UsefulLinks
Mathematics
Multivariable Calculus
1. Foundations of Three-Dimensional Space
2. Vector-Valued Functions and Space Curves
3. Functions of Several Variables
4. Partial Derivatives
5. Optimization of Multivariable Functions
6. Multiple Integrals
7. Vector Calculus
4.
Partial Derivatives
4.1.
Introduction to Partial Derivatives
4.1.1.
Definition of Partial Derivatives
4.1.2.
Notation for Partial Derivatives
4.1.3.
Computing First Partial Derivatives
4.1.4.
Geometric Interpretation
4.1.4.1.
Slopes of Tangent Lines
4.1.4.2.
Rate of Change
4.2.
Higher-Order Partial Derivatives
4.2.1.
Second Partial Derivatives
4.2.2.
Mixed Partial Derivatives
4.2.3.
Clairaut's Theorem
4.2.4.
Higher-Order Derivatives
4.3.
The Total Differential
4.3.1.
Definition of Differentials
4.3.2.
Linear Approximation
4.3.3.
Error Estimation
4.3.4.
Applications of Differentials
4.4.
The Chain Rule for Multivariable Functions
4.4.1.
Chain Rule with One Independent Variable
4.4.2.
Chain Rule with Multiple Independent Variables
4.4.3.
Tree Diagrams
4.4.4.
Applications of the Chain Rule
4.5.
Implicit Differentiation
4.5.1.
Implicit Functions of Two Variables
4.5.2.
Implicit Functions of Three Variables
4.5.3.
Related Rates in Multiple Variables
4.6.
Directional Derivatives
4.6.1.
Definition of Directional Derivatives
4.6.2.
Computing Directional Derivatives
4.6.3.
Properties of Directional Derivatives
4.6.4.
Maximum Rate of Change
4.7.
The Gradient Vector
4.7.1.
Definition of the Gradient
4.7.2.
Properties of the Gradient
4.7.3.
Gradient as Direction of Steepest Ascent
4.7.4.
Gradient and Level Curves
4.7.5.
Gradient and Normal Vectors
4.8.
Tangent Planes and Normal Lines
4.8.1.
Tangent Planes to Surfaces
4.8.1.1.
Equation of Tangent Plane
4.8.1.2.
Finding Tangent Planes
4.8.2.
Normal Lines to Surfaces
4.8.3.
Linear Approximation of Functions
Previous
3. Functions of Several Variables
Go to top
Next
5. Optimization of Multivariable Functions