Category Archive for: Numerical Calculus And Differential Equations

Numerical Differentiation

Numerical Differentiation As we have seen the derivative of a function can be interpreted graphically as the slope of the function. This interpretation leads to methods for computing the derivative numerically. Numerical differentiation must be performed when we do not have the function represented as a formula that can be differentiated using the rules presented in Section 8.1. Two…

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Numerical Integration

Numerical Integration This section shows how to use MATLAB to calculate values of definite integrals using approximate methods. We show how to use MATLAB to obtain the closed-form solution of some integrals. Trapezoidal Integration The simplest way to find the area under a curve is to split the area into rectangles Figure 8.2-1a). If the widths of the…

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Review of Integration and Differentiation

Review of Integration and Differentiation The integral of a function f(x) for a ≤ x ≤ b can be interpreted as the area between the f(x) curve and the x-axis, bounded by the limits x = a and x = b. Figure 8.1-1 illustrates this area. If we denote this area by A, then we can write A as    …

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Numerical Calculus and Differential Equations

OUTLINE 8.1     Review of Integration and Differentiation 8.2     Numerical Integration 8.3     Numerical Differentiation 8.4    Analytical Solutions to Differential Equations 8.5     Numerical Methods for Differential Equations 8.6     Extension to Higher-Order Equations 8.7     ODE Solvers in the Control System Toolbox 8.8     Advanced Solver Syntax 8.9…

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