カテゴリー 全て - equations - differentiation - functions - integration

によって David Kedrowski 14年前.

285

MAT.126 Overview

This course provides a comprehensive introduction to the foundational concepts of calculus, emphasizing the preparation needed for higher-level calculus courses. It begins with an exploration of functions and their graphical representations, including linear models and rates of change.

MAT.126 Overview

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