# Splines in Single & Multivariable Calculus (UMAP)

### Author: Yves Nievergelt

This module seeks to: 1) stregnthen students' intuition in multidimensional geometry; 2) provide exercises that are at a level between mechanical and theoretical; and 3) show applications of calculus that are important but rarely appear in calculus texts.** Table of Contents:INTRODUCTIONSPLINES IN SINGLE-VARIABLE CALCULUS** Piecewise Affine Splines

Complete Cubic Splines

Splines for Regression with Least Absolute Value

Regression with Least Absolute Value for Concave Functions

**SPLINES IN MULTIVARAIBLE CALCULUS**

Spline Curves in the Plane and in Space

Spline Surfaces in Space

**SPLINES BEYOND CALCULUS AND LINEAR ALGEBRA**

SAMPLE EXAM PROBLEMS

Problems in One Variable

SAMPLE EXAM PROBLEMS

Problems in Two Variables

**SOLUTIONS TO THE EXERCISES**

SOLUTIONS TO SAMPLE EXAM PROBLEMS

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR

SOLUTIONS TO SAMPLE EXAM PROBLEMS

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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