# Calculus 1 - Lecture Notes & Resources

### Steve Kifowit - Waubonsee Community College - Math 131

SageMathCell | SageMath
Quick Reference:

General or

Calculus

Lecture
1 - Review: Lines, equations, and rationalizing --

Notes,

Clicker
Lecture
2 - Review: Functions, change, and graphing -- Notes

Lecture
3 - Estimating limits graphically and numerically -- Notes, Slides,
Clicker

Lecture
4 - Finding limits analytically - Limits laws and substitution -- Notes, Slides

Lecture
5 - Finding limits analytically - Simple indeterminate forms
-- Notes,
Slides, Clicker

Lecture
6 - One-sided limits -- Notes

Lecture
7 - Continuity -- Notes,
Slides

Lecture
8 - Infinite limits --- Notes

Lecture
9 - Formal definition of limit --- Notes,
Slides,
GeoGebra
applet (new tab)

Lecture
10 - Introduction to tangent lines --- Notes,
Slides, Clicker

Lecture
11 - The limit definition of the derivative --- Notes,
Slides,
GeoGebra
applet (new tab)

Lecture
12 - Some basic differentiation rules --- Notes

Lecture 13 - Product rule and quotient rule --- Notes

Lecture 14 - Rates of change and higher-order derivatives --- Notes

Lecture 15 - Chain rule ---
Notes, Clicker

Lecture 16 - Implicit differentiation ---

Notes
Lecture 17 - Derivatives of inverse functions --- Notes

Lecture 18 - Derivatives of exponential and logarithmic functions
--- Notes

Lecture 19 - Related rates --- Notes

Lecture 20 - Linearizations --- Notes, Slides

Lecture 21 - Differentials --- Notes, Slides

Lecture 22 - Extreme values on closed and bounded intervals --- Notes, Slides

Lecture 23 - Rolle's theorem and the Mean Value Theorem --- Notes, Slides, GeoGebra
Applet (new tab)

Lecture 24 - First derivative test --- Notes,
Slides

Lecture 25 - Second derivative test --- Notes,
Slides

Lecture 26 - Limits at infinity --- Notes,
Slides, Clicker

Lecture 27 - Optimization --- Notes

Lecture 28 - L'Hopital's rule --- Notes, Slides

Lecture 29 - Newton's method --- Notes, Slides, Python code

Lecture 30 - Antiderivatives and indefinite integrals --- Notes,
Slides

Lecture 31 - Area, lower sums, and upper sums --- Notes, Slides, GeoGebra
applet (new tab), Wolfram
MathWorld (new tab)

Lecture 32 - Riemann sums and the definite integral ---

Notes,

Slides,

Python code,

GeoGebra applet
(new tab),

Wolfram MathWorld (new tab)

Lecture 33 - Properties of the definite integral ---

Notes,

Slides
Lecture 34 - The 1st Fundamental Theorem of Calculus ---

Notes,

Slides
Lecture 35 - The 2nd Fundamental Theorem of Calculus ---

Notes,

Slides
Lecture 36 - Integration by substitution ---

Notes,

Clicker
Lecture 37 - Inetgrals resulting in exponential, logarithmic, or inverse trigonometric functions ---

Notes

*Last updated June 17, 2020.*