Limit of Functions of a Real Variable Summary: This class thoroughly reviews the formal definition of limits of functions of a real variable, and from this, the main properties that lead to the algebra of limits are demonstrated. Learning Objectives: At the end of this class, the student will be...
Solved Problems: Finite Limits Summary: This class offers solved problems on the calculation of finite limits, accompanied by a video tutorial. Students are guided to solve the problems and compare their results with the provided solutions. Key techniques such as rationalization and the use of graphs are highlighted, encouraging different...
The Squeeze Theorem for Calculating Limits Summary: This class presents the Squeeze Theorem, a key tool in calculus for evaluating difficult limits using simpler functions that bound from above and below. It offers a graphical explanation and a formal proof, followed by practical examples. The goal is for students to...
One-Sided Limits: Definitions, Development, and Exercises Summary: This post explains one-sided and bilateral limits in calculus, showing how they are defined and applied both intuitively and formally. Graphical and algebraic examples are presented, the conditions for using limit algebra in these cases are discussed, and solved exercises are included to...
Normal Form Algorithm and Applications SUMMARYIn this class, we will review the DNF/CNF algorithm, which will allow us to find, from any expression in propositional logic, its equivalent expression in conjunctive or disjunctive normal form. We will begin by explaining the three steps that make up this algorithm, which consist...
Work and Mechanical Energy Summary: We will dedicate this series of classes to studying the relationship between work, energy, and some of its forms: kinetic and potential. From these analyses, we will calculate the stopping distance of a mobile that starts with an initial speed and travels until it stops....
Newton's Laws Summary: This class addresses Newton's laws and their role in the dynamics of bodies. It explores how mass and velocity determine linear momentum and describes the three laws: inertia, which maintains the state of motion in the absence of external forces, the relationship between force and acceleration, and...
Variational Calculus in Classical Mechanics and the Euler-Lagrange Equation Abstract:In this class, we will review the derivation of the Euler-Lagrange equation of Analytical Mechanics through the use of variational calculus techniques, and from this, we will show in detail its application in solving the Brachistochrone problem. Learning Objectives: By the...
Limit at Infinity: Definitions and Examples Summary: This class will cover limits at infinity, describing the behavior of as tends to infinity. Basic limits like and are explained, along with algebraic properties similar to those of finite limits. Learning Objectives: By the end of this class, the student will be...
Infinite Limits and Divergence Summary: In this class, we will address infinite limits and the different types of divergence in limits, exploring fundamental concepts to understand how certain functions do not converge to a defined real value. We will review disparate lateral limits, infinitely oscillating functions, and situations where limits...
