Find All Critical Points & Determine Each Critical Points Type & Stability Exercise
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7838383992123 
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Essay/Research Paper 
Writer Level 
Masters 
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APA/Harvard/MLA 
Citations 
4 
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620 
Find All Critical Points & Determine Each Critical Points Type & Stability Exercise
Find all critical points and determine each critical points type and stability
1.dx/dt = 8x2x^2y^4 , dy/dt= 8y+yx^3
 dx/dt = 2x5y , dy/dt= x2y
 MATH 533 Heliocentric vs Geocentric Solar System Keplers Laws Essay
 Heliocentric vs. geocentric solar system, Kepler’s laws, Inductive reasoning and Galileo
 Analytic geometry and deductive reasoning: Descartes and Fermat—What purpose does coordinate geometry have for Descartes, and what relationship does it have with geometric construction and problemsolving? How does it relate to his Method?
 Indivisibles: Galileo’s paradoxes of the infinite, Cavalieri’s principle
 Was there any work before Newton and Leibniz about finding equations of tangent and normal lines to curves? or about quadrature (areas under curves)? If so, why do we credit Newton and Leibniz with the discovery of calculus instead of Isaac Barrow and some of these other folks?
 Isaac Newton’s method of fluxions, fluents, moments
 Newton’s Principia Mathematica—What is it about, why is it important, how does it differ from his earlier version of calculus with fluxions?
 G.W. Leibniz’s infinitesimals—How are these different from indivisibles? How are they different from Newton’s infinitesimals? What complaints do some contemporaries have about them?
 Who are some folks who applied calculus ideas in the early 1700s and what is an example of how they did?
 Why are power series important in the development of calc? Why was it important that Euler’s work with infinite series and analysis was so formal and symbolic? How does this influence Lagrange’s development of calculus?
 How does the idea of function change between 1700 and 1850?
 Why does each of the following examples of 19thcentury mathematics reflect a crisis of the Enlightenment perspective of the previous century? How did things not work quite so smoothly as previously thought? Examples:
o Fourierseries
o Insolvabilityof5thdegreepolynomials,andofthe3toughGreekconstructionproblems o NonEuclideangeometry(whatisthis,whodowecreditwithitsdiscovery,andwhydoes
it reflect a change of perspective?)
o Infinitesimalsgetreplacedbylimits(when,bywho?)
 What is set theory and how does it relate to the axiomatization of mathematics? Who are the characters in that story?
 What are formalism, platonism, intuitionism, and logicism? More specifically:
o Whywereintuitionists(constructivists)opposedtoCantor’sideasaboutinfinitesets? o Whatareacoupleimportantmathematicalideaswemightnothavehadifwewereall
platonists, and why?
o HowdoGødel’sincompletenesstheoremschallengetheformalistprogram?
o Asaformalist,whydoesitmakesensethatHilbertthoughttheContinuumHypothesis
was an important question?
 Chinese math examples: counting boards, number representations and calculation methods, systems of equations, magic squares, Pythagorean theorem, Chinese remainder theorem
 Mayan math: calendars, pure base20 system vs. positional almostbase20 solar calendar system, zero
 Inca math: what were quipus for, how were numbers represented, yupanas (weird abacuses) and calculation
Score 
Evaluation Criteria 
Total score 100% 
Meets all the criteria necessary for an A+ grade. Well formatted and instructions sufficiently followed. Well punctuated and grammar checked. 
Above 90% 
Ensures that all sections have been covered well, correct grammar, proofreads the work, answers all parts comprehensively, attentive to passive and active voice, follows professor’s classwork materials, easy to read, well punctuated, correctness, plagiarismfree 
Above 75% 
Meets most of the sections but has not checked for plagiarism. Partially meets the professor’s instructions, follows professor’s classwork materials, easy to read, well punctuated, correctness 
Above 60% 
Has not checked for plagiarism and has not proofread the project well. Out of context, can be cited for plagiarism and grammar mistakes and not correctly punctuated, fails to adhere to the professor’s classwork materials, easy to read, well punctuated, correctness 
Above 45% 
Instructions are not well articulated. Has plenty of grammar mistakes and does not meet the quality standards needed. Needs to be revised. Not well punctuated 
Less than 40% 
Poor quality work that requires work that requires to be revised entirely. Does not meet appropriate quality standards and cannot be submitted as it is to the professor for marking. Definition of a failed grade 
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