Calculus Manual

Explanation of the most important concepts in one variable and several variables Calculus with applied examples.

Analytic Geometry

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.

Calculus Exams

Calculus exams of the last courses with solutions.

Calculus Cheat Sheets

Everything you have to know at a glance

Problems of Derivatives

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.

One variable differential calculus

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 $\Delta x$.

Integral calculus

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

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.

Several variables differentiable calculus

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 $\mathbb{R}^n$:

Pharmacy exam 2019-12-16

Degrees: Pharmacy and Biotechnology Date: Dic 16, 2019 Question 1 A lagoon contaminated with nitrates contains 1000 tons of nitrates dissolved in 6 millions of cubic meters of water. To decontaminate the lagoon, we start to introduce pure water into the lagoon at a rate of 100000 cubic meters per day, and we take out the same amount of contaminated water.