Science helps us in understanding nature. The nature could be that of physical objects, individual human beings, groups, nations as well as that of individual animals plants and trees and their groups.
So scientific approach involves observation and recording of facts relating to a natural phenomenon. From these facts cause and effect relations are identified as theoretical conjectures and are converted into hypotheses. Theoretical conjecture building is inducting thinking and development of hypotheses is deducting thinking. From the various hypotheses deduced from a theoretical conjecture, some will be testable hypotheses. They will be tested using experimental data or field study data and the results are evaluated to assess whether they support the hypothesis. Any support to the hypothesis will be regarded as stengthening the case of the theoretical conjecture. A theoretical conjecture supported by a number of hypothesis tests can be used to get useful outputs or events from the nature.
Engineering is applied to invention, development and production, fabrication or construction of man made objects that satisfy the needs of people for food, shelter, entertainment, and security. Engineering approach to problem solving involves laboratory experimentation, sciences and mathematics. But the most distinguising feature of engineering is the amount of attention paid to detail and documentation. A machine design is complete only when an assembly drawing supported by a drawing for each and every element required for the assembly is complete. Each and every element must have all the required dimenions and tolerances and the materials from which they are to be made. The design changes are to be properly documented in each drawing. Engineering approach inherently takes care of first identifying elements of a system that is the solution to a problem and the issues involved in combining the elements are also taken care of in engineering approach.
Management approach is more like an engineer repairing a machine rather than a engineer designing a machine. Managers have to come out with solutions that require the acceptance of people all the time and successful managers have a knack of understanding the people around them and the people affected by their decisions. Lee Iacocca said in his book, that Psychology courses that he has taken helped him a lot in his managerial career.