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

Optional Lecture - Curve sketching --- Notes

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

Optinal Lecture - Area between curves --- Notes

Lecture 37 - Integrals resulting in exponential, logarithmic, or inverse trigonometric functions --- Notes

---

Last updated December 28, 2020.