Lectures related to Distributed Forces: Calculations and Analysis

Distributed forces: integrals and resultant forces

Covers the calculation of beams with distributed loads and resultant forces.

Functions xr, r>0, on 10,1

Covers the properties of functions xr, r>0, on 10,1, including limits and integrals.

Comparison Series and Integrals

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

Introduction to Structural Mechanics

Covers beams with distributed and concentrated forces, bending moment, shear force, and internal load diagrams.

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.

Residue Theorem: Calculating Integrals on Closed Curves

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

Two-loop Computations: External Legs and Internal Propagators

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

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.

Non-Straight Beams in Structural Mechanics

Covers non-straight beams, frames, and matching conditions in structural mechanics.

Structural Mechanics: Systems of Forces

Covers systems of forces, moments, couples, and stress in 2D and 3D, as well as the effect of force-couple systems.

Notation in Multivariable Calculus

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

Advanced Analysis II: Generalisations and Gradients

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

Periodic Functions: Integrals and Approximations

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

Mathematical Reminders: Derivatives, Primitives, Integrals

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

End of Semester Contact Session

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

Green's Functions in Laplace Equations

Covers the concept of Green's functions in Laplace equations and their solution construction process.

Generalized Integrals: Definitions and Criteria

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