Multivariable Calculus

Review
 
Vectors
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The Dot Product
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The Cross Product
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Matrices
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Representations of Lines and Planes
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Coordinate Systems
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Coordinate Systems and Functions
 
Functions
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Graphing Functions
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Quadric Surfaces
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Cylindrical Coordinates
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Spherical Coordinates
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Topology
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Curves and Surfaces
 
Parametric Curves
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Velocity, Speed, and Acceleration
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Properties of Velocity and Speed
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The Length of a Curve
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Arclength Function
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Curvature
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Defining the Moving Frame
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Moving Frame Computations
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Decomposition of Acceleration
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Limits and Derivatives
 
Partial Derivatives
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Geometric Interpretation of Partial Derivatives
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Higher Order Partial Derivatives
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Introduction to Limits
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Evaluating Limits
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Continuity and Limits in General
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Geometry of Differentiability
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Differentiability of Functions of Two Variables
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The Gradient
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Differentiability in General
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Differentiation Properties
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Chain Rule
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Directional Derivatives
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The Gradient and Level Sets
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Implicit Curves and Surfaces
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Behavior of Functions
 
Taylor Polynomials
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Quadratic Forms
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The Hessian Matrix
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Local Extrema
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Absolute Extrema
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Optimization with Constraints
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Lagrange Multipliers
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Homework
 
Homework 1: Coordinates
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Homework 2: Graphing
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Homework 3: Parametrized Curves
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Homework 4: Arclength and Curvature
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Homework 5: Moving Frames and Acceleration
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Homework 6: Limits
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Homework 7: Partial Derivatives
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Homework 8: Differentiability
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Homework 9: Properties of Derivatives
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Homework 10: Directional Derivatives
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Homework 11: Taylor’s Theorem
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Homework 12: Extrema
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Winter Assignment: Substitution and Lagrange Multipliers
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Practice Problems
 
Practice Problems: Review
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Practice Problems: Coordinate Systems
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Overall
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