Merge branch 'main' of https://github.com/PB2204/Advanced-Math

Author: PB2204

adv-math/src/equation-solvers/equations.js

@@ -18,6 +18,48 @@ class Equations {
         const x2 = (-b - sqrtDiscriminant) / (2 * a);
         return [x1, x2];
     }
+
+    // Method to solve a cubic equation of the form: ax^3 + bx^2 + cx + d = 0
+    static solveCubic(a, b, c, d) {
+        // Implementation of Cardano's method to solve cubic equations
+        if (a === 0) {
+            throw new Error('The coefficient of x^3 cannot be zero.');
+        }
+
+        const delta0 = b * b - 3 * a * c;
+        const delta1 = 2 * b * b * b - 9 * a * b * c + 27 * a * a * d;
+        const C = Math.cbrt((delta1 + Math.sqrt(delta1 * delta1 - 4 * delta0 * delta0 * delta0)) / 2);
+        const x1 = -(1 / (3 * a)) * (b + C + delta0 / C);
+        return [x1];
+    }
+
+    // Method to solve an exponential equation of the form: a^x = b
+    static solveExponential(a, b) {
+        if (a <= 0 || a === 1 || b <= 0) {
+            throw new Error('Values of a and b must be positive, and a cannot be equal to 1.');
+        }
+        return Math.log(b) / Math.log(a);
+    }
+
+    // Method to solve a logarithmic equation of the form: log_a(bx + c) = d
+    static solveLogarithmic(a, b, c, d) {
+        if (a <= 0 || a === 1 || b <= 0 || c < 0) {
+            throw new Error('Values of a, b, and c must be positive, and a cannot be equal to 1.');
+        }
+        const logValue = d / Math.log(a);
+        return (Math.pow(a, logValue) - c) / b;
+    }
+
+    // Method to solve a system of linear equations
+    static solveLinearSystem(a1, b1, c1, a2, b2, c2) {
+        const determinant = a1 * b2 - a2 * b1;
+        if (determinant === 0) {
+            throw new Error('The system of equations has no unique solution.');
+        }
+        const x = (c1 * b2 - c2 * b1) / determinant;
+        const y = (a1 * c2 - a2 * c1) / determinant;
+        return [x, y];
+    }
 }
 
 module.exports = Equations;

adv-math/src/financial/financial.js

@@ -1,8 +1,7 @@
 class Financial {
     // Method to calculate the future value of an investment with compound interest
     static futureValue(principal, rate, time) {
-        const compoundInterest = principal * Math.pow(1 + rate, time);
-        return compoundInterest;
+        return principal * Math.pow(1 + rate, time);
     }
 
     // Method to calculate the compound interest earned on an investment
@@ -14,6 +13,72 @@ class Financial {
     static presentValue(futureValue, rate, time) {
         return futureValue / Math.pow(1 + rate, time);
     }
+
+    // Method to calculate the loan amortization schedule
+    static loanAmortization(principal, rate, time) {
+        const monthlyRate = rate / 12 / 100; // Monthly interest rate
+        const numPayments = time * 12; // Number of monthly payments
+        const monthlyPayment = (principal * monthlyRate) / (1 - Math.pow(1 + monthlyRate, -numPayments));
+
+        const amortizationSchedule = [];
+        let remainingBalance = principal;
+
+        for (let month = 1; month <= numPayments; month++) {
+            const interestPayment = remainingBalance * monthlyRate;
+            const principalPayment = monthlyPayment - interestPayment;
+            remainingBalance -= principalPayment;
+
+            amortizationSchedule.push({
+                month,
+                monthlyPayment,
+                principalPayment,
+                interestPayment,
+                remainingBalance,
+            });
+        }
+
+        return amortizationSchedule;
+    }
+
+    // Method to calculate the effective interest rate
+    static effectiveInterestRate(principal, futureValue, time) {
+        return Math.pow(futureValue / principal, 1 / time) - 1;
+    }
+
+    // Method to convert annual interest rates to monthly
+    static annualToMonthlyInterestRate(annualRate) {
+        return (Math.pow(1 + annualRate, 1 / 12) - 1) * 100;
+    }
+
+    // Method to calculate the net present value (NPV) of cash flows
+    static netPresentValue(cashFlows, discountRate) {
+        let npv = 0;
+        for (let i = 0; i < cashFlows.length; i++) {
+            npv += cashFlows[i] / Math.pow(1 + discountRate, i);
+        }
+        return npv;
+    }
+
+    // Method to adjust a value for inflation
+    static adjustForInflation(value, inflationRate, years) {
+        return value / Math.pow(1 + inflationRate, years);
+    }
+
+    // Method to calculate the periodic payment needed to reach a future value goal
+    static calculateRequiredPaymentForFutureValue(futureValue, rate, time) {
+        return futureValue / ((Math.pow(1 + rate, time) - 1) / rate);
+    }
+
+    // Method to calculate asset depreciation
+    static calculateDepreciation(initialValue, salvageValue, usefulLife) {
+        return (initialValue - salvageValue) / usefulLife;
+    }
+
+    // Method to calculate the total return on an investment
+    static totalReturn(initialInvestment, finalValue, additionalInvestments) {
+        return (finalValue - initialInvestment + additionalInvestments) / initialInvestment;
+    }
 }
 
 module.exports = Financial;
+

adv-math/src/geometry-trigonometry/geometry.js

@@ -18,6 +18,74 @@ class Geometry {
     static circleCircumference(radius) {
         return 2 * Math.PI * radius;
     }
+
+    // Method to calculate the area of a triangle given base and height
+    static triangleArea(base, height) {
+        return (base * height) / 2;
+    }
+
+    // Method to calculate the volume of a sphere given its radius
+    static sphereVolume(radius) {
+        return (4 / 3) * Math.PI * Math.pow(radius, 3);
+    }
+
+    // Method to calculate the area of an equilateral triangle given its side length
+    static equilateralTriangleArea(side) {
+        return (Math.sqrt(3) / 4) * Math.pow(side, 2);
+    }
+    //Method to calulate the area of the triangle given its side lengths
+    static triangleArea_sides(side1, side2, side3) {
+        const s = (side1 + side2 + side3) / 2;
+        return Math.sqrt(s * (s - side1) * (s - side2) * (s - side3));
+    }
+    //Method to calulate the area of a square given its side length
+    static squareArea(side) {
+        return Math.pow(side, 2);
+    }
+    //Method to calculate the perimeter of a square given its side length
+    static squarePerimeter(side) {
+        return 4 * side;
+    }
+
+    // Method to calculate the volume of a cube given its side length
+    static cubeVolume(side) {
+        return Math.pow(side, 3);
+    }
+
+    // Method to calculate the volume of a rectangular prism given length, width, and height
+    static rectangularPrismVolume(length, width, height) {
+        return length * width * height;
+    }
+
+    // Method to calculate the surface area of a rectangular prism given length, width, and height
+    static rectangularPrismSurfaceArea(length, width, height) {
+        return 2 * (length * width + width * height + height * length);
+    }
+
+    // Method to calculate the volume of a cylinder given its radius and height
+    static cylinderVolume(radius, height) {
+        return Math.PI * Math.pow(radius, 2) * height;
+    }
+
+    // Method to calculate the surface area of a cylinder given its radius and height
+    static cylinderSurfaceArea(radius, height) {
+        const baseArea = Math.PI * Math.pow(radius, 2);
+        const lateralArea = 2 * Math.PI * radius * height;
+        return 2 * baseArea + lateralArea;
+    }
+
+    // Method to calculate the volume of a cone given its radius and height
+    static coneVolume(radius, height) {
+        return (1 / 3) * Math.PI * Math.pow(radius, 2) * height;
+    }
+
+    // Method to calculate the surface area of a cone given its radius and height
+    static coneSurfaceArea(radius, height) {
+        const slantHeight = Math.sqrt(Math.pow(radius, 2) + Math.pow(height, 2));
+        const baseArea = Math.PI * Math.pow(radius, 2);
+        const lateralArea = Math.PI * radius * slantHeight;
+        return baseArea + lateralArea;
+    }
 }
 
 module.exports = Geometry;

adv-math/src/geometry-trigonometry/trigonometry.js

@@ -79,6 +79,48 @@ class Trigonometry {
         }
         return this.arctangent(1 / value);
     }
+
+    // Method to calculate the hyperbolic sine of an angle in degrees
+    static sinh(degrees) {
+        const radians = (degrees * Math.PI) / 180;
+        return Math.sinh(radians);
+    }
+
+    // Method to calculate the hyperbolic cosine of an angle in degrees
+    static cosh(degrees) {
+        const radians = (degrees * Math.PI) / 180;
+        return Math.cosh(radians);
+    }
+
+    // Method to calculate the hyperbolic tangent of an angle in degrees
+    static tanh(degrees) {
+        const radians = (degrees * Math.PI) / 180;
+        return Math.tanh(radians);
+    }
+
+    // Method to calculate the hyperbolic arcsine in degrees
+    static arsinh(value) {
+        const result = Math.asinh(value);
+        return (result * 180) / Math.PI;
+    }
+
+    // Method to calculate the hyperbolic arccosine in degrees
+    static arcosh(value) {
+        if (value < 1) {
+            throw new Error('Invalid input for arcosh.');
+        }
+        const result = Math.acosh(value);
+        return (result * 180) / Math.PI;
+    }
+
+    // Method to calculate the hyperbolic arctangent in degrees
+    static artanh(value) {
+        if (value < -1 || value > 1) {
+            throw new Error('Invalid input for artanh.');
+        }
+        const result = Math.atanh(value);
+        return (result * 180) / Math.PI;
+    }
 }
 
 module.exports = Trigonometry;

adv-math/src/units-conversions/units.js

@@ -18,9 +18,19 @@ class Units {
     static convertTemperature(value, fromUnit, toUnit) {
         if (fromUnit === 'Celsius' && toUnit === 'Fahrenheit') {
             return (value * 9 / 5) + 32;
+        } else if (fromUnit=='Celsius' && toUnit=='Kelvin') {
+            return value + 273.15;
         } else if (fromUnit === 'Fahrenheit' && toUnit === 'Celsius') {
             return (value - 32) * 5 / 9;
-        } else {
+        } else if (fromUnit=='Fahrenheit' && toUnit=='Kelvin') {
+            return (value + 459.67) * 5 / 9;
+        } else if (fromUnit=='Kelvin' && toUnit=='Celsius') {
+            return value - 273.15;
+        } else if (fromUnit=='Kelvin' && toUnit=='Fahrenheit') {
+            return (value * 9 / 5) - 459.67;
+        }
+
+        else {
             throw new Error('Invalid temperature unit conversion.');
         }
     }

adv-math/tests/geometry-trigonometry.test.js

@@ -17,7 +17,45 @@ describe('Geometry', () => {
     test('calculates the circumference of a circle', () => {
         expect(Geometry.circleCircumference(3)).toBeCloseTo(18.850, 3);
     });
-
+    test('calculates the area of a triangle', () => {
+        expect(Geometry.triangleArea(3, 4)).toBe(6);
+    });
+    test('calculates the volume of a sphere', () => {
+        expect(Geometry.sphereVolume(3)).toBeCloseTo(113.097, 3);
+    });
+    test('calculates the area of an equilateral triangle', () => {
+        expect(Geometry.equilateralTriangleArea(3)).toBeCloseTo(3.897, 3);
+    });
+    test('calculates the area of a triangle given its side lengths', () => {
+        expect(Geometry.triangleArea_sides(3, 4, 5)).toBe(6);
+    });
+    test('calculates the area of a square given its side length', () => {
+        expect(Geometry.squareArea(3)).toBe(9);
+    });
+    test('calculates the perimeter of a square given its side length', () => {
+        expect(Geometry.squarePerimeter(3)).toBe(12);
+    });
+    test('calculates the volume of a cube given its side length', () => {
+        expect(Geometry.cubeVolume(3)).toBe(27);
+    });
+    test('calculates the volume of a rectangular prism given length, width, and height', () => {
+        expect(Geometry.rectangularPrismVolume(3, 4, 5)).toBe(60);
+    });
+    test('calculates the surface area of a rectangular prism given length, width, and height', () => {
+        expect(Geometry.rectangularPrismSurfaceArea(3, 4, 5)).toBe(94);
+    });
+    test('calculates the volume of a cylinder given radius and height', () => {
+        expect(Geometry.cylinderVolume(3, 5)).toBeCloseTo(141.371, 3);
+    });
+    test('calculates the surface area of a cylinder given radius and height', () => {
+        expect(Geometry.cylinderSurfaceArea(3, 5)).toBeCloseTo(150.796, 3);
+    });
+    test('calculates the volume of a cone given radius and height', () => {
+        expect(Geometry.coneVolume(3, 5)).toBeCloseTo(47.123, 3);
+    });
+    test('calculates the surface area of a cone given radius and height', () => {
+        expect(Geometry.coneSurfaceArea(3, 5)).toBeCloseTo(83.229, 3);
+    });
     // Add more test cases as needed
 });
 

adv-math/tests/units-conversions.test.js

@@ -12,10 +12,21 @@ describe('Units', () => {
     test('converts Celsius to Fahrenheit', () => {
         expect(Units.convertTemperature(25, 'Celsius', 'Fahrenheit')).toBeCloseTo(77, 1);
     });
-
+    test('converts Celsius to Kelvin', () => {
+        expect(Units.convertTemperature(25, 'Celsius', 'Kelvin')).toBeCloseTo(298.15, 1);
+    });
+    test('converts Fahrenheit to Kelvin', () => {
+        expect(Units.convertTemperature(68, 'Fahrenheit', 'Kelvin')).toBeCloseTo(293.15, 1);
+    });
     test('converts Fahrenheit to Celsius', () => {
         expect(Units.convertTemperature(68, 'Fahrenheit', 'Celsius')).toBeCloseTo(20, 1);
     });
+    test('converts Kelvin to Celsius', () => {
+        expect(Units.convertTemperature(300, 'Kelvin', 'Celsius')).toBeCloseTo(26.85, 1);
+    });
+    test('converts Kelvin to Fahrenheit', () => {
+        expect(Units.convertTemperature(300, 'Kelvin', 'Fahrenheit')).toBeCloseTo(80.33, 1);
+    });
 
     // Add more test cases as needed
 });