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APPM 5360: Methods in Applied Mathematics:Complex Variables and Applications
3.00 Credits
University of Colorado Boulder
Prereq., graduate status in engineering or arts and sciences, or instructor consent. Same as APPM 4360.
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APPM 5360 - Methods in Applied Mathematics:Complex Variables and Applications
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APPM 5380: Modeling in Applied Mathematics
3.00 Credits
University of Colorado Boulder
Same as APPM 4380.
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APPM 5380 - Modeling in Applied Mathematics
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APPM 5430: Methods in Applied Mathematics:Applications of Complex Variables
3.00 Credits
University of Colorado Boulder
Reviews basic ideas of complex analysis, including solutions of ODEs and PDEs of physical interest via complex analysis; conformal mapping, including Schwarz-Christoffel transformations and generalizations; computational methods; Riemann-Hilbert problems; and topics in asymptotic methods. Prereq., APPM 4360 or 5360, or instructor consent.
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APPM 5430 - Methods in Applied Mathematics:Applications of Complex Variables
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APPM 5440: Applied Analysis
3.00 Credits
University of Colorado Boulder
Discusses the elements of basic real and complex analysis, Banach spaces, LP spaces, and many relevant inequalities. Includes applications of existence and uniqueness of solutions to various types of ordinary differential equations, partial differential equations, and integral equations. Prereqs., MATH 4310 and 4320, or equivalent; MATH 3130 or equivalent; or instructor consent.
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APPM 5440 - Applied Analysis
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APPM 5450: Applied Analysis
3.00 Credits
University of Colorado Boulder
Continuation of APPM 5440. Prereq., APPM 5440 or instructor consent.
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APPM 5450 - Applied Analysis
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APPM 5460: Methods in Applied Mathematics:Dynamical Systems and Differential Equations and Chaos
3.00 Credits
University of Colorado Boulder
Introduces the theory and applications of dynamical systems through solutions to differential equations. Covers existence and uniqueness theory, local stability properties, qualitative analysis, global phase portraits, perturbation theory, and bifurcation theory. Special topics may include Melnikov methods, averaging methods, bifurcations to chaos, and Hamiltonian systems. Prereqs., undergraduate courses equivalent to APPM 2360, 3310, and MATH 4310.
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APPM 5460 - Methods in Applied Mathematics:Dynamical Systems and Differential Equations and Chaos
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APPM 5470: Methods of Applied Mathematics:Partial Differential and Integral Equations
3.00 Credits
University of Colorado Boulder
Studies properties and solutions of partial differential equations. Covers methods of characteristics for partial differential equations, well-posed problems, main results for the well-known equations, Green's functions, and related integral equations. Prereqs., APPM 4350 and 4360, or MATH 4430, or equivalent.
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APPM 5470 - Methods of Applied Mathematics:Partial Differential and Integral Equations
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APPM 5480: Methods of Applied Mathematics:Approximation Methods
3.00 Credits
University of Colorado Boulder
Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods, and applications to differential and integral equations. Prereq., APPM 5470 or instructor consent.
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APPM 5480 - Methods of Applied Mathematics:Approximation Methods
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APPM 5520: Introduction to Mathematical Statistics
3.00 Credits
University of Colorado Boulder
Same as APPM 4520 and MATH 5520.
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APPM 5520 - Introduction to Mathematical Statistics
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APPM 5540: Introduction to Time Series
3.00 Credits
University of Colorado Boulder
Same as APPM 4540 and MATH 5540.
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APPM 5540 - Introduction to Time Series
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