Mathematics Dept

CALCULUS

The mathematical study of continuous change. The language used to describe the motion of stars, the flow of electricity, and the growth of economies.

Foundation

Limits & Continuity

lim⁡x→af(x)=L\lim_{x \to a} f(x) = L

The behavior of a function as it approaches a specific input. The bedrock upon which all calculus is built.

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Core I

Differential Calculus

ddxf(x)\frac{d}{dx}f(x)

The study of instantaneous rates of change and the slope of curves.

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Core II

Integral Calculus

∫f(x)dx\int f(x) dx

The study of accumulation, area under curves, and the reverse process of differentiation.

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Core III

Multivariate Calculus

∂f∂x\frac{\partial f}{\partial x}

Calculus extended to 3D space. Partial derivatives and multiple integrals over surfaces and volumes.

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Advanced

Vector Calculus

∇⋅F\nabla \cdot \mathbf{F}

Differentiation and integration of vector fields. Essential for electromagnetism and fluid dynamics.

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Mastery

Differential Equations

dydt=ky\frac{dy}{dt} = ky

Equations involving functions and their derivatives. The language used to model physical reality.

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Mastery Level
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"If I have seen further, it is by standing on the shoulders of giants." — Isaac Newton