1, trigonometric function method: For transcendental equations with trigonometric functions, we can use the properties and lemma of trigonometric functions to transform transcendental equations into algebraic equations and then solve them.
2. Power series method: Power series is a method of expanding transcendental function into infinite series. By expanding transcendental function into power series, transcendental equation can be transformed into infinite series equation, and then solved one by one.
3. Numerical methods: For transcendental equations that cannot be solved analytically, numerical methods, such as Newton method and dichotomy, can be used to obtain approximate solutions through iterative calculation.
4. Symbol calculation method: Symbol calculation refers to the method of using computer algebra system to perform symbol operation. Using symbolic computing system, the symbolic solution of transcendental equation can be automatically solved.
5. Graphical solution: By drawing the graphs of transcendental function and corresponding equation, we can observe the position of the intersection point, thus estimating the approximate solution of the equation. The graphic method is intuitive and easy to understand, especially suitable for some simple and easy-to-draw transcendental equations.
The usage scenario of transcendental equation:
1, Physics: Transcendental equations are widely used in physics. For example, the equations describing quantum mechanics, electromagnetism, fluid mechanics and other problems are usually transcendental equations. For example, the Schwarzschild equation describing a black hole is a transcendental equation.
2. Chemical engineering: In chemical engineering, transcendental equations are used to describe the dynamic process of chemical reactions, such as rate equations and equilibrium equations. These equations usually contain transcendental functions, such as exponential functions and logarithmic functions.
3. Financial mathematics: In financial mathematics, transcendental equation is used to describe the price behavior of some financial derivatives, such as options and futures. These equations usually contain transcendental functions, such as exponential functions and logarithmic functions.
4. Biology: In biology, transcendental equations are used to describe some biological phenomena, such as population growth. These equations usually contain transcendental functions, such as exponential functions and logarithmic functions.
5. Engineering field: In engineering field, transcendental equation is used to describe some engineering problems, such as circuit design and mechanical vibration. These equations usually contain transcendental functions such as trigonometric functions and exponential functions.