Multivariable Analysis - Winter 2012

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Date Assignment Description
Tues, 11/27 HW 27 Functions of several variables
Wed, 11/28 HW 28 Delta-epsilon definition of a limit in R^2
Thurs, 11/29 HW 29 Delta-epsilon limit proofs for linear and quadratic functions
Fri, 11/30 HW 30 Multivariable limits: delta-epsilon proof, examples of non-existant limits
Mon, 12/3 HW 31 Partial derivatives, including higher order derivatives; Clairaut's theorem
Wed, 12/5   HW Q&A
Thurs, 12/6 HW 32 Implicit partial derivatives; tangent planes
Fri, 12/7 HW 33 Differentials; introduction to the chain rule
Mon, 12/10 HW 34 Chain rule; implicit function theorems
Tues, 12/11 HW 35 Directional derivatvies; definition of the gradient
Wed, 12/12 HW 36 Relationships between the gradient and directional derivatives and level curves
Thurs, 12/13   Review
Mon, 12/17   Test - Unit 5
Tues, 12/18 HW 37 Finding tangent planes and normal lines with the gradient
Wed, 12/19   Happy holidays!
Mon, 1/7 HW 38 Local extrema; second derivatives test
Tues, 1/8 HW 39 Absolute extrema
Thurs, 1/10   More discussion of absolute extrema
Fri, 1/11 HW 40 Lagrange multipliers
Mon, 1/14 HW 41 Lagrange multipliers with 2 constraints
Tues, 1/15   HW Q&A, including lots of discussion of how to solve non-linear systems of equations
Wed, 1/16 HW 42 Introduction to double integrals, including Riemann sum approximations
Thurs, 1/17   Review
Tues, 1/22   Test - Unit 6
Wed, 1/23 HW 43 Iterated integrals; Fubini's Theorem
Thurs, 1/24 HW 44 Double integrals over general regions
Fri, 1/25 HW 45 HW Q&A; started discussion of integrals with polar coordinates
Mon, 1/28 HW 46 Evaluating double integrals with polar coordinates
Tues, 1/29   HW Q&A; discussion of torque and balance point for discrete masses
Thurs, 1/31 HW 47 Center of mass
Fri, 2/1   HW Q&A (shortened class due to special speaker)
Wed, 2/6 HW 48 Triple integrals
Thurs, 2/7   HW Q&A (senior night)
Fri, 2/8 HW 49 Cylindrical coordinates: definition and use in integrals
Mon, 2/11 HW 50 Spherical coordinates: definition and conversion formulas
Wed, 2/13 HW 51 Integrals with spherical coordinates
Thurs, 2/14   HW Q&A
Fri, 2/15 HW 52 More HW Q&A; definition of the Jacobian of a transformation
Mon, 2/18 HW 53 Evaluating multiple integrals using a change of variables
Tues, 2/19   HW Q&A
Wed, 2/20   Review
Fri, 2/22   Test - Unit 7
Mon, 2/25 HW 54 Vector fields, including conservative vector fields
Tues, 2/26   Parametrizing a line segment (power outage)
Wed, 2/27   HW Q&A
Thurs, 2/28   Alhambra

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