16010 Lecture Notes

• Lesson 1: Course Information and Review

• Lesson 2: Finding Limits Numerically and Graphically, One-sided Limits

• Lesson 3: Finding Limits Analytically

• Lesson 4: Continuity

• Lesson 5: The Derivative (Limit Definition)

• Lesson 6: Basic Differentiation Rules, Derivatives of Sine/Cosine and the Natural Exponential Function

• Lesson 7: Instantaneous Rate of Change

• Lesson 8: The Product Rule

• Lesson 9: The Quotient Rule

• Lesson 10: The Chain Rule

• Lesson 11: The Chain Rule, Derivative of Natural Log

• Lesson 12: Higher Order Derivatives

• Lesson 13: Implicit Differentiation

• Lesson 14: Related Rates

• Lesson 15: Related Rates Part II

• Lesson 16: Relative Extrema and Critical Numbers

• Lesson 17: Increasing and Decreasing Functions; the First Derivative Test

• Lesson 18: Concavity, Inflection Points, and the Second Derivative Test

• Lesson 19: Absolute Extrema on an Interval

• Lesson 20: Graphical Interpretation of Derivatives

• Lesson 21: Limits at Infinity 

• Lesson 22: Curve Sketching

• Lesson 23: Optimization 

• Lesson 24: Optimization

• Lesson 25: Optimization

• Lesson 26: Antiderivatives and Indefinite Integration

• Lesson 27: Antiderivatives and Indefinite Integration

• Integral Rules 

• Lesson 28: Area and Riemann Sums 

• Lesson 29: Definite Integrals

• Lesson 30: Definite Integrals

• Lesson 31: The Fundamental Theorem of Calculus

• Lesson 32: The Fundamental Theorem of Calculus 

• Lesson 33: Numerical Integration (Trapezoid Rule)

• Lesson 34: Exponential Growth 

• Lesson 35: Exponential Decay