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Consortium for Mathematics and its Applications

Product ID: 99718
Supplementary Print
Undergraduate

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:

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

©1999 by COMAP, Inc.
UMAP Module
66 pages

Mathematics Topics:

Calculus

Application Areas:

Computers & Technology , Engineering & Construction , typography

Prerequisites:

first and second derivatives for linear combinations of integer or fractional powers; trigonometric functions or integrals; concepts of curves in the plane and in space; Green's Theorem or Stokes's Theorem

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