A look back at the London smog of 1952 and the half century since

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...

Gas exchange, the intake of molecular oxygen (O2) from the environment and the outflow of carbon dioxide (CO2) into the environment, is necessary for cellular function. Gas exchange during respiration occurs largely via the movement of gas molecules along pressure gradients. Gas travels from areas of higher partial pressure to areas of lower partial pressure. In mammals, gas exchange occurs in the alveoli of the lungs, which are adjacent to capillaries and share a membrane with them.

Chronic bronchitis is a key phenotype of chronic obstructive pulmonary disease (COPD), characterized by airway-centered inflammation and mucus overproduction. It develops from long-term exposure to harmful particles or gases, most commonly cigarette smoke, which triggers a persistent inflammatory response.Cellular and Structural ChangesInflammation initially affects the large bronchi and later the smaller airways, with infiltration by immune cells, including neutrophils, macrophages, and...

Physical assessment of the respiratory tract is critical to patient care. It allows healthcare professionals to identify and manage various respiratory conditions. The process involves a combination of subjective and objective data collection.
Subjective Data
Subjective data provides vital information about the patient's health history and symptoms. This data is typically collected through interviews in which patients describe their experiences, symptoms, and concerns.
Health history and key...

Gas behavior plays a vital role in understanding bodily processes such as external and internal respiration. External respiration involves the diffusion of oxygen into the blood and carbon dioxide out of it in the lungs. In contrast, internal respiration happens in body tissues, where these gases move in opposite directions.
Gas Laws Governing Respiration
The behavior of gases is guided by Dalton's Law of partial pressures and Henry's Law.
Dalton's Law asserts that the total pressure exerted by...

Sputum studies are a critical part of diagnosing and treating numerous respiratory conditions. These studies involve obtaining sputum samples for analysis to identify pathogenic organisms and assess the presence of abnormal cells indicative of malignant conditions. This lesson will delve into three fundamental sputum studies: Gram Stain, Cytology, and Acid-fast Smear and Culture.
Gram Stain
The Gram Stain is an integral part of sputum studies. It involves the staining of sputum, which permits...