Differential Calculus
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The Role of Integrals in Solving Differential Equations
Differential equations are at the core of mathematical modeling. They describe how things change. This could be the motion of a pendulum. It might also refer to the growth of a population. Moreover, it could mean the cooling of a metal rod. But identifying the equation is only part of the task. The real challenge…
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Unbounded limits
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Understanding Improper Integrals in Calculus
In calculus, integration is often introduced as a way to measure area under a curve. For most functions and intervals, this is straightforward. But not all mathematical problems are that well-behaved. Some functions spike to infinity. Others stretch endlessly across the number line. Standard integrals can’t handle these cases. Improper integrals can. What Are Improper…
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Gravitational potential energy – quite short
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Still struggling with the concept of Integration—watch this!
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Fundamental theorem of calculus, how it works (Animation) – short
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Definite vs Indefinite integrals – short
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Calculus: math with infinity – short
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Stress vs. Strain – short
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Stress and Strain in Engineering Materials
Differentiation in Engineering Have you ever wondered about the strength of a massive bridge stretching over a river? Or a skyscraper standing tall against the wind? How do engineers make sure these structures don’t fail under pressure? The answer lies in a powerful mathematical tool—differential calculus. Engineers use differentiation to analyze how materials behave under…