AMATH – Introduction to Differential Equations. David Harmsworth. Spring Course Notes by John Wainwright. AMATH is an advanced-level version of AMATH Compared to AMATH , AMATH offers a more theoretical treatment of differential equations and . Is this really as easy as people say? Is the difficulty prof dependant? How is the course otherwise (proof vs computation)?.
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System theory in both time and frequency domain, state-space computations, stability, system uncertainty, loopshaping, linear quadratic regulators and estimation.
Second order linear differential equations with non-constant coefficients, Sturm comparison, oscillation and separation theorems, series solutions and special functions. The difficult of any course is not only prof-dependent.
Almost no proofs and those you get just require the definitions. Treat every course like it’s a hard course.
AMATH – Introduction to Differential Equations
Stable and unstable manifolds. The relation between symmetries and conservation laws. Fourier series and the Fourier transform.
Is the difficulty prof dependant?
Methods of solution – separation of variables and eigenfunction expansions, the Fourier transform. An introduction to contemporary mathematical concepts in signal analysis. Want to add to the discussion? Complex numbers, Cauchy-Riemann equations, analytic functions, conformal maps and applications to the solution of Laplace’s equation, contour integrals, Cauchy integral formula, Taylor and Laurent expansions, residue calculus and applications.
That being said I don’t think you should try to bank on a course being easy and fall into a place of comfort because other people say you can. If you don’t mind physics questions you’re fine. Frequency analysis of signals. Uncertainty, correspondence and superposition principles.
AMATH 250: Introduction to Differential Equations
AM counts as a credit for all programs in the Math Faculty, and is also open to students in other faculties. Applications are discussed throughout. Numerical methods for differential equations. Applications to continuous compounding and the dynamics of supply and demand.
Feedback control with applications. Nonlinear systems, stability of equilibria and Lyapunov functions. Bell inequality and basics of quantum computing. Basic equations of elasticity. Laplace transforms applied to linear vector differential equations, transfer functions, the convolution theorem. The solution of problems using variational methods – the Euler-Lagrange equations. First order non-linear partial differential equations and the method of characteristics.
AMATH : uwaterloo
Critical experiments and old quantum theory. The course focuses on amwth widely used methods and highlights applications in the natural sciences, the health sciences, engineering and finance. Includes collaborative projects and computer labs. Physical systems which lead to differential equations examples include mechanical vibrations, population dynamics, and mixing processes.
Most questions will come from physical problems e. Equations of continuity, motion and energy, constitutive equations. Is this really as easy as people say? A variety of cellular phenomena are discussed, including ion pumps, membrane potentials, intercellular communication, genetic networks, regulation of metabolic pathways, and signal transduction. If you’re like me and don’t know physics that well it can be pretty annoying. Difference equations, Laplace and 2250 transforms amaht to discrete and continuous mathematical models taken from ecology, biology, economics and other fields.
The Fourier Transform and the diffusion equation. Introduction to linear partial differential equations. How is the course otherwise proof vs computation?
AMATH 250 – Introduction to Differential Equations
This course may be substituted for CS in any degree plan or for prerequisite purposes; lab is not scheduled and students are expected to find time in open hours to complete their work. AM will benefit students who are interested in Scientific Computation e.
The course overall is difficult for students who lack these skills and intuition. Applications to physical problems will be a motivating influence. Concept of functional and its variations.