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Calculus I (Dr. McGuffey, MATH 141, USC)
Limits and Continuity
Limits and Derivatives
Differentiation Rules
Implicit Differentiation
Extrema and Optimization
Integration
Calculus I (Dr. McGuffey, MATH 141, USC)
Author:
Will McGuffey
Topic:
Calculus
"Daily" interactive graphs to introduce various Calculus concepts in Dr. McGuffey's Math 141 Calculus I course at University of South Carolina. Updated: Fall 2024
Table of Contents
Limits and Continuity
1-A Instantaneous Rates of Change
1-B Investigating Limits
1-B One-Sided Limits
1-C Continuity
1-D Limits of Difference Quotients
1-D Formal Definition of Limit
Limits and Derivatives
2-A The Derivative at a Point
2-B Differentiability
2-B Linearization & Differentials
2-C Derivative Function
2-D Derivatives Graphically
2-D Second Derivatives
Differentiation Rules
3-A Basics of Differentiation
3-B Product Rule
3-C Chain Rule
3-E Free Fall
3-E Simple Harmonic Oscillators
3-E Damped Oscillations
Implicit Differentiation
4-A Implicit Differentiation Examples
4-B Derivatives of Inverse Functions
4-C Related Rates (Circle Example)
4-C Related Rates Sphere
4-D Linear Approximation
Extrema and Optimization
5-A Extreme Values & Critical Points
5-B First Derivative Test
5-C Second Derivative Test
Integration
6-A Estimating Area with Riemann Sums
6-B Area and Motion
6-C Antiderivatives
Next
1-A Instantaneous Rates of Change
New Resources
Proving Triangles Congruent (2): Multi-Step Transformations
z`]]
Rolle's Theorem
以百分數比較兩個數值
Constructing the Perpendicular Line Through a Point Not on the Line
Discover Resources
Cartesian Axis
Angle between Chord and Tangent
Geometry - Basics
GeoGebra Pentominoes
Comparing fractions
Discover Topics
Division
Exponential Functions
Pythagoras or Pythagorean Theorem
Cylinder
Fractal Geometry
