Lecture

History and Applications of Numerical Methods

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Description

This lecture covers the history of numerical methods, starting from their development 50 years ago and their rapid evolution today, including Moore's Law and the growth of computer power. It also explores the applications of numerical modeling in bioengineering, such as molecular modeling, bioinformatics, and the design of artificial organs. The lecture delves into the use of numerical techniques in orthopedics, cardiovascular research, and medical companies for conception, development, and risk analysis. Additionally, it discusses multi-scale modeling, modeling techniques in solid mechanics, fluid mechanics, heat, chemicals, and electromagnetism. The presentation concludes with the advantages of numerical methods in reducing development time, costs, and risks, as well as their role in testing hypotheses and understanding complex systems.

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Related concepts (23)

Computer hardware

Computer hardware includes the physical parts of a computer, such as the case, central processing unit (CPU), random access memory (RAM), monitor, mouse, keyboard, computer data storage, graphics card, sound card, speakers and motherboard. By contrast, software is the set of instructions that can be stored and run by hardware. Hardware is so-termed because it is "hard" or rigid with respect to changes, whereas software is "soft" because it is easy to change. Hardware is typically directed by the software to execute any command or instruction.

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Power supply unit (computer)

A power supply unit (PSU) converts mains AC to low-voltage regulated DC power for the internal components of a computer. Modern personal computers universally use switched-mode power supplies. Some power supplies have a manual switch for selecting input voltage, while others automatically adapt to the main voltage. Most modern desktop personal computer power supplies conform to the ATX specification, which includes form factor and voltage tolerances.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Computer

A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. A computer system is a nominally complete computer that includes the hardware, operating system (main software), and peripheral equipment needed and used for full operation.

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