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MA35 Labs

1 Single Variable Calculus

2 » Two Variable Calculus

3 Three Variable Calculus

Polar Coordinate Labs

Two Variable Functions

Contents

2.1 Functions of Two Variables

2.1.1 Introduction

2.1.2 Linear Functions

2.1.3 Domain, Range & Function Graphs

2.1.4 Slice Curves

2.1.5 Level Sets & Contour Lines

2.1.6 Continuity

2.1.7 Normal Vectors for Linear Function Graphs

2.2 Differentiation

2.3 More Derivatives

2.4 Integration

2.5 Vector Analysis

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Slice Curves (Page: 1 | 2 | 3 | 4 | 5 | 6 )

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We can describe a slice curve with x = x₀ as a parametric curve x(t) = x₀, y(t) = t, so f(x(t),y(t)) = f(x₀,t). Similarly the slice curve with y = y₀ can be given as (x(t),y(t),f(x(t),y(t))) = (t, y₀,f(t,y₀)).

The slice curve through (x₀,y₀) with slope m can be described as (x₀ + t. y₀ + mt, f((x₀ + t. y₀ + mt). In polar coordinates, this can be written (x₀ + tcos(θ₀), y₀ + tsin(θ₀),f(x₀ + tcos(θ₀), y₀ + tsin(θ₀), where m = tan(θ₀).

In general the slice curve over the parametric curve (x(t),y(t)) in the domain of a function f is the curve (x(t),y(t),f(x(t),y(t))).

Demos

Parametric Slice Curves
	Define an interval for t, and two functions x(t), y(t). Show this curve on the domain of the function. In another window, show (x(t), y(t), 0),(x(t), y(t), f(x(t),y(t))) and (0,0,f(x(t),y(t))), with the option of showing the "fence" connecting the first of these points to the second.