Inverse Problems: Activities for UndergraduatesCambridge University Press, 2 dic 1999 - 222 pagine Problem solving in mathematics is often thought of as a one way process. For example: take two numbers and multiply them together. However for each problem there is also an inverse problem which runs in the opposite direction: now take a number and find a pair of factors. Such problems are considerably more important, in mathematics and throughout science, than they might first appear. This book concentrates on these inverse problems and how they can be usefully introduced to undergraduate students. A historical introduction sets the scene and gives a cultural context for what the rest of the book. Chapters dealing with inverse problems in calculus, differential equations and linear algebra then follow and the book concludes with suggestions for further reading. Whatever their own field of expertise, this will be an essential purchase for anyone interested in the teaching of mathematics. |
Sommario
INTRODUCTION TO INVERSE PROBLEMS | 1 |
INVERSE PROBLEMS IN PRECALCULUS | 25 |
3 | 33 |
6 | 44 |
INVERSE PROBLEMS IN CALCULUS | 69 |
5 | 84 |
INVERSE PROBLEMS IN DIFFERENTIAL EQUATIONS | 91 |
INVERSE PROBLEMS IN LINEAR ALGEBRA | 133 |
Altre edizioni - Visualizza tutto
Parole e frasi comuni
Activities Algebra angle approximation assume Background ball body cable Calculation called central centroid function coefficient Computation concentration condition Consider constant corresponding Course curve density depth derivative determining difference differential equations direct problem discrete distance drain earth effect elementary elevation equal equation estimate Exercise falling Figure Find fixed flow force function given gives gravitational heat hence horizontal initial Inputs integral interest Introduction inverse problem known Level linear mass Mathematical MATLAB matrix measurements method module motion natural Newton's Notes object observations obtained orbit origin parabolic parameters physical plane plot positive possible problem of determining Problem Show Problem Suppose projectile projection Question range reflected relationship resistance respectively result satisfies seconds shape shot simple solution solved square surface temperature unique unit values vector velocity vertical weight weight distribution