Lectures related to Functions xr, r>0, on 10,1

Comparison Series and Integrals

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

Improper Integrals: Convergence and Comparison

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

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Two-loop Computations: External Legs and Internal Propagators

Covers the computation of two-loop diagrams with external legs and internal propagators.

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Unclosed Curves Integrals

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

Integrals of Functions

Covers integrals as the reciprocal function of the derivative and explains displacement integral of velocity and variation of speed and acceleration in rectilinear motion.

Mathematical Reminders: Derivatives, Primitives, Integrals

Covers mathematical reminders on derivatives, primitives, and integrals, including common functions and Taylor series expansions.

Periodic Functions: Integrals and Approximations

Discusses periodic functions, integrals, and approximations using trigonometric polynomials and proofs of related theorems.

Advanced Analysis II: Generalisations and Gradients

Explores generalisations of functions and the concept of gradients in advanced analysis.

Convergence and Divergence: Integrals Analysis

Explores the convergence and divergence of integrals, analyzing their behavior under specific limits.

Notation in Multivariable Calculus

Reviews the notation used in multivariable calculus, emphasizing accurate translation between different forms of integrals.

End of Semester Contact Session

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

Generalized Integrals: Definitions and Criteria

Covers the definition of generalized integrals and comparison theorems for convergence.

Integrals in Higher Dimensions

Explores integrals in higher dimensions, emphasizing the versatility of integration methods and the significance of changing the order of integration.

Fundamental Analysis: Integrals and Primitives

Covers the fundamental concepts of integrals and primitives, including properties and examples.

Calculus: Derivatives and Integrals

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Example Type 3

Covers changing variables in integrals with a focus on exponential functions.

Multiple Integrals: Problematic Cases and Compact Domains

Covers integrals doubles in compact domains with negligible borders and problematic cases.