Analysis and Numerical Analysis of Some Properly and Improperly Posed Problems in Applied Mathematics

1988 ◽  
Author(s):  
Howard A. Levine
Keyword(s):  
Numerical Analysis ◽  
Applied Mathematics ◽  
Improperly Posed Problems

Numerical Analysis: Pure or Applied Mathematics?

Science ◽  
1965 ◽  
Vol 149 (3688) ◽  
pp. 1049-1050
Author(s):  
Jerome Rothstein
Keyword(s):  
Numerical Analysis ◽  
Applied Mathematics

Numerical Analysis: Pure or Applied Mathematics?

Science ◽  
1965 ◽  
Vol 149 (3688) ◽  
pp. 1049-1050
Author(s):  
J. Rothstein
Keyword(s):  
Numerical Analysis ◽  
Applied Mathematics

Numerical Analysis for Applied Mathematics, Science and Engineering

1989 ◽  
Vol 73 (466) ◽  
pp. 354
Author(s):  
D. W. Arthur ◽  
D. Greenspan ◽  
V. Casulli
Keyword(s):  
Numerical Analysis ◽  
Applied Mathematics ◽  
Science And Engineering

scholarly journals Teaching and Learning Numerical Analysis and Optimization: A Didactic Framework and Applications of Inquiry-based Learning

2018 ◽  
Vol 8 (1) ◽  
pp. 42
Author(s):  
Pantelis Z. Lappas ◽  
Manolis N. Kritikos
Keyword(s):  
Higher Education ◽  
Numerical Analysis ◽  
Scientific Inquiry ◽  
Teaching And Learning ◽  
Concept Maps ◽  
Applied Mathematics ◽  
Cognitive Tools ◽  
Cognitive Tool ◽  
Inquiry Based Learning ◽  
Considerable Potential

The main objective of this paper is to propose a didactic framework for teaching Applied Mathematics in higher education. After describing the structure of the framework, several applications of inquiry-based learning in teaching numerical analysis and optimization are provided to illustrate the potential of the proposed framework. The framework is based on the Process of Scientific Inquiry (PoSI), while it consists of three pillars, each characterized by the use of a particular cognitive tool: Algorithm for presenting a list of steps to follow in order to solve a problem, CMAP software for constructing concept maps and MATLAB software for computer programming. In addition to this, a WebQuest Scenario can be used as an “auxiliary” cognitive tool by providing students with the opportunity to combine technology (e.g., MATLAB and CMAP software) with educational concepts (e.g., optimization), and to incorporate inquiry-based learning (i.e., PoSI). Introducing these cognitive tools to the design of the proposed didactic framework provides considerable potential of knowledge consolidation with reference to solving complex numerical problems using efficient algorithms.

4. Do you know the way to solve equations? Spinning tops and chaotic rabbits

2018 ◽  
pp. 48-69
Author(s):  
Alain Goriely
Keyword(s):  
Numerical Analysis ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Numerical Solution ◽  
Applied Mathematics ◽  
Scientific Models ◽  
Henri Poincaré ◽  
Principal Tool ◽  
The Difference ◽  
The Way

In applied mathematics it is of the greatest importance to solve equations. These solutions provide information on key quantities and allow us to give specific answers to scientific problems. ‘Do you know the way to solve equations? Spinning tops and chaotic rabbits’ describes the ways to solve equations and differential equations, outlining the key work of mathematicians Sofia Kovalevskaya, Pierre-Simon Laplace, Paul Painlevé, and Henri Poincaré, whose discovery led to the birth of the theory of chaos and dynamical systems. The difference between an exact and a numerical solution is also explained. Numerical analysis has become the principal tool for querying and solving scientific models.

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