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What are the common mathematical principles in calculus?
Calculus is an important branch of mathematics, which mainly studies the concepts of limit, derivative and integral of functions. In calculus, there are many commonly used mathematical principles, including:

1. limit: limit is one of the basic concepts of calculus and describes the behavior of a function near a certain point. Limit can be used to calculate the function value, and can also be used to derive many important theorems and formulas.

2. Derivative: Derivative is a concept that describes the rate of change of a function. It can be used to calculate the tangent slope of a function at a certain point, and it can also be used to solve optimization problems.

3. Integration: Integration is a concept that describes the area or volume of a function. It can be used to calculate the area under the curve, and it can also be used to solve definite integral and indefinite integral.

4. Taylor series: Taylor series is a method of expressing functions with infinite series. It can be used to approximate complex values and solve differential equations.

5. Newton-Leibniz formula: Newton-Leibniz formula is one of the most important formulas in calculus, which links differential and integral, and gives a general method to find definite integral.

6. Differential equation: Differential equation is an equation describing the relationship between variables. It can be used to solve unknown functions and predict future trends.

7. Extreme value theorem: Extreme value theorem is an important theorem in calculus, which describes the conditions for a function to obtain the maximum or minimum value at a certain point.