development

Explains integration by parts and Taylor series development for finding explicit formulas and understanding term orders.

Integrals of Paths

Covers the concept of integrals of paths with examples and applications.

Absolute Value

Covers the concept of absolute value and its properties, including graphical interpretation and equation solving.

General Mathematics I: Derivatives and Tangents

Explores derivatives, tangents, and elementary function rules in general mathematics.

Curvilinear Coordinates: Calculations and Examples

Covers curvilinear coordinates and area calculations using double integrals with examples of different curves.

Geometric Sequences: Recurrence System

Covers geometric sequences and recurrence systems to find sequence terms and patterns.

Volume Calculation: Spheres and Loops

Explores volume calculation for spheres, function definition, and loop logic.

Calculating with Taylor, Convexity

Covers calculating with Taylor series and convexity concepts, including sin(x) and cos(x) approximations.

Exam Problem Examples

Presents exam problem examples illustrating the application of mathematical concepts in practical problem-solving.

Exercise 07: Series 20, Exercise 4

Covers Exercise 4 from Series 20, focusing on mathematical problem-solving strategies.

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Fourier Analysis: Stokes Theorem

Explores the application of Stokes' theorem to surfaces and vector spaces in Fourier analysis.

Optimization Methods: Convergence and Trade-offs

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Verification Strategies for Exercises

Covers general verification strategies for solving exercises in science and engineering, emphasizing the importance of verifying solutions.

Optimal Transport: From Theory to Applications

Explores the history, theory, and applications of optimal transport in various fields, showcasing its importance in solving complex mathematical problems.

Eigenvalues and Eigenvectors

Covers eigenvalues and eigenvectors in linear algebra.

Primal-dual Optimization: Extra-Gradient Method

Explores the Extra-Gradient method for Primal-dual optimization, covering nonconvex-concave problems, convergence rates, and practical performance.

Discriminant Analysis: Bayes Rule

Covers the Bayes discriminant rule for allocating individuals to populations based on measurements and prior probabilities.

Eigenvalues and Eigenvectors: Understanding Matrices

Explores eigenvalues and eigenvectors in matrices through examples and calculations.