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Calculus I (MAT 131-770) Syllabus and Topical Outline – Study Guide

Study Guide - Learn with Videos

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Introduction to Limits

Finding Limits Algebraically

Continuity

Tangent Lines and Derivatives

Derivatives as Functions

Basic Rules of Differentiation

Product and Quotient Rules

Derivatives of Trig Functions

The Chain Rule

Implicit Differentiation

Related Rates

Linearization

Differentials

Intro to Extrema

The First Derivative Test

Concavity

The Second Derivative Test

Curve Sketching

Applied Optimization

Antiderivatives

Indefinite Integrals

Estimating Area with Finite Sums

Riemann Sums

Introduction to Definite Integrals

Fundamental Theorem of Calculus

Substitution

Area Between Curves

Introduction to Trigonometric Functions

Inverse Trigonometric Functions

Derivatives of Inverse Trigonometric Functions

Separable Differential Equations