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# Three Variable Jacobian Calculator

Three Variable Jacobian Calculator

The three variable Jacobian calculator solves the Jacobian matrix for four input variables and one output variable. The Jacobian matrix is a matrix of partial derivatives of the output variable with respect to all input variables. The Jacobian matrix is useful in the study of stability, transient, and closed loop behavior. The calculator is contained in the following areas: 1. The fourth row of the calculator gives the equation for calculating the Jacobian of the output with respect to the input variables. 2. The calculator allows input to be entered with respect to the output variable. There are four input variables and one output variable. The input variables are X1, X2, X3, and X4. Input variables are entered in the calculator as follows: a. Variable X1 is entered in the first row of the calculator. b. Variable X2 is entered in the second row of the calculator. c. Variable X3 is entered in the third row of the calculator. d. Variable X4 is entered in the fourth row of the calculator. e. The output variable is entered in the fifth row of the calculator. 3. The calculator also allows input to be entered with respect to the input variables. f. Variable Y1 is entered in the first row of the calculator. g. Variable Y2 is entered in the second row of the calculator. h. Variable Y3 is entered in the third row of the calculator. i. Variable Y4 is entered in the fourth row of the calculator. 4. A variable, AK, is entered in the sixth row of the calculator. 5. A variable, R, is entered in the seventh row of the calculator. 6. A variable, S, is entered in the eighth row of the calculator. 7. The calculator solves for the Jacobian matrix in the last three rows of the calculator. The Jacobian matrix is given in the three rows starting with the ninth row of the calculator.