殷琦,佐々木渚沙,gf106
ax2 + bx + c = 0. (1) The formulas often used for calculating the roots of eq.(1) are x+ = −b + pb2 − 4ac 2a , (2) x− = −b − pb2 − 4ac 2a · (3) These formulas are, however, p inaccurate when |b| b2 − 4ac. The equivalent formulas are x+ = −2c b + pb2 − 4ac , (4) x− = −2c b − pb2 − 4ac . (5) When |b| pb2 − 4ac one must proceed with caution to avoid loss of precision. If b > 0, then x+ should be computed with the formula given by eq.(2) and x− should be computed with the formula given by eq.(3). If b < 0 then x+ should be evaluated using eq.(4) and x− should be evaluated using eq.(5). Here the two formulas constitute the method of finding roots of the equation of the form given by eq.(1). If you use the formulas given by eqs.(4– 5) instead of the formulas given by eqs.(2–3) (often used and familiar to us) to compute the roots then you should clearly explain why the formulas in eqs.(4–5) were chosen and why the other formulas given by eqs.(2–3) were not considered. This is what we mean by a research methodology. That is, research methodology tells you which method or formula or algorithm has to be used out of the various existing methods or formulas or algorithms. More precisely, research methods help us get a solution to a problem. On the other hand, research methodology is concerned with the explanation of the following: (1) Why is a particular research study undertaken? (2) How did one formulate a research problem? (3) What types of data were collected? (4) What particular method has been used? (5) Why was a particular technique of analysis of data used? The study of research methods gives training to apply them to a problem. The study of research methodology provides us the necessary training in choosing methods, materials, scientific tools and training in techniques relevant for the problem chosen. Assignment: (1) List out at least 10 methods which you have learned in your UG and PG courses and write their purpose or application. (2) Distinguish between research methods and research techniques. (3) Distinguish between research methods and research methodology with an example of your own choice. III. TYPES OF RESEARCH Research is broadly classified into two main classes: 1. Fundamental or basic research 2. Applied research A. Basic Research Basic research is an investigation on basic principles and reasons for occurrence of a particular event or process or phenomenon. It is also called theoretical research. Study or investigation of some natural phenomenon or relating to pure science are termed as basic research. Basic researches some times may not lead to immediate use or application. It is not concerned with solving any practical problems of immediate interest. But it is original or basic in character. It provides a systematic and deep insight into a problem and facilitates extraction of scientific and logical explanation and conclusion on it. It helps build new frontiers of knowledge. The outcomes of basic research form the basis for many applied research. Researchers working on applied research have to make use of the outcomes of basic research and explore the utility of them. Research on improving a theory or a method is also referred as fundamental research. For example, suppose 4 a theory is applicable to a system provided the system satisfies certain specific conditions. Modifying the theory to apply it to a general situation is a basic research. Attempts to find answers to the following questions actually form basic research. Why are materials like that? What they are? How does a crystal melt? Why is sound produced when water is heated? Why do we feel difficult when walking on seashore? Why are birds arrange them in ‘>’ shape when flying in a group? Fundamental research leads to a new theory or a new property of matter or even the existence of a new matter, the knowledge of which has not been known or reported earlier. For example, fundamental research on (1) astronomy may lead to identification of new planets or stars in our galaxy, (2) elementary particles results in identification of new particles, (3) complex functions may leads to new patterns or new properties associated with them, (4) differential equations results in new types of solutions or new properties of solutions not known so far. (5) chemical reactions leads to development of new compounds, new properties of chemicals, mechanism of chemicals reactions, etc. (6) medicinal chemistry leads to an understanding of physiological action of various chemicals and drugs. (7) structure, contents and functioning of various parts of human body helps us identify the basis for certain diseases. B. Applied Research In an applied research one solves certain problems employing well known and accepted theories and principles. Most of the experimental research, case studies and interdisciplinary research are essentially applied research. Applied research is helpful for basic research. A research, the outcome of which has immediate application is also termed as applied research. Such a research is of practical use to current activity. For example, research on social problems have immediate use. Applied research is concerned with actual life research such as research on increasing efficiency of a machine, increasing gain factor of production of a material, pollution control, preparing vaccination for a disease, etc. Obviously, they have immediate potential applications. Some of the differences between basic and applied research are summarized in table 1.1. Thus, the central aim of applied research is to find a solution for a practical problem which warrants solution for immediate use, whereas basic research is directed towards finding information that has broad base of applications and thus add new information to the already existing scientific knowledge. C. Quantitative and Qualitative Methods The basic and applied researches can be quantitative or qualitative or even both. Quantitative research is based on the measurement of quantity or amount. Here a process is expressed or described in terms of one or more quantities. Qualitative research is concerned with qualitative phenomenon involving quality. It is non-numerical, descriptive, applies reasoning and uses words. Its aim is to get the meaning, feeling and describe the situation. We measure and weigh things in the study of substance or structure. Can we measure or weigh patterns? We cannot measure or weigh patterns. But to study patterns we must map a configuration of relationships. That is, structures involve quantities whereas patterns involve qualities. If one wishes to investigate why certain data are random then it is a qualitative research. If the aim is to study how random the data is, what is the mean, variance and distribution function then it becomes quantitative. Explaining how digestion of food takes place in our body is a qualitative description. It does not involve any numbers or data and quantities. The detection of a particular compound is a qualitative analysis. This can be done by carrying out physical or chemical tests. Determination of exact amount of a par- TABLE I: Differences between basic and applied researches. Basic research Applied research Seeks generalization Studies individual or specific cases without the objective to generalize Aims at basic processes Aims at any variable which makes the desired difference Attempts to explain why things happen Tries to say how things can be changed Tries to get all the facts Tries to correct the facts which are problematic Reports in technical language of the topic Reports in common language 5 ticular compound present in a volume is essentially quantitative analysis. This can be done by volumetric, gravimetric and calorimetric methods or instrumental methods. Experimental and simulation studies are generally quantitative research. D. Other Types of Research Other types of research include action research (fact findings to improve the quality of action in the social world), explanatory research (searching explanations for events and phenomena, for example finding answer to the question why are the things like what they are?), exploratory research (getting more information on a topic) and comparative research (obtaining similarities and differences between events, methods, techniques, etc.). For discussion on these types of research see refs.[1–3]. Assignment: (4) List out at least 10 theoretical and applied methods which you have learned in your UG, PG courses and write their features in two or three sentences. (5) Write at least 20 questions in your subject the investigation of which forms basic research. Then point out how many of them have already been solved and how many were found in applications. |
