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Single Variable Calculus I: Core Topics and Learning Outcomes

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Introduction to Limits

Finding Limits Algebraically

Continuity

Tangent Lines and Derivatives

Basic Rules of Differentiation

Product and Quotient Rules

Derivatives of Trig Functions

The Chain Rule

Implicit Differentiation

Derivatives of Exponential & Logarithmic Functions

Related Rates

Intro to Extrema

The First Derivative Test

Concavity

The Second Derivative Test

Curve Sketching

Applied Optimization

Linearization

Differentials

Antiderivatives

Indefinite Integrals

Estimating Area with Finite Sums

Riemann Sums

Introduction to Definite Integrals

Fundamental Theorem of Calculus

Substitution