# Tutorial

## 0. Introduction

Explains the structure and the basic use of the Excel numerical software XLPack.

## 1. How to obtain and use example worksheets

Where to obtain example worksheets / Structure of example book / How to use example worksheets

## 2. System of linear equations

Examples of solving systems of linear equations using worksheet function WDgesv and VBA subroutine Dgesv.

## 3. Eigenvalue problems

Examples of solving eigenvalue problems of symmetric matrices using worksheet function WDsyev and VBA subroutine Dsyev.

## 4. Linear least squares problems

Examples of solving linear least squares problems using worksheet function WDgels and VBA subroutine Dgels.

## 5. Interpolation

Examples of computing interpolation by cubic spline function using worksheet functions WPchse and Wpchfe and VBA subroutines Pchse and Pchfe.

## 6. Algebraic equations (roots of polynomials)

Examples of solving algebraic equations (finding roots of polynomials) using worksheet function WRpzero2 and VBA subroutine Rpzero2.

## 7. Solution of nonlinear equation

Examples of solving a single variable nonlinear equation (finding a root of arbitrary one-dimensional nonlinear function) using VBA subroutine Dfzero and XLPack solver.

## 8. System of nonlinear equations

Examples of obtaining real solutions of a system of general nonlinear equations using VBA subroutine Hybrd1 and XLPack solver.

## 9. Nonlinear optimization of univariate function

Examples of solving a nonlinear optimization of univariate function (finding a minimum point of general one-dimensional nonlinear function) using VBA subroutine Dfmin and XLPack solver.

## 10. Nonlinear optimization of multivariate function

Examples of solving a nonlinear optimization of multivariate function (finding a minimum point of general multidimensional nonlinear function) using VBA subroutine Optif0 and XLPack solver.

## 11. Numerical integration

Examples of numerical integration (quadrature) using worksheet functions WPchse and Wpchia, VBA subroutine Qag and Qk15, and XLPack solver.

## 12. Ordinary Differential Equations

Examples of solving an initial value problem of ordinary differential equations using VBA subroutine Derkf and XLPack solver.

## 13. Fast Fourier transform (FFT)

Examples of fast Fourier transform (FFT) computations including power spectrum analysis using worksheet functions WRfft1f and WRfft1b.

## 14. Nonlinear least squares problems

Examples of solving nonlinear least squares problem using VBA subroutine Lmdif1 and XLPack solver.