Math 20C Multivariable Calculus
Lecture 21
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Double integrals on regions (Sec. 15.3)
Slide 1 Regions function of y . Regions function of x. Properties of double integrals.
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Regions functions of y
Theorem 1 (Type I) Let g0 (x), g1 (x) be two con
Math 20C Multivariable Calculus
Lecture 19
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Double integrals (Sec. 15.1 - 15.2)
Review of the integral of single variable functions. Slide 1 Denition of double integral on rectangles. Average of a function. Double integrals general domains (Sec. 15.
Print Name: TA Name: Math 20C. Final Exam June 15, 2006
Section Number: Section Time:
No calculators or any other devices are allowed on this exam. Write your solutions clearly and legibly; no credit will be given for illegible solutions. Read each questi
Name: TA Name: Math 20C. Midterm Exam 1 April 28, 2006
Section Number: Section Time:
No calculators or any other devices are allowed on this exam. Write your solutions clearly and legibly; no credit will be given for illegible solutions. Read each questio
Print Name: TA Name: Math 20C Final Exam. June 15, 2006
Section Number: Section Time:
No calculators or any other devices are allowed on this exam. Write your solutions clearly and legibly; no credit will be given for illegible solutions. Read each questi
Math 20C Multivariable Calculus
Lecture 16
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Directional derivative and gradient vector (Sec. 14.6)
Slide 1
Denition of directional derivative.
Directional derivative and partial derivatives.
Gradient vector.
Geometrical meaning of the gradient.
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Math 20C Multivariable Calculus
Lecture 1
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Coordinates in space
Slide 1
Overview of vector calculus.
Coordinate systems in space.
Distance formula. (Sec. 12.1)
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Vector calculus studies derivatives and integrals
of functions of more than one
Math 20C Multivariable Calculus
Lecture 8
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Arc length function, Examples
Slide 1
Review: Arc length of a curve.
Arc length function.
Examples Sec. 13.4.
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Arc length of a curve
The arc length of a curve in space is a number. It measures the
Math 20C Multivariable Calculus
Lecture 11
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Limits and Continuity
Slide 1
Review of Limit.
Side limits and squeeze theorem.
Continuous functions of 2,3 variables.
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Review: Limits
Slide 2
Denition 1 Given a function f (x, y) : D I 2 I and a
Math 20C Multivariable Calculus
Lecture 25
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Cylindrical and spherical coordinates
Slide 1
Review of Polar coordinates in I 2 .
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Cylindrical coordinates in I 3 .
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Spherical coordinates in I 3 .
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Exercises.
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Polar coordinates in I 2
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Sli
Math 20C Multivariable Calculus
Lecture 5
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Lines and planes
Slide 1
Equations of lines (Vector, parametric, and symmetric eqs.).
Equations of planes.
Distance from a point to a plane.
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Equations of lines
Slide 2
Denition 1 Let P0 be a point