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Multivariable Calculus

Thinking About Multivariable Functions

Visualizing Scalar-Valued Functions

Introduction to 3D Graphs

Introduction to 3D Graphs.png

Interpreting Graphs with Slices

Interpreting Graphs with Slices.png

Contour Plots

Contour Plots.png

Visualizing Vector-Valued Functions

Parametric Curves

Parametric Curves.png

Parametric Surfaces

Parametric Surfaces.png

Vector Fields Introduction

Vector Fields Introduction.png

3D Vector Fields Introduction

3D Vector Fields Introduction.png

Derivatives of Multivariable Functions

Partial Derivatives

Graphical Understanding of Partial Derivatives

Graphical Understanding of Partial Deriv

Gradient and Directional Derivatives

Gradient and Graphs

Gradient and Graphs.png

Gradient and Contour Maps

Gradient and Contour Maps.png

Directional Derivatives and Slope

Directional Derivatives and Slope.png

Differentiating Parametric Curves

Vector Valued Functions Differentiation

Vector Valued Functions Differentiation.

Multivariable Chain Rule

Multivariable Chain Rule

Multivariable Chain Rule.png

Partial Derivatives of Vector-Valued Functions

Partial Derivative of a Parametric Surface

Partial Derivative of a Parametric Surfa

Partial Derivatives of Vector Fields

Partial Derivatives of Vector Fields.png

Divergence & Curl

Divergence and Curling of Vector Fields

Divergence and Curling of Vector Fields.

Laplacian

The Laplacian

The Laplacian.png

Jacobian

The Jacobian Matrix

The Jacobian Matrix.png

The Jacobian Determinant

The Jacobian Determinant.png

Applications of Multivariable Derivatives

Tangent Planes and Local Linearization

Tangent Planes

Tangent Planes.png

Local Linearization

Local Linearization.png

Quadratic Approximations

Quadratic Approximation

Quadratic Approximation.png

Integrating Multivariable Functions

Line Integrals for Scalar Functions

Introduction to the Line Integral

Introduction to the Line Integral.png

Line Integrals in Vector Fields

Line Integrals and Vector Fields

Line Integrals and Vector Fields.png

Double Integrals

Double Integrals

Double Integrals.png

Double Integrals Over Non-Rectangular Regions I

Double Integrals Over Non-Rectangular Re

Double Integrals Over Non-Rectangular Regions II

Double Integrals Over Non-Rectangular Re

Triple Integrals

Triple Integrals

Triple Integrals.png

Surface Integrals

Surface Integrals

Surface Integrals.png

The Archimedes Method of Exhaustion.png

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