MAT 300/500 - Previous Lecture Notes by Topic

Lecture 1 --- Bezier Curves, Nested Linear Interpolation, Vector Spaces of Polynomials

Lecture 2 --- Midpoint Subdividision, Bernstein, Shifted, Vandermonde, and Top-down bases

Lecture 3 --- Polynomial vector spaces, proofs of basis properties

Lecture 4 --- Properties of Bernstein and Cumulative Bernstein polynomials

Lecture 5 --- Piecewise polynomial vector spaces

Lecture 6 --- Shifted truncated power function bases

Lecture 7 --- Polynomial Interpolation: Existence and Uniqueness

Lecture 8 --- Divided differences, Newton form, and Leibniz formula

Lecture 9 --- Derivations of Newton form and Leibniz rule, Osculating polynomials

Lecture 10 --- Newton form and Existence/Uniqueness for Osculating polynomial

Lecture 11 --- More derivations for osculating polynomial

Lecture 12 --- Order of continuity and standard basis for splines, cubic splines

Lecture 13 --- Midterm review, examples for order of continuity for splines and bases

Lecture 14 --- Polar forms for polynomials and Bezier curves

Lecture 15 --- Polar forms, Existence/Uniqueness, Control point property

Lecture 16 --- Derivatives and Implicit forms for Bezier curves

Lecture 17 --- Quadratic Bezier curves, parabolas, and conics

Lecture 18 --- Tangent construction and quadratic implicit forms

Lecture 19 --- Quadratic Bezier curve examples

Lecture 20 --- Order of continuity vector, and knot sequences

Lecture 21 --- B-splines and B-spline curves, orders of continuity

Lecture 22 --- B-spline recursion formula

Lecture 23 --- Writing B-splines as sums of truncated power functions with Cramer's rule

Lecture 24 --- Equivalence of DeBoor algorithm and B-spline summation

Lecture 25 --- Curry-Schoenberg Theorem on B-spline change of basis

Lecture 26 --- Interpolation with B-splines, Schoenberg-Whitney Theorem

Lecture 27 --- Introduction to surfaces, tensor products, Review

Lecture 28 --- Polar forms for B-splines

Lecture 29 --- Derivatives of B-splines

Matt Klassen