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calculo2718
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I was wondering if it is too ambitious to take both Real Analysis and Complex Analysis in the same semester.
Thanks.
Thanks.
micromass said:What are the prereqs for the courses? Do you meet the prereqs? What book do they use?
Are you comfortable with proofs?
apolanco115 said:for real analysis they use Boundary Value Problems and Partial Differential Equations, Fifth Edition, by David L. Powers, Elsevier Academic Press, 2006.
I can say that I've personally read Complex Variables and Applications (by James Ward Brown, et al.) in its third edition. I remember enjoying it, though I seem to remember its section on Riemann surfaces was fairly disappointing. I don't know what I'd expect in its eighth edition, but I get the feeling it is still an excellent introduction to complex analysis.apolanco115 said:The pre-reqs are Multivariable Calculus and differential equations
for complex analysis they use Complex Variables and Applications by James Ward Brown and Ruel V. Churchill, eighth edition, McGraw-Hill, 2009.
for real analysis they use Boundary Value Problems and Partial Differential Equations, Fifth Edition, by David L. Powers, Elsevier Academic Press, 2006.
That material is but the foothold of real analysis.TomServo said:...since a lot of real analysis stuff you probably already covered in your calc classes.
TomServo said:II'm not sure I know what the point of taking both real analysis and complex analysis is, seems to me that you should just take complex analysis since a lot of real analysis stuff you probably already covered in your calc classes.
Many programs designate differential equations a first year course and analysis a second year course. One might argue about that, but taking every class last is not workable. Also the naming is silly the second year analysis course often should really be called calculus.Mandelbroth said:You need to take differential equations before you take real and complex analysis?
Real Analysis studies the properties and behavior of real numbers, while Complex Analysis deals with the properties and behavior of complex numbers. Complex numbers have both a real and imaginary component, while real numbers only have a single real component. Additionally, Complex Analysis involves the study of functions that are defined on the complex plane, while Real Analysis focuses on functions defined on the real line.
Real Analysis is used in various fields such as physics, engineering, and economics to model and understand real-world phenomena. Complex Analysis is applied in fields such as electrical engineering, fluid dynamics, and quantum mechanics. It is also used in many areas of mathematics, such as number theory and topology.
Some important concepts in Real Analysis include limits, continuity, derivatives, and integrals. These concepts allow for the study of the behavior of functions and their properties, such as differentiability and convergence.
Complex Analysis is an extension of Calculus to functions of a complex variable. It includes many of the same concepts and techniques as Calculus, such as derivatives and integrals, but applied to functions that are defined on the complex plane. Complex Analysis also introduces new concepts, such as analytic functions and complex integration.
In Real Analysis, some common theorems include the Intermediate Value Theorem, Mean Value Theorem, and Fundamental Theorem of Calculus. In Complex Analysis, some common theorems include the Cauchy-Riemann equations, Cauchy's Integral Theorem, and the Cauchy Integral Formula. These theorems are used to prove important results and properties in both fields of analysis.