Multivariate Calculus - Stewart

Surya, Jul 27, 2021

Table of Contents

  1. Chapter 12 Vectors and the Geometry of Space
    1. Vectors
    2. Planes, Cylinders, and Quadric Surfaces
  2. Chapter 13 Vector Functions
    1. Arc Length of a Curve (2D and 3D)
    2. Curvature of a 3D Curve
    3. Arc Length of a Curve (2D and 3D)
    4. Curvature, Tangent, Normal, and Binormal Vectors
    5. Position, Velocity, and Acceleration Vectors of a moving particle
  3. Chapter 14 Partial Derivatives
    1. 14.1 Level Curves and Contour Map
    2. Geometric Meaning of Partial Derivatives
    3. Tangent Plane Approximation
    4. 14.6 Directional Derivative and Gradient Vector
    5. 14.7 Maximum and Minimum Values
    6. 14.8 Lagrange Multipliers Method of Optimization.
    7. Lagrange's Multiplier Method: An example
  4. Chapter 15 Multiple Integrals
    1. Parametric Curves in 2D and 3D
    2. Double Integrals over a Rectangle
    3. 15.5 Computing Surface Area
  5. Chapter 16 Vector Calculus
    1. Graph the Line

1.

Chapter 12 Vectors and the Geometry of Space

  • 1. Vectors
  • 2. Planes, Cylinders, and Quadric Surfaces

1.1.

Vectors

– Surya

1.2.

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2.

Chapter 13 Vector Functions

  • 1. Arc Length of a Curve (2D and 3D)
  • 2. Curvature of a 3D Curve
  • 3. Arc Length of a Curve (2D and 3D)
  • 4. Curvature, Tangent, Normal, and Binormal Vectors
  • 5. Position, Velocity, and Acceleration Vectors of a moving particle

2.1.

Arc Length of a Curve (2D and 3D)

[size=100][size=150][b][color=#980000][size=200]Type in parametric equations (in terms of t) of any curves . [br]You can also change starting point (lower t) and the ending point (upper t) in the curve . The default values are t=0 to t=6.28. You can type in any numbers from -20 to 20. [br]Two sketch 2D curves, type 0 for z. [br]The integral represents the arc length formula of the curve from point A to B. [br]You can verify the answers by hand calculation. [/size][/color][/b][/size][/size]
– Surya

2.2.

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2.3.

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2.4.

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2.5.

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3.

Chapter 14 Partial Derivatives

  • 1. 14.1 Level Curves and Contour Map
  • 2. Geometric Meaning of Partial Derivatives
  • 3. Tangent Plane Approximation
  • 4. 14.6 Directional Derivative and Gradient Vector
  • 5. 14.7 Maximum and Minimum Values
  • 6. 14.8 Lagrange Multipliers Method of Optimization.
  • 7. Lagrange's Multiplier Method: An example

3.1.

14.1 Level Curves and Contour Map

Level Curves
We consider functions of two variables of the form [math]z=f(x,y)[/math]. The domain of z is the set of all [math](x,y)[/math] in the xy-plane for which [math]f(x,y)[/math] is defined. [br]The graph of [math]z[/math] is a surface in 3D. You can sketch the graph of any function by typing in the box below. [br][br]Definition:- The level curves of a function f of two variables are the curves with equations [math]f(x,y)=k[/math], where [math]k[/math] is a constant (in the range of f). [br] A level curve f(x,y)= = k is the set of all points in the domain of f at which f takes on the given value k. [br] In other words, it is a curve in the xy-plane that shows where the graph of f has height k (above or [br] below the xy-plane).[br]You can sketch these level curves by typing their equations in the given boxes. [br]A collection of level curves is called a contour map. [br][br]
– Surya

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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4.

Chapter 15 Multiple Integrals

  • 1. Parametric Curves in 2D and 3D
  • 2. Double Integrals over a Rectangle
  • 3. 15.5 Computing Surface Area

4.1.

Parametric Curves in 2D and 3D

– Surya

4.2.

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4.3.

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5.

Chapter 16 Vector Calculus

  • 1. Graph the Line

5.1.

Graph the Line

Drag points A and B so the line matches the equation.
– Steve Phelps

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