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Lecture05_Vector_Functions_9-1

# Lecture05_Vector_Functions_9-1 - This unit is based on...

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1 Vector Functions ± This unit is based on Section 9.1, Chapter 9, of the textbook . ± All assigned readings and exercises are from the textbook ± Objectives : Make certain that you can define, and use in context, the terms, concepts and formulas listed below: 1. scalar and vector functions and fields 2. differentiate a vector function 3. calculate the second derivative and the integral of a vector function 4. find the limit (if it exists) of a vector function as t t o . 5. sketch the curve traced by a vector function and identify the vector function that traces a given curve. 6. identify the vector function , given its derivative . 7. apply operations of vector algebra to vector functions to form new vectors 8. determine the length of a given curve. 9. define a vector tangent to a given curve at a given point. 10. solve practical problems ± Reading : Read Section 9.1, pages 452-457. ± Exercises : Complete problems ) ( t r r ) ( t r r ) ( t r r ) ( t r r ) ( ' t r r

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2 Prerequisites ± Before starting this Section you should . . . 1. be familiar with the concept of vectors 2. be familiar with vector algebra 3. be familiar with scalar functions
3 Vector Calculus: Scalar Fields and Vector Fields ± Engineers use vector calculus to define and measure the variation of temperature, fluid velocity, force, magnetic flux etc. over all three dimensions of space. In the real 3D engineering world, one wants to know things like the stress and strain inside a structure, the velocity of the air flow over a wing, or the induced electromagnetic field inside a human body. ± A scalar field in a given region of 3D space is a scalar function defined at each point in the region, i.e. f(x,y, z) . Examples: electric potential, gravitational potential, … ± A vector field in a given region of 3D space is a vector function defined at each point in the region, v (x,y,z). Examples: electric force field, gravitational force field, … ± A field may also depend on time, i.e., temperature inside a room

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Lecture05_Vector_Functions_9-1 - This unit is based on...

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