Taught by Mr. Walstein, Analysis II is the continuation of the calculus learned in Analysis I. It is also known as Multivariable Calculus and Differential Equations. Non-Magnet students may also take this course if they have scored a 4 or 5 on the A.P. Calculus Exam. It is a two-semester course.

Topics include:

• Vectors and Analytic Geometry
  • Vectors in a Plane
  • Rectangular Coordinate System in Three Dimensions
  • Vectors in Space
  • The Dot and Cross Products
  • Parametric Equations in Space
  • Planes
  • Cylinders and Surfaces of Revolution
  • Quadric Surfaces
• Vector-Valued Functions
  • Definitions
  • Limits, Derivatives, and Integrals
  • Motion
  • Curvature
  • Tangential and Normal Components of Acceleration
  • Kepler's Laws
• Partial Differentiation
• Functions of Several Variables
• Limits and Continuity
• Partial Derivatives
• Increments and Differentials
• The Chain Rule
• Directional Derivatives and Gradients
• Tangent Planes and Normal Lines to Surfaces
• Extrema of Functions of Several Variables
• LaGrange Multipliers
• Multiple Integrals
  • Double Integrals
  • Evaluation of Double Integrals
  • Areas and Volumes
  • Moments and Center of Mass
  • Double Integrals in Polar Coordinates
  • Triple Integrals
  • Applications of Triple Integrals
  • Triple Integrals in Cylindrical and Spherical Coordinates
• Vector Analysis
  • Vector Fields
  • Line Integrals
  • Independence of Path
  • Green's Theorem
  • Surface Integrals
  • The Divergence Theorem
  • Stokes' Theorem
  • Transformation of Coordinates
  • Change of Variables in Multiple Integrals
• More Differential Equations
  • Review of First Order Differential Equations
  • Higher Order Linear Differential Equations
  • Series Solutions of Differential Equations
  • Applications