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638 cataloged entries (Calculus 1 264, Calculus 2 60, Colloquia 18, Combinatorial Commutative Algebra 36, Coxeter Groups 42, CSc 890 Software Architecture 78, DNA Topology 22, Dynamical Systems 18, General Physics 2 (Phys 122) 19, Matroid Theory 43, ...). Five most recently indexed files are:
We use the derivative of tangent at $x=pi/4$ and the point-slope formula.
A lecture excerpt from Calculus 1 by Arek Goetz | May 2009, length 7 min.
Review of the definitions of sine and cosine. The derivation of $\frac{d}{dx} \sin x = \cos x$. Trigonometric limits. Other derivatives of trigonometric functions.
A lecture from Calculus 1 by Arek Goetz | May 2009, length 71 min.
The unit circle. Definitions of the sine, cosine, tangent functions. Also defined are cotangent, secant, and cosecant. Basic properties of sine and cosine. The trigonometric identity $cos^2 \theta + \sin^2 \theta =1$. Sine and cosine of the summation. Double angle formula for sine. Special angles, $pi/4$ and $pi/3$.
A lecture from Calculus 1 by Arek Goetz | May 2009, length 48 min.
We present a topological/combinatorial formula for the graded Betti numbers and the Hilbert series of a lattice ideal.
A lecture from Combinatorial Commutative Algebra by Federico Ardila | May 2009, length 50 min.
We describe the initial ideal of a lattice ideal in terms of an optimization problem in integer programming. We also describe the initial complex of a lattice ideal in terms of regular subdivisions.
A lecture from Combinatorial Commutative Algebra by Federico Ardila | May 2009, length 53 min.
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