Slavisa Velickovic

Introduction Delving into the world of calculus can often feel like navigating a complex labyrinth. Integrals, in particular, present unique challenges that require a deep understanding of mathematical principles and innovative problem-solving techniques. This article explores solutions to intricate integral problems, providing a step-by-step guide to mastering these advanced calculations. We will tackle specific examples, … Read more

Introduction to arctan(x) and Its Derivative The inverse tangent function, arctan(x), is foundational in calculus, trigonometry, and many applied sciences. Its derivative, [arctan(x)]’ = 1/(1 + x²), often appears in integration problems, differential equations, and modeling phenomena in physics and engineering. In this blog post, we will explore two clear, step-by-step proofs and explain the … Read more

The Lambert W function is a fascinating and powerful tool in mathematics, often overlooked but invaluable for solving complex equations and optimization problems. Known as the inverse of f(x) = x e^x, it helps us tackle equations where variables appear both inside and outside exponential terms. In this blog post, we’ll dive into what the … Read more

Complex numbers – made up of real and imaginary parts – often yield surprising results when raised to imaginary powers. In this article, we explore four fascinating cases: (-1)^i The i-th root of -1 i^i The i-th root of i Remarkably, all four produce real numbers – not just one, but infinitely many – thanks … Read more

Euler’s number (or Napier’s constant), e ≈ 2.718281828459045, is one of mathematics’ most important constants. Like π, it appears in diverse fields, from finance to physics. This blog post dives into its mathematical definitions, fascinating properties, and real-world relevance. What is Euler’s Number e The number e is the base of natural logarithms and a cornerstone of … Read more

Have you ever wondered if trigonometric functions like cosine can exceed 1? In school, we’re taught that cos(θ) and sin(θ) for real angles θ always lie between -1 and 1. But what happens when we input a complex number like i (the imaginary unit)? Let’s dive into the fascinating world of complex trigonometry and uncover why cos(i) ≈ 1.543, defying traditional rules. Euler’s Formula: The Bridge to Complex Cosine To … Read more

Arithmetic progressions (AP) are a cornerstone in algebra and have widespread applications in mathematics, finance, physics, and everyday problem-solving. This post explores the fundamental concepts, key formulas, and real-life applications of arithmetic sequences, enabling you to master AP and apply it effectively. Understanding Arithmetic Progression What is an Arithmetic Progression An arithmetic progression (AP) is … Read more

Geometric progressions (GPs) are fascinating sequences of numbers where each term is obtained by multiplying the previous term by a constant value, called the common ratio. They appear in diverse real-world scenarios, from compound interest and population growth to fractal geometry and the physics of bouncing balls. Understanding geometric progressions is crucial for anyone working … Read more