Calculus I - Math 171 - Lecture Notes

# Calculus 1 - Lecture Notes & Resources

### Steve Kifowit - Prairie State College - Math 171

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 - Related rates --- Notes

Lecture 18 - Extreme values on closed, bounded intervals --- Notes, Slides

Lecture 19 - Rolle's theorem and the Mean Value Theorem --- Notes, Slides, GeoGebra Applet

Lecture 20 - First derivative test --- Notes, Slides

Lecture 21 - Second derivative test --- Notes, Slides

Lecture 22 - Limits at infinity --- Notes, Slides, Clicker

Lecture 23 - Curve sketching --- Notes

Lecture 24 - Optimization --- Notes

Lecture 25 - Linearizations --- Notes, Slides

Lecture 26 - Newton's method --- Notes, Slides, Maxima, Programs

Lecture 27 - Differentials --- Notes, Slides

Lecture 28 - Antiderivatives and indefinite integrals --- Notes, Slides

Lecture 29 - Area, lower sums, and upper sums --- Notes, Slides, GeoGebra applet (new tab), Wolfram MathWorld (new tab)

Lecture 30 - Riemann sums and the definite integral --- Notes, Slides, Maxima, Programs, GeoGebra applet (new tab), Wolfram MathWorld (new tab)

Lecture 31 - Properties of the definite integral --- Notes, Slides

Lecture 32 - The 1st Fundamental Theorem of Calculus --- Notes, Slides

Lecture 33 - Integration by substitution --- Notes, Clicker

Lecture 34 - Area between curves --- Notes

Lecture 35 - The trapezoid rule --- Notes, Slides, Maxima, Programs

Lecture 36 - Simpson's rule --- Slides, Maxima, Programs

Lecture 37 - Volume by the disk method

Lecture 38 - Volume by cross section

Lecture 39 - Volume by the shell method

Lecture 40 - The 2nd Fundamental Theorem of Calculus

Lecture 41 - Center of mass in 1-D

Lecture 42 - Center of mass in 2-D

Last updated October 16, 2015.