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mathematics Exponential, trigonometric and hyperbolic functions of complex variable |L-1|Bsc 1st year
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Approximations and Estimations with Algebraic Formulas: Complex Trigonometric Functions and Identitie
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Exponential, trigonometric and hyperbolic functions ofcomplex variable |L-1|Bsc 1st year|
Approximations and Estimations with
Algebraic Formulas: Complex
Trigonometric Functions and Identities
Complex Numbers
● Complex numbers: a number of the form a + bi, where a and b are real numbers
and i is the imaginary unit, such that i^2 = -1.
● Modulus of a complex number: the distance from the origin to the point in the
complex plane that represents the number. It is calculated using the formula |a +
bi| = sqrt(a^2 + b^2).
● Argument of a complex number: the angle that the line connecting the origin to
the point in the complex plane makes with the positive real axis. It is calculated
using the formula arg(a + bi) = atan2(b, a).
Trigonometric Functions and Identities
● Trigonometric functions: functions of an angle that describe the ratios of the
sides of a right triangle. The three main trigonometric functions are sine, cosine,
and tangent.
● Trigonometric identities: equations that are true for all values of the angles
involved. Some examples include the Pythagorean identity, the cofunction
identities, and the even-odd identities.
Approximations and Estimations with Algebraic Formulas
● Approximations and estimations: using algebraic formulas to find approximate
values for mathematical expressions that cannot be easily calculated exactly.
, ● Taylor series: a way of approximating functions using infinite series. The Taylor
series for a function f(x) at a point x = a is given by f(a) + f'(a)(x-a) +
(1/2!)f''(a)(x-a)^2 + (1/3!)f'''(a)(x-a)^3 + ....
● Linear approximations: a way of approximating a function near a point using a
tangent line. The equation of the tangent line to a curve at a point (a, f(a)) is
given by y = f(a) + f'(a)(x-a).
Hydraulic and Circular Functions
● Hydraulic functions: functions that describe the behavior of fluids in motion.
● Circular functions: trigonometric functions applied to angles between -π and π,
represented as points on the unit circle.
● Inverse trigonometric functions: functions that "undo" the trigonometric functions,
finding the angle that corresponds to a given ratio of sides in a right triangle.
Note: This is a summary of the topic "Approximations and Estimations with Algebraic
Formulas: Complex Trigonometric Functions and Identities". It covers complex numbers,
trigonometric functions and identities, approximations and estimations, and hydraulic and
circular functions. It does not include the topics "Studying Complex Numbers and Their
Applications", "Various Types of Functions in Mathematics".
Various Types of Functions in Mathematics
Complex Trigonometric Functions and Identities
● Define and understand the properties of complex trigonometric functions such as
$\sin(z)$, $\cos(z)$, and $\tan(z)$.
● Learn and apply trigonometric identities in the complex plane, such as $\sin^2(z)
+ \cos^2(z) = 1$.
Approximations and Estimations with Algebraic Formulas
● Learn to approximate and estimate values of functions using various algebraic
formulas.
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