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axeae
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I'm wondering if anyone can recommend a good intro to complex variables book for an undergrad (calc1-3,diffeq). Preferably something that can be found cheap on amazon (Dover?)
axeae said:Thanks for the suggestions. Tom Mattson, you were my Calculus I teacher.
I have a few Shaum's Outlines but I was looking for something closer to an actual textbook since I'm planning on self-studying.
axeae said:Tom Mattson, it was last summer, session II. Your calculus class actually made me want to be a math major, so I've been doing math nonstop since.
A complex variable is a mathematical quantity that has both a real and an imaginary component. It is typically represented in the form of a+bi, where a is the real part and bi is the imaginary part. Complex variables are useful in many fields of science, including physics, engineering, and economics.
The basic operations on complex variables include addition, subtraction, multiplication, and division. These operations follow the same rules as real numbers, with the added consideration of the imaginary component. For example, the product of two complex numbers is found by multiplying their real parts and adding their imaginary parts.
Complex functions are functions that have a complex variable as an input and output. They are different from real functions in that they can have multiple values for a given input, as the imaginary component can vary. Additionally, complex functions can exhibit behaviors such as poles and branch cuts, which do not exist in real functions.
Complex variables have many applications in science, including in the fields of electromagnetism, fluid dynamics, quantum mechanics, and signal processing. They are used to model and solve problems that involve oscillations, rotations, and waves, and are also useful in understanding and analyzing systems with multiple variables and constraints.
Complex variables can be visualized using the complex plane, also known as the Argand plane. This is a two-dimensional plane where the horizontal axis represents the real component and the vertical axis represents the imaginary component. Points on the plane can be represented as complex numbers, and operations on these numbers can be visualized as movements on the plane.