IILM College of Engineering and Technology

# Mathematical Biology: Measuring Life

Mathematical biology aims at the mathematical representation, treatment and modeling of biological processes, using a variety of applied mathematical techniques and tools. It has both theoretical and practical applications in biological, biomedical and biotechnology research. By describing the systems in a quantitative manner, their behavior can be better simulated, and hence properties can be predicted that might not be evident to the experimenter.

Such mathematical areas are calculus, probability theory, statistics, linear algebra, graph theory, combinatory, algebraic geometry, dynamical systems; differential equations are now being applied in biology.

Mathematical models are important tools in basic scientific research in many areas of biology, including physiology, ecology, evolution, toxicology, immunology, natural resource management, and conservation biology. These models are equations or formulas that can predict or describe natural occurrences, such as organism behavior patterns or population changes over time. The result obtained from analysis and simulation of system models are used to test and extend biological theory, and to suggest new hypotheses or experiments. Models are also widely used to synthesize available information and provide quantitative answers to practical questions.

Another field of mathematical biology is statistics which is known as biostatistics. Biostatistics deals with the application of statistics to a wide range of topics in biology. It is one of the disciplines of biological sciences concerned with the application of mathematical-statistical theory, principles, and practices to the observation, measurement, and analysis of biological data and phenomena. Biostatistics often involves the design of experiments in medicine, online pharmacy, agriculture, and fishery. It also involves collecting, summarizing, and analyzing the data received from those experiments as well as the decided results. # Mathematics in Engineering

The history of mathematics is nearly as old as humanity itself. Since antiquity, Mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today.

Engineering can be defined as a specialized branch of science which constantly monitors the changing needs of the world. It also deals with the designing and manufacturing of the products that could make life simpler, fast and efficient. Engineers are people who solve problems and focus on making things work more efficiently and effectively. Engineers apply the theories, principles and concepts of Mathematics to research and develop economical solutions to technical problems. Their work is the link between perceived social needs and commercial applications. From the above itself it is clear that the application of Mathematics becomes indispensable for engineering. It is impossible to engineer something without the help of Mathematics. Since the applications of mathematics in engineering are so vast and varied, it is not possible to summarize them. Below are some important mathematical concepts used in various branches of Engineering.

The most important areas of Mathematics in Engineering are trigonometry, calculus, differential equations, statistics, and geometry. The Civil Engineering depends greatly on the vectors, trigonometric and geometric logics and concepts of the same are used in structural engineering, surveying, traffic and geotechnical engineering.  The Computer Science Engineering is largely dependent on numerical analysis, combinatorics, logic analysis, and algebra. Electrical/Electronics Engineering entails a lot of complex numbers analysis, crypto analysis, operation research, matrices and management which is applied in resistors, capacitors, inductors, power engineering, electrical networks, digital signal processing, image processing. Mechanical engineers use the concepts of calculus, matrices, vectors, trigonometry in Fluid flow, mechanics, heat transfer, temperature distribution, combustion (internal combustion engines), and computational solid mechanics. This branch of engineering heavily utilizes the mathematical principles, formulae, and calculations. Biomedical engineers use statistics, probability, Laplace transforms in measuring performance of drugs, analysis of defibrillator systems, drug delivery, fluid flow.

Thus, it can be concluded that in order to be a good engineer one should be capable of handling mathematical problems efficiently.