Applied mathematics is a field of mathematics which uses mathematics to solve problems of other branches of science. There are many fields:
 Approximation theory: Sometimes it is not possible to get an exact solution to a problem, because this might take too long, or it may not be possible at all. Approximation theory looks at ways to get a solution which is close to the exact one, and which can be obtained faster.
 Numerical analysis and simulation: This field investigates various algorithms to get approximations for mathematical problems. The study of numerical linear algebra and validated numerics are also included in this field.
 Probability and Statistics: How likely is it that something will happen?  If a coin is flipped 100 times, and lands heads up 53 times, is this coin good for games of chance, or should another one be taken?
 Optimization is about finding better solutions to problems.
 In ecology certain things are known about populations of animals or plants. This is usually called Population model. Biologists use them to tell how a population changes over time.
Related pages
 Society for Industrial and Applied Mathematics (SIAM)
 International Association for Mathematics and Computers in Simulation (IMACS)
 International Congress on Industrial and Applied Mathematics
 Japan Society for Industrial and Applied Mathematics (JSIAM, Japanese counterpart of SIAM)
 Japan Society for Simulation Technology (JSST, Japanese counterpart of IMACS)
 The Society for Industrial and Applied Mathematics (SIAM) is a professional society for promoting the interaction between mathematics and other scientific and technical communities. With organizing and sponsoring many conferences, SIAM is a major publisher of research journals and textbooks in applied mathematics.
Images for kids

A numerical solution to the heat equation on a pump casing model using the finite element method.
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Applied mathematics Facts for Kids. Kiddle Encyclopedia.