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Calculus

A system of rules used for the evaluation and analysis of functions.

Amazon: Calculus

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Differentiation

Differentiation Basics

Differentiation Gradients Limits Derived Function Notation Kindle : Basic Differentiation

First Principles

First Principles xⁿ Kindle : First Principles

Differentiation Examples

xⁿ axⁿ Sums (x + a)^n (ax + b)^n Chain Rule Product Rule Quotient Rule Trig Logs & Exponentials Rectilinear Motion Optimisation

Sketching & Tangents

Tangents Stationary Points Maxima & Minima using 2nd derivative Critical Points Closed Intervals curve sketching Graphing Derived Functions

Further Differentiation

Extrema Approximating Roots Formulae Table of derived functions
Differential Equations

Differential Equations

Overview First‑Order Second‑Order Applications

Motion & Higher Derivatives

Rectilinear Motion Higher Derivatives
Integration

Integration Basics

Integral Calculus Indefinite Integrals Basic Rules (ax + b)ⁿ Infinite Integrals Kindle: Basic Integration

Integration & Graphs

Areas of Graphs Definite Integrals Fundamental Theorem Area Between Graphs

Further Integration

eˣ, 1/x, sec²xIntegration by substitution Volumes of RevolutionInverse trig functions Velocity & Acceleration Integration by Parts Standard Integrals Kindle : Quick 40