MAT.126
Overview
Preparation for Calculus
Graphs and Models
Linear Models and Rates of Change
Functions and Their Graphs
Fitting Models to Data
Limits and Their Properties
A Preview of Calculus
Finding Limits Graphically and Numerically
Evaluating Limits Analytically
Continuity and One-Sided Limits
Infinite Limits
Differentiation
The Derivative and the Tangent Line Problem
Basic Differentiation Rules and Rates of Change
Product and Quotient Rules and Higher-Order Derivatives
The Chain Rule
Implicit Differentiation
Related Rates
Differential Equations
Slope Fields and Euler's Method
Differential Equations: Growth and Decay
Logarithmic, Exponential, and Other Transcendental Functions
The Natural Logarithmic Function: Differentiation
The Natural Logarithmic Function: Integration
Exponential Functions: Differentiation and Integration
Bases Other Than e and Applications
Inverse Trigonometric Functions: Differentiation
Inverse Trigonometric Functions: Integration
Integration
Antiderivatives and Indefinite Integration
Area
Riemann Sums and Definite Integrals
The Fundamental Theorem of Calculus
Integration by Substitution
Applications of Differentiation
Extrema on an Interval
Rolle's Theorem and the Mean Value Theorem
Increasing and Decreasing Functions and the First Derivative Test
Concavity and the Second Derivative Test
Limits at Infinity
A Summary of Curve Sketching
Optimization Problems