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

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Matt Klassen