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• Three-dimensional coordinate systems

  • Plotting points in three dimensions

  • Distance between points in three dimensions

  • Center, radius, and equation of the sphere

  • Describing a region in three-dimensional space

  • Using inequalities to describe the region

• Sketching graphs and level curves

  • Sketching graphs of multivariable functions

  • Matching the function with the graph and level curves

• Lines and planes

  • Vector and parametric equations of a line

  • Parametric and symmetric equations of a line

  • Symmetric equations of a line

  • Parallel, intersecting, skew and perpendicular lines

  • Equation of a plane

  • Intersection of a line and a plane

  • Parallel, perpendicular and angle between planes

  • Parametric equations for the line of intersection of two planes

  • Symmetric equations for the line of intersection of two planes

  • Distance between a point and a line

  • Distance between a point and a plane

  • Distance between parallel planes

• Cylinders and quadric surfaces

  • Reducing equations to standard form

  • Sketching the surface

  • Traces to sketch and identify the surface

• Limits and continuity

  • Domains

  • Limits

  • Precise definition of the limit

  • Discontinuities

• Partial derivatives

  • Partial derivatives in two variables

  • Partial derivatives in three or more variables

  • Second order and higher order partial derivatives

• Differentials

  • Differential of a multivariable function

• Chain rule

  • Chain rule for multivariable functions

  • Chain rule and tree diagrams

• Implicit differentiation

• Directional derivatives

  • In the direction of the vector

  • In the direction of the angle

• Linear approximation and linearization

  • Linear approximation

  • Linearization

• Gradient vectors

  • Gradient vectors

  • Gradient vectors and the tangent plane

  • Maximum rate of change and its direction

• Tangent planes and normal lines

  • Equation of the tangent plane

  • Normal line to the surface

• Optimization

  • Critical points

  • Second derivative test

  • Local extrema and saddle points

  • Global extrema

  • Extreme value theorem, extrema in the set D

• Applied optimization

  • Maximum product of three real numbers

  • Maximum volume of a rectangular box inscribed in a sphere

  • Minimum distance between the point and the plane

  • Points on the cone closest to the given point

• Lagrange multipliers

  • Two dimensions and one constraint

  • Three dimensions and one constraint

  • Three dimensions and two constraints

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By signing up for the Partial Derivatives course, you'll gain access to:

• Step-by-step videos

• Course notes and flashcards

• Practice quizzes

• Bonus practice workbooks

• Comprehensive formula sheets

• Summary study sheets

• Practice final exams

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