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School: Austin College
Functions of Several Variables You can use level curves or contour curves to graph a function of 3 variables. Just set z = C, a constant. Pick several values of C and visualize the curve from these level curves. If z = C intersects z x, y , the conto
School: Austin College
1. A vector function is a function that assigns to each x a vector r. Just like a regular function assigns a point. 2. A vector function can be represented by a space curve. A space curve is just a plane curve in 3 dimensions. (A vector function can
School: Austin College
If the statement of the problem uses terms you aren't entirely comfortable with, translate it into simpler language, or even paraphrase the problem in regular English. For example, a statement about the linearity of the derivative might be shortened to "t
School: Austin College
Course: Diff Eq
~1~ Electrostatics Experiment 2 Scott Grzyb Janua ry 27, 2011 Engineering Physics I I (2426-004) John A. Under wood ~2~ ~3~ I. Objective: Method: 1. The first thing we did was measured the voltage of the emf, or in this case, a 6 volt lead/acid battery (F
School: Austin College
Course: Diff Eq
Voltage (v) Current (I) Time (t) Resistance () measured value 6.25 6.28E-03 20.02 993 Uncertainty(+/-) 0.01 5.00E-06 0.01 0.5 Relative Uncertainty (%) 0.08 0.08 0.02 0.05
School: Austin College
Course: Diff Eq
~1~ Electrostatics Experiment 2 Scott Grzyb January 27, 2011 Engineering Physics II (2426-004) John A. Underwood ~2~ ~3~ I. Objective: During this experiment, we will observe the effects of static electricity. We will also investigate induced charge distr
School: Austin College
Course: Diff Eq
~1~ Electric Field Plotting Experiment Experiment 3 Scott Grzyb February 03, 2011 Engineering Physics II (2426-004) John A. Underwood ~2~ ~3~ I. Objective: The objective of this experiment is to successfully map the field lines of three different electrod
School: Austin College
Course: Diff Eq
Lab 3 Electric Field Plotting Experiment Instructions: This experiment involves the calculation of the electric field pattern around and between a pair of metal electrodes of various shapes, embedded in a semi-conductive sheet medium to facilitate measure
School: Austin College
Course: Diff Eq
~1~ Capacitance Lab Testing Q=CV Experiment 4 Scott Grzyb Februa ry 10, 2011 Engineering Physics I I (2426-004) John A. Under wood ~2~ ~3~ I. Objective: In this experiment we will study and observe the relationship between Capacitance, Voltage, and Charge
School: Austin College
Course: Diff Eq
PART 1 Separation (mm) 2 Voltage vs distance Voltage (v) 6 12 18 24 55 50 45 40 separation (mm) 4 PART 2 Separation (cm) 0.17 0.25 0.33 0.5 PART 3 Voltage (v) 3000 2000 1000 Voltage (v) 6 12 18 24 Voltage (v) 35 30 25 20 1 3 4 5 6 8 Voltage (v) 6 7.5 9 10
School: Austin College
Functions of Several Variables You can use level curves or contour curves to graph a function of 3 variables. Just set z = C, a constant. Pick several values of C and visualize the curve from these level curves. If z = C intersects z x, y , the conto
School: Austin College
15.1 Functions of Several Variables We write a function of 2 variables as f x, y = z. Ex. Let f x, y = 9 x2 4 y2 f 2, 1 = 1 Domain: All x, y R such that x2 4 y2 9 (all points on or inside the ellipse x2 4 y2 = 9). Operations of functions with 2 varia
School: Austin College
Kepler's Laws: 1. A planet revolves around the sun in an elliptical orbit with the sun at one focus. 2. A line joining the sun to a planet sweeps out equal areas in equal times. 3. The square of the period of revolution of a planet is proportional to
School: Austin College
f F t = f F t = f t F t (scalar function times vector function) F x G t =F t xG t F G t = blah blah blah.all operations pretty much work You can even stick limits on both sides. Continuity is defined the same way as before. Thm 14.2.3: If the nonzer
School: Austin College
1. A vector function is a function that assigns to each x a vector r. Just like a regular function assigns a point. 2. A vector function can be represented by a space curve. A space curve is just a plane curve in 3 dimensions. (A vector function can
School: Austin College
If s is scalar, s = s Proving iff statement: two vectors v+w are orthogonal iff v w = 0. 1. Assume v+w are orthogonal. Then angle between them, , is 2. So v w = v w cos 2 = = 0. w cos = 0. Since v+w are nonzero, v ie. the vectors are orthogonal. 0 an
School: Austin College
Functions of Several Variables You can use level curves or contour curves to graph a function of 3 variables. Just set z = C, a constant. Pick several values of C and visualize the curve from these level curves. If z = C intersects z x, y , the conto
School: Austin College
1. A vector function is a function that assigns to each x a vector r. Just like a regular function assigns a point. 2. A vector function can be represented by a space curve. A space curve is just a plane curve in 3 dimensions. (A vector function can