Splines in Single & Multivariable Calculus (UMAP)

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:

INTRODUCTION

SPLINES 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
Problems in Two Variables

SOLUTIONS TO THE EXERCISES

SOLUTIONS TO SAMPLE EXAM PROBLEMS

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR