Calculus
Calculus 1: An Introduction
Calculus 1, the mathematical wizardry behind change and motion, holds immense power in unraveling the secrets of our world. Whether you're a high school...
P-Series Test: Series and Integrals
The p-Series test provides a criterion for determining the convergence of a particular type of series known as the p-Series. A p-Series is defined...
Root test for series
Exploring the root Test and determining series convergence through limiting roots. In fact, in the realm of mathematical analysis, the convergence of infinite...
Geometric Series
Geometric series are a fundamental concept in mathematics, frequently encountered in various fields, including calculus, finance, and physics. A such series is a sequence...
Parameter dependent integral
Parameter-dependent integral is studied in this article. We propose a selection of exercises on continuity, limit, and differentiability of such parametric integrals. Some known...
Exercises on convex functions and applications
In this article, we offer exercises on convex functions. In fact, our objectives are: to be able to show that a function is convex;...
Recurring sequences exercises
Recurring sequences are generally involved in the modeling of discrete systems. In fact, such sequences replace the differential equation by discretizing the time variable.
To...
Convergence of sequences
We discuss the convergence of sequences and how to calculate the limit of a sequence. This subject is fundamental in real analysis because many...
Exercises on differential calculus
We offer exercises on differential calculus with detailed answers. In fact, our objectives are as follows: knowing how to calculate the derivative of a...
Maximal solution to Cauchy problems
The maximal solution to Cauchy's problems is a solution that gives full information on the physical model. In fact, we obtain this solution by...