Professor's Notes

These lecture notes are provided for students in Calculus II and are based on the presentation in Smith and Minton. They guide but do not necessarily correspond exactly to the classroom presentation.

• Riemann Sums and Area
• Definite Integrals
• Numerical Integration
• Numerical Integration Errors
• Fundamental Theorem of Calculus
• Integration by Substitution
• Area Between Curves
• Volume: Slicing, Disks, and Washers
• Other Applications of Integration
• Review for Exam 1
• Review of Formulas and Techniques
• Integration by Parts
• Trigonometric Techniques of Integration
• Partial Fractions
• Vectors in the Plane and in Space
• The Dot Product
• The Cross Product
• Lines and Planes in Space
• Surfaces in Space
• Functions of Several Variables
• Partial Derivatives
• Tangent Planes and Linear Approximations
• The Chain Rule
• The Gradient and Directional Derivatives
• Extrema of Functions of Several Variables
• Double Integrals
• Area, Volume, and Center of Mass
• Double Integrals in Polar Coordinates
• Triple Integrals
• Cylindrical Coordinates
• Spherical Coordinates