Einstein's theory of special relativity is a fundamental theory in physics that describes the behavior of objects moving at high speeds, specifically in the absence of gravitational effects. While it is possible to understand and appreciate the key concepts of special relativity using simple mathematical reasoning, a complete and accurate mathematical treatment of the theory usually requires the use of calculus.
Calculus provides the necessary tools for dealing with quantities that change continuously, such as velocities and accelerations. Special relativity involves concepts like time dilation, length contraction, and relativistic velocities, which are best expressed and understood using calculus.
However, it is worth noting that you can gain an intuitive understanding of special relativity using basic algebraic manipulation and geometric reasoning. Concepts such as the constancy of the speed of light, time dilation, and length contraction can be explored without explicitly resorting to calculus.
To gain a deeper understanding and to make precise calculations involving relativistic effects, calculus is usually employed. Differential calculus is particularly useful for studying rates of change and understanding the behavior of quantities as they approach limits. Integral calculus helps to deal with the accumulation of small changes over time or distance.
In summary, while it is possible to grasp the core concepts of special relativity without using calculus, a more rigorous treatment and precise calculations typically require the use of calculus.