Multivariable Differential Calculus

Multivariable Functions

• Video on Finding & Sketching Domain of Multivariable Functions (Patrick JMT)
• Video on Domain of a Vector Function  (Patrick JMT)
• Notes on 3D Coordinate Space - Distance, Graphs  (Paul's Online Notes)
• Notes on Equation of a Line in 3D Space - Introduction to Vectors (Paul's Online Notes)
• Notes on Functions of Several Variables - Domain, Level Curves  (Paul's Online Notes)
• Notes on Equation of a Plane  (Paul's Online Notes)
• Notes on Equations of Quadratic Surfaces (Paul's Online Notes)
• Notes on Limits & Continuity  (Paul's Online Notes)

 Partial Derivatives & Implicit Differentiation

• Videos on Two Variable Functions, Level Curves, Partial Derivatives, Optimization Problems & the Second Derivative Test  (MIT)
• Notes on Partial Derivatives & Implicit differentiation (Paul's Online Notes)
• Notes on Interpretation of Partial Derivatives (Paul's Online Notes)
• Videos on Partial Derivatives (Khan Academy)
• Video on Partial Derivatives (Patrick JMT)
• Video on Implicit Differentiation - Multivariable Functions (Patrick JMT)
• Video on Partial Derivatives (integralCALC)

 Higher Order Partial Derivatives

• Notes on Higher Order of Partial Derivatives (Paul's Online Notes)
• Video on Higher Order Partial Derivatives (Patrick JMT)
• Video on 2nd Order Partial Derivatives (integralCALC)
• Video on Generalized Chain Rule (Patrick JMT)

 Directional Derivatives, Tangent Planes & Gradient Vectors

• Notes on Directional Derivatives  (Paul's Online Notes)
• Video on the Directional Derivative (Patrick JMT)
• Video on Directional Derivatives  (integralCALC)
• Notes on Tangent Planes  (Paul's Online Notes)
• Notes on Gradient Vector, Tangent Planes, Normal Lines  (Paul's Online Notes)
• Videos on Gradients (Khan Academy)
• Video on the Gradient Vector (Patrick JMT)
• Video on Gradient Vectors  (integralCALC)
• Videos on Chain Rule, Gradient & Directional Derivatives  (MIT)

 Local & Absolute Extrema

• Notes on Relative Extrema - Max, Min, Saddle  (Paul's Online Notes)
• Video on Local Max & Min - Multivariable Function (Patrick JMT)
• Notes on Absolute Extrema - Max, Min,(Extreme Value Theorem)  (Paul's Online Notes)
• Video on Absolute Max & Min - Multivariable Function (Part 1 of 2) (Patrick JMT)
• Video on Global Extrema in Two Variables (integralCALC)

 Lagrange Multipliers

• Notes on Lagrange Multipliers  (Paul's Online Notes)
• Video on Lagrange Multipliers (Patrick JMT)
• Video on Lagrange Multipliers with 2 Constraints (Part 1 of 2) (Patrick JMT)
• Video on Lagrange Multipliers (Part 1 of 2) (integralCALC)
• Videos on Lagrange Multipliers & Constrained Differentials  (MIT)