MAT.126 Overview

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MAT.126 Overview

Applications of Differentiation

Optimization Problems

A Summary of Curve Sketching

Limits at Infinity

Concavity and the Second Derivative Test

Increasing and Decreasing Functions and the First Derivative Test

Rolle's Theorem and the Mean Value Theorem

Extrema on an Interval

Integration

Integration by Substitution

The Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals

Area

Antiderivatives and Indefinite Integration

Logarithmic, Exponential, and Other Transcendental Functions

Inverse Trigonometric Functions: Integration

Inverse Trigonometric Functions: Differentiation

Bases Other Than e and Applications

Exponential Functions: Differentiation and Integration

The Natural Logarithmic Function: Integration

The Natural Logarithmic Function: Differentiation

Differential Equations

Differential Equations: Growth and Decay

Slope Fields and Euler's Method

Differentiation

Related Rates

Implicit Differentiation

The Chain Rule

Product and Quotient Rules and Higher-Order Derivatives

Basic Differentiation Rules and Rates of Change

The Derivative and the Tangent Line Problem

Limits and Their Properties

Infinite Limits

Continuity and One-Sided Limits

Evaluating Limits Analytically

Finding Limits Graphically and Numerically

A Preview of Calculus

Preparation for Calculus

Fitting Models to Data

Functions and Their Graphs

Linear Models and Rates of Change

Graphs and Models