Java supports mathematical computations through built-in operators and the Math class, enabling developers to implement formulas directly in code.

For basic algebraic expressions, standard arithmetic operators (+, -, *, /) combined with methods like Math.pow() suffice. Consider the quadratic expression ( y = x^2 + 2x + 1 ):

public class QuadraticEvaluator {
    public static void main(String[] args) {
        double input = 5.0;
        double result = Math.pow(input, 2) + 2 * input + 1;
        System.out.println("Result: " + result);
    }
}

This computes the value of the polynomial at ( x = 5 ), using Math.pow() for exponentiation.

In financial modeling, compound interest is a common use case. The future value of an investment is given by: [ FV = PV \times (1 + r)^n ] where ( PV ) is present value, ( r ) is annual interest rate, and ( n ) is the number of years.

public class InvestmentCalculator {
    public static void main(String[] args) {
        double initialValue = 1000.0;
        double annualRate = 0.05;
        int duration = 5;
        
        double finalValue = initialValue * Math.pow(1 + annualRate, duration);
        System.out.printf("Value after %d years: %.2f%n", duration, finalValue);
    }
}

For more advanced mathematics—such as linear algebra, statistics, or differential equations—libraries like Apache Commons Math provide optimized, tested implementations. However, many practical formulas can be expressed concisely using core Java features without external dependencies.