Curriculum Overview

Calculus Subject Catalog

A structured path through the mathematical foundations of change, from foundational limits to complex differential equations.

01 Pre-calculus Foundations

Review of functions, trigonometry, and essential algebra for calculus.

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02 Limits and Continuity

The formal definition of limits and the criteria for continuous functions.

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03 Differentiation

Master the mechanics of derivatives, power rules, and chain rules.

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04 Applications of Differentiation

Optimization problems, curve sketching, and related rates.

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05 Integration

Understanding anti-differentiation and the Fundamental Theorem of Calculus.

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06 Applications of Integration I

Area between curves and volumes of revolution.

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07 Techniques of Integration

Integration by parts, trigonometric substitution, and partial fractions.

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08 Applications of Integration II

Arc length, surface area, and applications to physics.

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09 Differential Equations

Solving first-order differential equations and modeling growth.

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10 Parametric & Polar Coordinates

Calculus in parametric equations and polar coordinate systems.

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11 Infinite Sequences and Series

Convergence tests, Taylor series, and Maclaurin series.

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12 Vectors and Space Geometry

Dot products, cross products, and lines/planes in 3D space.

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13 Vector-Valued Functions

Calculus of vector functions, motion in space, and curvature.

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14 Partial Derivatives

Functions of several variables, gradients, and Lagrange multipliers.

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15 Multiple Integrals

Double and triple integrals in rectangular, polar, and spherical coordinates.

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16 Vector Calculus

Vector fields, line integrals, Green's Theorem, and Stokes' Theorem.

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17 Advanced Differential Equations

Second-order linear equations and non-homogeneous systems.

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