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MATH 53: Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications

Ordinary differential equations and initial value problems, linear systems of such equations with an emphasis on second-order constant-coefficient equations, stability analysis for non-linear systems (including phase portraits and the role of eigenvalues), and numerical methods. Partial differential equations and boundary-value problems, Fourier series and initial conditions, and Fourier transform for non-periodic phenomena. n Throughout the development we harness insights from linear algebra, and software widgets are used to explore course topics on a computer (no coding background is needed). The free e-text provides motivation from applications across a wide array of fields (biology, chemistry, computer science, economics, engineering, and physics) described in a manner not requiring any area-specific expertise, and it has an appendix on Laplace transforms with many worked examples as a complement to the Fourier transform in the main text.n Prerequisite: Math 21 and Math 51, or equivalents.
Terms: Aut, Win, Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

MATH 53A: Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications, ACE

Additional problem solving session for Math 53 guided by a course assistant. Concurrent enrollment in Math 53 required. Application required: https://engineering.stanford.edu/students-academics/equity-and-inclusion-initiatives/undergraduate-programs/additional-calculus
Terms: Aut, Win, Spr | Units: 1
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