Specific use:
Specifically, if the Laplace transform of function f(t) is F(s), Laplace theorem gives the relationship between Laplace transform of n-order derivative of function f(t) and F(s). According to Laplace theorem, for any positive integer n, the following equation holds:
L{f'(t)} = sF(s) - f(0)？ (first derivative).
L{f''(t)} = s^2F(s) - sf(0) - f'(0)？ (second derivative).
...
l{f^n(t)} = s^nf(s)-s^(n- 1)f(0)-s^(n-2)f'(0)-...- f^(n- 1)(0)？ (n-order derivative).
Where L{f(t)} represents the Laplace transform of function f(t), f'(t) represents the first derivative of f(t), f' (t) represents the second derivative of f(t), and f n (t) represents the n derivative of f(t).
Solution:
Through Laplace theorem, we can turn the problem of solving differential equations into the problem of solving algebraic equations. The concrete steps are as follows: firstly, the differential equation is laplace transformed to obtain the algebraic equation about F(s); Then solve f (s); Finally, the solution of the original function f(t) is obtained by inverse Laplace transform.
Ways to learn mathematics well:
1. Theoretical learning
Learn the theoretical knowledge of mathematics, including various mathematical concepts, theorems and formulas. You can learn by reading textbooks, participating in classroom teaching and watching math-related videos.
2. Exercise questions
Consolidate what you have learned by doing a lot of math exercises. You can choose the exercises in the textbook, or you can use exercises and question banks to practice. It is important to do more different types of problems and improve the ability to solve problems.
3. Problem-solving skills
Learn some common problem-solving skills and methods, such as algebra, geometry, sequence and so on. These skills can help solve some common mathematical problems and improve the efficiency of solving them.
4. Organizational thinking
Learning mathematics requires good thinking habits and logical thinking ability. Mathematical thinking ability can be cultivated by analyzing problems, summarizing and constructing logical chains.
5. Innovative thinking
Mathematics is a creative subject, which encourages students to innovate in mathematical thinking. You can try to ask your own questions, explore new ways to solve problems, and cultivate creativity and innovation in mathematical thinking.
Step 6 study together
Cooperate with classmates or teachers to study, communicate, discuss and answer questions. Through cooperative learning, we can deepen our understanding of mathematics knowledge, find our own problems and get answers.
7. Application practice
Apply mathematical knowledge to real life or other disciplines, such as applied mathematics, physics, economics, etc. Through practical application, deepen the understanding and application ability of mathematical knowledge.