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Mathematical biology aims at the mathematical representation and modeling of biological processes, using techniques and tools of applied mathematics. It can be useful in both theoretical and practical research. Describing systems in a quantitative manner means their behavior can be better simulated, and hence properties can be predicted that ...
For quasi-static and reversible processes, the first law of thermodynamics is: d U = δ Q − δ W {\displaystyle dU=\delta Q-\delta W} where δQ is the heat supplied to the system and δW is the work done by the system.
The Interactive Mathematics Program (IMP) is a four-year, problem-based mathematics curriculum for high schools. It was one of several curricula funded by the National Science Foundation and designed around the 1989 National Council of Teachers of Mathematics (NCTM) standards .
Biological processes are regulated by many means; examples include the control of gene expression, protein modification or interaction with a protein or substrate molecule. Homeostasis : regulation of the internal environment to maintain a constant state; for example, sweating to reduce temperature
Kirchhoff's diffraction formula; Klein–Gordon equation; Korteweg–de Vries equation; Landau–Lifshitz–Gilbert equation; Lane–Emden equation; Langevin equation; Levy–Mises equations; Lindblad equation; Lorentz equation; Maxwell's equations; Maxwell's relations; Newton's laws of motion; Navier–Stokes equations; Reynolds-averaged ...
Clark–Ocone theorem (stochastic processes) Continuous mapping theorem (probability theory) Cramér's theorem (large deviations) (probability) Dawson–Gärtner theorem (asymptotic analysis) Donsker's theorem (probability theory) Doob decomposition theorem (stochastic processes) Doob's martingale convergence theorems (stochastic processes)
Writer Alex Bellos described The Mathematics of Life as "a testament to the versatility of maths and how it is shaping our understanding of the world." [4] Kirkus Reviews called the book "an ingenious overview of biology with emphasis on mathematical ideas—stimulating but requiring careful reading despite the lack of equations."
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.