微积分
使用 Symbolic Math Toolbox™，您可以对符号表达式进行求导和积分、执行级数展开、求符号表达式的变换，以及使用列出的函数执行向量微积分运算。
在对问题进行建模时，请使用假设返回正确的结果。请参阅Use Assumptions on Symbolic Variables。要简化结果，请参阅Simplify Symbolic Expressions。
函数
主题
- 求导
对符号表达式和函数求导。
- 创建符号函数
使用接受符号输入的符号函数进行解析计算。
- Integration
Integrate symbolic expressions and functions.
- Taylor Series
Taylor series expansion of symbolic expressions and functions.
- Fourier and Inverse Fourier Transforms
Fourier and inverse Fourier transforms of symbolic expressions.
- Solve Differential Equations of RLC Circuit Using Laplace Transform
Solve differential equations of an RLC circuit by using Laplace and inverse Laplace transforms.
- Solve Difference Equations Using Z-Transform
Z-Transforms and inverses of symbolic expressions and functions.
- Symbolic Summation
Sum symbolic vectors, matrices, or symbolic series.
- Padé Approximant
Pade approximant of symbolic expressions and functions.
- 极限
符号表达式和函数的极限。
- Find Asymptotes, Critical, and Inflection Points
Find minima, maxima, and asymptotes by using derivatives and limits.
- Functional Derivatives Tutorial
This example shows how to use functional derivatives in Symbolic Math Toolbox using the context of a wave equation.
相关信息
精选示例
Learn Calculus in the Live Editor
Learn calculus and applied mathematics using the Symbolic Math Toolbox™. The example shows introductory functions fplot and diff.
Differentiation
Analytically find and evaluate derivatives using Symbolic Math Toolbox™. In the example you will find the 1st and 2nd derivative of f(x) and use these derivatives to find local maxima, minima and inflection points.
Integration
Compute definite integrals using Symbolic Math Toolbox™.
Interactive Calculus in Live Editor
Add interactive controls to solve a calculus problem in a live script.
Maxima, Minima, and Inflection Points
This demonstration shows how to find extrema of functions using analytical and numerical techniques using the Symbolic Math Toolbox™.
Find Extremum of Multivariate Function and Its Approximation
Use symbolic matrix variables to find the extremum of a multivariate function and its approximation.
Padé Approximant of Time-Delay Input
Use a Padé approximant in control system theory to model time delays in the response of a first-order system. Time delays arise in systems such as chemical and transport processes where there is a delay between the input and the system response. When these inputs are modeled, they are called dead-time inputs.
Heating of Finite Slab
Find the temperature distribution of a one-dimensional finite slab by solving the differential equation using the method of separation of variables.
Solve Partial Differential Equation of Nonlinear Heat Transfer
Solve a partial differential equation (PDE) of nonlinear heat transfer in a thin plate.
Derive Equations of Motion and Simulate Cart-Pole System
Derive the equations of motion for the cart-pole system using Symbolic Math Toolbox™ and then simulate the cart-pole system using the ode45 solver. In the later sections of the example, you explore how to derive the equations in other forms that can be used to numerically simulate the system (and validate the results) using different tools, such as Simulink®, Simscape™ Multibody™, and Robotics System Toolbox™.
Finite Element Formulation for Timoshenko Beam Problem
Apply the finite element method (FEM) to solve a Timoshenko beam problem, using both linear and quadratic basis functions for analysis. The Timoshenko beam theory is a 1-D problem that reduces the complex 3-D problem of beam deformation to a set of 1-D differential equations along the length of the beam. In contrast to the Euler–Bernoulli beam theory, which does not consider shear deformation, the Timoshenko beam theory accounts for both shear deformation and rotational bending effects. The Timoshenko beam theory is generally more accurate for short, thick beams where shear deformation cannot be neglected. Using a cantilever beam and a beam fixed at both ends, this example discusses the analytical solutions of the Timoshenko beam problem and compares them with the FEM solutions.
