# newtons method

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newtons method - another numerical method for solving an equation f...

3 unknowns using Cramers Rule
Solves for 3 unknowns with equations in the form ax + by + cz = d using Cramers Method.

4 unknowns using Cramers Rule
Solves for 4 unknowns with equations in the form aw + bx + cy + dz = e using Cramers Method.

Activity Method Depreciation
Calculates the following: Depreciable Base, Depreciation per Unit, Depreciation for Period

Approximate Square Root Using Exponential Identity
Calculates the square root of a positive integer using the Exponential Identity Method

Babylonian Method
Determines the square root of a number using the Babylonian Method.

Bakshali Method
Calculates the square root of a positive integer using the Bakshali Method

Binomial Multiplication (FOIL)
Multiplies out the product of 2 binomials in the form (a + b)(c + d) with 1 unknown variable.
This utilizes the First-Outside-Inside-Last (F.O.I.L.) method.

Black-Scholes
Calculates the call or put option value of a stock based on inputs related to the option using Black Scholes method.

Bond Flat Price-Accrued Coupon-Market Price
Calculates the flat price, accrued coupon, and market price for a bond between valuation dates using the following methods:
1) Theoretical Method
2) Practical Method
3) Semi-Theoretical Method

Bond Yield Rates
Calculates the yield rate of bonds using the Yield Approximation Method or the Bond Salesman Method.

Chinese Remainder Theorem
Given a set of modulo equations in the form:
x ≡ a mod b
x ≡ c mod d
x ≡ e mod f

the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.
Given that the ni portions are not pairwise coprime and you entered two modulo equations, then the calculator will attempt to solve using the Method of Successive Subsitution

Confidence Interval for the Mean
Calculates a (90% - 99%) estimation of confidence interval for the mean given a small sample size using the student-t method with (n - 1) degrees of freedom or a large sample size using the normal distribution Z-score (z value) method including Standard Error of the Mean. confidence interval of the mean

Confidence Interval for Variance and Standard Deviation
Calculates a (95% - 99%) estimation of confidence interval for the standard deviation or variance using the χ2 method with (n - 1) degrees of freedom.

Cost Recovery Method
Given a sales price, cost, and set of payments, this determines the gross profit per year based on the cost recovery method.

Covariance and Correlation coefficient (r) and Least Squares Method and Exponential Fit
Given two distributions X and Y, this calculates the following:
* Covariance of X and Y denoted Cov(X,Y)
* The correlation coefficient r.
* Using the least squares method, this shows the least squares regression line (Linear Fit) and Confidence Intervals of α and Β (90% - 99%)
Exponential Fit
* Coefficient of Determination r squared r2
* Spearmans rank correlation coefficient
* Wilcoxon Signed Rank test

Cox-Ross-Rubenstein Pricing
Using the Cox-Ross-Rubenstein method, this calculates the call price and put price of an option.

Cubic Equation
Solves for cubic equations in the form ax3 + bx2 + cx + d = 0 using the following methods:
1) Solve the long way for all 3 roots and the discriminant Δ
2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

Declining Balance Depreciation
Solves for Depreciation Charge, Asset Value, and Book Value using the Declining Balance Method

Dollar Weighted Interest Method
Solves for Interest Rate, Starting Asset Value, Ending Asset Value, and Expenses using the Dollar Weighted Method.

Double Declining Balance Depreciation
Calculates Depreciation and Book Value using the Double Declining Balance Depreciation Method.

Gravitational Force
Using Sir Isaac Newtons Law of Gravitational Force, this calculator determines the force between two objects with mass in kilograms at a distance apart in meters using the constant of gravity.

Greatest Common Factor and Least Common Multiple
Given 2 or 3 numbers, the calculator determines the following:
* Greatest Common Factor (GCF) using Factor Pairs
* Rewrite Sum using the Distributive Property and factoring out the GCF
* Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs
* GCF using the method of Successive Division
* GCF using the Prime Factorization method
* Determine if the numbers are coprime and twin prime

High and Low Method
Calculates the variable cost per unit, total fixed costs, and the cost volume formula

High-Low Method
Calculates Variable Cost per Unit, Total Fixed Cost, and Cost Volume using the High-Low Method

Installment Sales Method of Accounting
Given a sales price, cost amount, installment payment amount and term, this will show the accounting for the Installment Payment method.

Inventory Method
Takes accounting entries using the FIFO (first in first out) and LIFO (last in first out) inventory methods.

Lattice Multiplication
Performs Lattice Multiplication or the Napiers Bones (Napier Rods) method of multiplication

Method of Equated Time-Exact Method-Macaulay Duration-Volatility
Given a set of cash flows at certain times, and a discount rate, this will calculate t using the equated time method and the exact method, as well as the macaulay duration and volatility

Newton Method
Calculates the square root of a positive integer using the Newton Method

Normal Distribution
Calculates the probability that a random variable is less than or greater than a value or between 2 values using the Normal Distribution z-score (z value) method (Central Limit Theorem).
Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability

Percentage of Completion
Given a sales price, total costs, and costs per period, this determines the gross profit to date using the percentage of completion method.

Quartic Equations
Solves quartic equations in the form ax4 + bx3 + cx2 + dx + e using the following methods:
1) Solve the long way for all roots and the discriminant Δ
2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.

Simultaneous Equations
Solves a system of simultaneous equations with 2 unknowns using the following 3 methods:
1) Substitution Method (Direct Substitution)
2) Elimination Method
3) Cramers Method or Cramers Rule Pick any 3 of the methods to solve the systems of equations 2 equations 2 unknowns

Sinking Fund Depreciation Method
Using the Sinking Fund method of Depreciation, this calculator determines the following:
* Depreciation at time t (Dt)
* Asset Value (A)
* Salvage Value (S)
* Book Value at time t (Bt)

Straight Line Depreciation
Solves for Depreciation Charge, Asset Value, Salvage Value, Time, N, and Book Value using the Straight Line Method.

Sum of the Years Digits (SOYD) Depreciation
Solves for Depreciation Charge, Asset Value, and Book Value using the Sum of the Years Digits Method

Time Weighted Interest Method
Solves for Interest Rate based on 2 annual asset value events other than beginning or ending value using the Time Weighted Method

Utility and Cost Utility Ratio
Given 2 methods with a set of utilities and weights/probabilities, this will calculate the utility for each method, as well as the total utility using the additive method, as well as the Cost Utility Ratio