[PDF] Applied Mathematics - MATH-0504 Exercise statements and solutions



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Applied Mathematics - MATH-0504 Exercise statements and solutions

Consider the following problem: yu x+ xu y= 0 with u(0;y) = exp( y2) (a)Solve this problem (b)Where is the solution uniquely determined in the xy-plane? (c)Sketch the characteristic lines Solution (a)The directional derivative of ualong the vector (y;x) must be 0 As long as y6= 0 , the equation of the characteristic lines is therefore dy dx



Mathematics Scoring Rubric – Problem-Solving (M6)

Complete evidence of an appropriate strategy that leads to a correct solution Communication – 3 Gives an explanation of solution strategy that is mostly logical, organized and accurate Conversion of 1 m = 100 cm not made explicit Incorrect use of the equal sign Mathematics in Grade 6, Problem-Solving Exemplar 4 Justification



Solutions to Practice Problems

Solution A sequence fa ng1 n=1 is not a Cauchy sequence if there is a real number >0 such that for all positive integers Nthere exist n;m2N such that n;m N and ja n a mj Exercise 8 12 Let fa ng1 n=1 and fb ng 1 n=1 be two Cauchy sequences De ne c n = ja n b nj: Show that fc ng1 n=1 is a Cauchy sequence Solution Let >0 be given There exist



I-Section Européenne DNL mathématiques 2nde Problem solving

Problem solving with Polya’s strategy : You’ve got problems (I) 2nde 2012-13 Problem 1 Determine the digit in the 100 place to the right of the decimal point in the decimal representation of 27 7 Problem 2 A traffic counter is a device designed to count the number of vehicles passing along a street It usually is a thin



The Oddball Problem - Les-Mathematiquesnet

This solution, which requires different courses of action depending on the outcomes of previous weighings, is not particularly elegant or easy to remember We shall give a solution which involves a fixed course of action in all circumstances and which has the advantage of showing how this particular problem can be generalised



Existence of solutions to ODEs

value ǫ > 0, there exists a unique solution x = x(t) to the initial value problem (1) within the range [a−ǫ,a+ǫ] Charles Emile Picard (1856-1941) was a leading French mathematicia´ n



COLLEGE LEVEL MATHEMATICS PRETEST

11 One solution of the equation xx2 7 2 0 is a 7 41 2 b 7 41 2 c 7 57 2 d 7 41 2 e 7 57 2 12 What is the slope of the line shown? You may assume that each tick mark represents one unit a 2 b 1 2 c 1 d 2 e 1 2 B 8 10 A 10 C E D x y



La d marche dÕinvestigation en math matiques

Ë travers la r solution de ces probl mes, la mod lisation de quelques situations et lÕargumentation, les l ves peuvent prendre conscience petit petit de ce qu'est une v ritable activit math matique 4) Les programmes et la place des probl mes



L’enseignement et l’apprentissage par la résolution de

Solution possible: L’élève peut d’abord déterminer les nombres à 3 chiffres contenant le chiffre 8 ou un chiffre plus grand: • La quantité de nombres à 3 chiffres (100 à 999) correspond à 900; • Les nombres à 3 chiffres qui contiennent seulement le chiffre 8 (ou un chiffre plus grand, ils sont moins nombreux): 888, 889, 898,



ELLIPTIC CURVES - tomlrfreefr

Solution to Exercise 4 8 9 N´eron Models 37 Weierstrass minimal models The work of Kodaira The complete N´eron model Summary 10 Elliptic Curves over the Complex Numbers 41 Lattices and bases Quotients of Cby lattices Doubly periodic functions The holomorphic maps C=Λ C=Λ0 The Weierstrass} function Eisenstein series The field of doubly

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