Scalars and Vectors Scalars Some phenomena of Nature can be described by a number and a unit of measurement.
Definition - Scalar. A scalar is a number that expresses a magnitude without direction.
Exercise 1 Compute the derivative function of $f(x)=x^3-2x^2+1$ at the points $x=-1$, $x=0$ and $x=1$. Explain your result. Find an equation of the tangent line to the graph of $f$ at each of the three given points.
Concept of derivative Increment Definition - Increment of a variable. An increment of a variable $x$ is a change in the value of the variable; it is denoted $\Delta x$. The increment of a variable $x$ along an interval $[a,b]$ is given by $$\Delta x = b-a.
Antiderivative of a function Definition - Antiderivative of a function. Given a function $f(x)$, the function $F(X)$ is an antiderivative or primitive function of $f$ if it satisfies that $F’(x)=f(x)$ $\forall x \in \mathop{\rm Dom}(f)$.
Ordinary Differential Equations Often in Physics, Chemistry, Biology, Geometry, etc there arise equations that relate a function with its derivative, or successive derivatives.
Definition - Ordinary differential equation. An ordinary differential equation (O.
Vector functions of a single real variable Definition - Vector function of a single real variable. A vector function of a single real variable or vector field of a scalar variable is a function that maps every scalar value $t\in D\subseteq \mathbb{R}$ into a vector $(x_1(t),\ldots,x_n(t))$ in $\mathbb{R}^n$:
Degrees: Pharmacy and Biotechnology
Date: Jan 17, 2022
Question 1 To analyze the hypoxemia tolerance of mammals, in a laboratory some rats are exposed to extreme conditions with variable levels of oxygen.