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Applications of Mathematics in Physics

Applications of Mathematics in Physics

Introduction

Mathematics is important as far as physics is concerned, but with due respect to other forms of knowledge domains. As far as physics is concerned, mathematics constitutes a large portion of its language. It is necessary to recognize this importance and make deliberate effort to sharpen physics students' mathematical knowledge needed for the moment - a moment when the mathematical knowledge appropriate to the teaching of the intended physics concept is required. Mathematics is the only subject which always demands the previous knowledge plus mathematical skills. During graduation course students are required to cope up with the algebra, equations, differential equations integration, and differentiation.

Students, who choose to ignore Mathematics, or not take it seriously, forfeit many future career opportunities that they could have. They essentially turn their backs on more than half the job market. The vast majority of university degrees require Mathematics. The importance of Mathematics for potential future careers cannot be more emphasized. Good knowledge of Mathematics and Statistics is required in the Physical Sciences (like Chemistry, Physics, and Engineering), Life and Health sciences (like Biology, Psychology, Pharmacy, and Nursing), Social Sciences (including Anthropology, Communications, Economics, Linguistics, Education, and Geography), Technical Sciences (like Computer Science, Networking, and Software development), Business and Commerce, Actuarial science (used by insurance companies) and Medicine.

Mathematics is Used in Physics

Every area of Mathematics has its own unique applications to the different career options. For example, Algebra is very important for computer science, cryptology, networking, study of symmetry in Chemistry and Physics. Calculus (including differential equations) is used in Chemistry, Biology, Physics, Engineering, the motion of water (hydrodynamics), rocket science, molecular structure, option price modeling in Business and Economics models, etc.

As the students lack a depth of mathematical competency, understanding of physics tends to be obscured by the students' attempt to understand the mathematics, which is used to develop the logical arguments that bring about understanding of the intended physics concepts, which Ausubel (1963, 1968) describes as meaningful leaning. The lack of mathematical competency could lead to an over-emphasis on qualitative methods by physics teachers. But, such an approach would necessarily be limited in scope, since certain aspects of physics explanations are rooted in and explicated through the mathematics knowledge domain (Nashon, 2006). Student opting physics have to face 2 types of material while studying.

Memory based: Definitions, descriptions e.g. Statement of Newton's laws, Description of Cathode ray oscilloscope. Even the logical thinking helps in the description with diagram.

Logical and Mathematical skills based: Derivations and Numerical problems.

E.g. proof of Gauss's theorem, derivation of expression for the Electric Intensity. The weight age given on the first part is very less as compared to the second part. Thus the student has to prepare logical mathematical base by heart.

Calculus-based Physics provides an opportunity to showcase how our attempt to understand our environment has driven a development of math to explain the relationships. Most students in this sequence progress through Introduction to Physics and Calculus simultaneously. Trust me, the classes really do compliment each other and will set the foundation for the type of studies involved in advance courses in almost every applied scientific ...

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