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Algebraic Manipulation   (Mathematica Overview)
Structural Operations on Polynomials Finding the Structure of a Polynomial Polynomial Orderings
Calculus   (Mathematica Overview)
Differentiation Total Derivatives Derivatives of Unknown Functions
Constrained Optimization in ...   (Mathematica Tutorial)
[1] Mehrotra, S. "On the Implementation of a Primal-Dual Interior Point Method." SIAM Journal on Optimization 2 (1992): 575–601. [2] Nelder, J.A. and R. Mead. "A Simplex ...
Straight Integration   (Mathematica Tutorial)
This equation is solved by simply integrating the right-hand side with respect to x. Here is a plot of the integral curves for different values of the arbitrary constant C[1].
Files, Streams, and External Operations   (Mathematica Overview)
Reading and Writing Mathematica Files External Programs Streams and Low-Level Input and Output
Input and Output in Notebooks   (Mathematica Overview)
Entering Greek Letters Entering Two-Dimensional Input Editing and Evaluating Two-Dimensional Expressions
Linear Algebra   (Mathematica Overview)
Constructing Matrices Getting and Setting Pieces of Matrices Scalars, Vectors, and Matrices
Manipulating Equations and Inequalities   (Mathematica Overview)
Equations Solving Equations The Representation of Equations and Solutions
Modularity and the Naming of Things   (Mathematica Overview)
Modules and Local Variables Local Constants How Modules Work
Series, Limits, and Residues   (Mathematica Overview)
Sums and Products Power Series Making Power Series Expansions
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