ShaneLogic/chebfun-operations

Chebfun Operations

Definite Integration

Basic Integration

sum(f)             % Integral over entire domain
sum(f, a, b)       % Integral over subdomain [a, b]

Method: Clenshaw-Curtis quadrature on the polynomial representation

Indefinite Integration (cumsum)

Cumulative Sum

fint = cumsum(f)   % Indefinite integral starting at 0 at left endpoint

Adjusting Integration Constant

fint = fint - fint(0)    % Make value 0 at t=0

Important Notes:

• If f is a fun of length n, cumsum(f) returns a fun of length n+1
• For piecewise chebfuns, integration is performed on each smooth piece separately
• Default integral has value 0 at left endpoint
• For functions with singularities, start integral at appropriate point (e.g., Soldner's constant for logarithmic integral)

Common Operations

Over 200 commands apply to chebfuns. View them with:

methods chebfun

Key Operations

• sum(f) - Definite integral
• diff(f) - Derivative
• roots(f) - Find zeros
• abs(f), acos(f), norm(f) - Standard math functions
• mean(f) - Average value

Arithmetic Operators

All standard MATLAB operators are overloaded:

f + g              % Addition
f * g              % Multiplication  
f.^2               % Power
1 ./ (1 + 25*x.^2) % Uses rdivide, plus, power, times

Evaluation

y = f(x)           % Evaluate chebfun at point x

Use When

• Computing integrals (definite or indefinite) of functions
• Applying mathematical transformations to functions
• Evaluating functions at specific points
• Performing calculus operations numerically
• Combining functions arithmetically