1. linear equation
Linear equation is the simplest algebraic equation, and its form is ax+b=0, where A and B are known constants and X is unknown. The steps to solve the linear equation are as follows:
1. Convert the equation into the standard form: ax =-b.
2. Solve the unknown x: x =-b/a.
Linear equations are widely used. For example, in physics, linear equations can be used to describe the relationship between the velocity and displacement of an object.
2. Quadratic equation
Quadratic equation is an algebraic equation with quadratic term, and its form is ax 2+bx+c = 0, where a, b and c are known constants and x is unknown. The steps to solve the quadratic equation are as follows:
1. Judging the solution of quadratic equation: According to the value of discriminant δ = b 2-4ac, the solution of the equation can be determined.
-When δ > 0, the equation has two unequal real number solutions.
-When δ = 0, the equation has two equal real number solutions.
-When δ
2. Solving the unknown number X: According to the root formula x = (-b√δ)/(2a), the solution of the equation can be obtained.
Quadratic equations are widely used in geometry and physics. For example, in the study of parabola, quadratic equation can describe the trajectory of an object.
3. Exponential function
Exponential function is a function with exponent as a variable, and its form is f (x) = a x, where a is the base and x is the exponent. The operation steps of exponential function are as follows:
1. Calculate the power of the base: multiply the base a by x times to get the result B.
2. Solve the function value: take the result b as the value of the function f(x).
Exponential function is widely used in finance, biology, physics and other fields. For example, in finance, an exponential function can be used to describe the growth trend of stock prices.
4. Logarithmic function
Logarithmic function is the inverse of exponential function, and its form is f(x)=loga(x), where a is the base and x is the function value. The operation steps of logarithmic function are as follows:
1. Calculate the logarithm of the base: calculate the logarithm of the base A of X to get the result B.
2. Solve the function value: take the result b as the value of the function f(x).
Logarithmic functions have important applications in computational complexity, signal processing and cryptography. For example, in the analysis of computational complexity, logarithmic function can be used to describe the relationship between algorithm running time and input scale.
5. Trigonometric function
Trigonometric function is a function with angle as a variable. Common trigonometric functions are sine function, cosine function and tangent function. The operation steps of trigonometric function are as follows:
1. Determine the unit of angle: trigonometric function can be represented by arc system or angle system.
2. Calculate the function value: according to the given angle, use the corresponding formula of trigonometric function to calculate the function value.
Trigonometric functions are widely used in geometry, physics and signal processing. For example, in geometry, trigonometric functions can be used to calculate the sides and angles of triangles.
final result
Through the introduction of this paper, we have learned some common mathematical expressions and their operation steps. These mathematical expressions play an important role in solving mathematical problems and application fields. Whether solving equations, describing functions or calculating geometry, these mathematical expressions are helpful for us to better understand and apply mathematical knowledge. I hope this paper can help readers learn and apply mathematics.