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Advanced Calculus II Exam 2 Review, Study notes of Advanced Calculus

Southern Utah University (SUU)Advanced Calculus

A review for exam 2 of math 4410 advanced calculus ii, including definitions to memorize, concepts for matching, in-class and take-home questions, and resources for estimating roots and using the intermediate value theorem. Topics covered include fixed points, jacobians, linear functions, induced norms, gradients, contractions, lipschitz continuity, c 1 (g), big oh, little oh, directional derivatives, affine functions, newton's method, finding fixed points, integrals of vector-valued functions, finding jacobians, linear approximations, and calculating various norms of a matrix.

Typology: Study notes

Pre 2010

Uploaded on 08/16/2009

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koofers-user-853 🇺🇸

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Math4410AdvancedCalculusII
ReviewforExam2,whichwillbeon Friday,March10.
Inclassportion:
1. Definitionstomemorize:
a. fixedpoint
b. Jacobian
c. linearfunction
d. inducednorm
e. gradient
f. standardbasisvectors
2. Definitionsformatching:
a. contraction
b. Lipschitzcontinuous
c. C
1
(G)
d. BigOh,littleoh
e. directionalderivative
f. affinefunction
3. UseIntermediateValueTheoremtoestimatearoot.
4. Wherethingsreside,Hw17#2,5
5. Hw16#6
6. Hw15#2,6
7. Hw14#9
8. DeterminewhetherafunctionisBigOh,littleoh,neither
9. Finddirectionalderivatives
Takehomeportion:
10. UseNewton’smethod
11. Findthefixedpointsofafunction
12. Takeanintegralofavectorvaluedfunction(p317)
13. FindtheJacobian
14. Findlinearapproximations
15. 10.3#4,6
16. CalculatethevariousnormsofamatrixexcludingtheinducedEuclideannorm.
17. 10.1#5

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Download Advanced Calculus II Exam 2 Review and more Study notes Advanced Calculus in PDF only on Docsity!

Math 4410 Advanced Calculus II Review for Exam 2, which will be on Friday, March 10. In class portion:

  1. Definitions to memorize: a. fixed point b. Jacobian c. linear function d. induced norm e. gradient f. standard basis vectors
  2. Definitions for matching: a. contraction b. Lipschitz continuous c. C^1 (G) d. Big Oh, little oh e. directional derivative f. affine function
  3. Use Intermediate Value Theorem to estimate a root.
  4. Where things reside, Hw 17 #2,
  5. Hw 16 #
  6. Hw 15 #2,
  7. Hw 14 #
  8. Determine whether a function is Big Oh, little oh, neither
  9. Find directional derivatives Take home portion:
  10. Use Newton’s method
  11. Find the fixed points of a function
  12. Take an integral of a vector valued function (p317)
  13. Find the Jacobian
  14. Find linear approximations
  15. 10.3 #4,
  16. Calculate the various norms of a matrix excluding the induced Euclidean norm.
  17. 10.1 #