There are many areas in which to shine in mathematics, but unfortunately, there are also many areas in which to struggle. These tasks change over time, demanding increased refinement or elaboration of skill sets, or the addition of new ones as a student progresses through school. Woodin encourages teachers to treat math problems with the same kind of thoughtful and targeted strategies that are applied to reading instruction. Topics include first-order equations by the method of characteristics linear, quasilinear, and nonlinear equations applications to traffic flow and geometrical optics principles for higher-order equations power series and Cauchy-Kowalevski theorem classification of second-order equations linear equations and generalized solutions wave equations in various space dimensions domain of dependence and range of influence Huygens’ principle conservation of energy, dispersion, and dissipation Laplace’s equation mean values and the maximum principle the fundamental solution, Green’s functions, and Poisson kernels applications to physics properties of harmonic functions the heat equation eigenfunction expansions the maximum principle Fourier transform and the Gaussian kernel regularity of solutions scale invariance and the similarity method Sobolev spaces and elliptic regularity.Ĭovers fundamental concepts in graph theory.In the classroom, we break down the complex processing tasks of reading and spelling into various subskills that can be tested and analyzed. Introduces partial differential equations, their theoretical foundations, and their applications, which include optics, propagation of waves (light, sound, and water), electric field theory, and diffusion. Topics include differential calculus: basics, the derivative, the rules of differentiation, curve plotting, exponentials and logarithms, and trigonometric functions using technology to understand derivatives biological kinetics: zero- and first-order processes, processes tending toward equilibrium, bi- and tri-exponential processes, and biological half-life differential equations: particular and general solutions to homogeneous and nonhomogeneous linear equations with constant coefficients, systems of two linear differential equations compartmental problems: nonzero initial concentration, two-compartment series dilution, diffusion between compartments, population dynamics and introduction to integration.Īttribute(s): NUpath Formal/Quant Reasoning Presents methods for the solutions of these equations and how the exact solutions are obtained from actual laboratory data. (4 Hours)īegins with the fundamentals of differential calculus and proceeds to the specific type of differential equation problems encountered in biological research. Calculus and Differential Equations for Biology 1.
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