The documents in the links that follow require either Mathematica 8 or later, or the free Mathematica CDF Viewer (you can find that here).
Mathematics as the study of objects, their relationships, and the structures created by their relationships. Numbers and Sets as Mathematical Objects. Arithmetic Operations as Relationships Between Numbers. Sets of Numbers as Having Properties Determined by the Operations Relating Numbers.
Properties of Sets. Properties of Arithmetic Operations. Symbolic Manipulation Techniques. Introduction to Calculating in Mathematica.
Using Numbers to Represent Measurable Quantities
Truth Tables and Proof
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Points and Sets of Points as Mathematical Objects. Distance, angles, and congruence as relationships. Triangles and Polygons. Coordinate Systems.
Circles. Solids. Conic sections. Introduction to Geometry in Mathematica.
Plotting data.
Geometric proofs.
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Equations and inequalities. Functions. Algebraic functions. Transcendental functions.
Trigonometric functions. Plotting functions. Vectors. Introduction to Functions, Plotting, and Equation-Solving in Mathematica.
Probability.
Approximation.
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Limits. Differentiation. Integration. Series.
Applications of derivatives. Applications of integrals. Differential equations. Introduction to calculus in Mathematica.
Error analysis.
Methods of integration.
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The nature of science. What it takes to be a scientist. Units and dimensions. Estimation.
Observational error. Unit conversions. Modeling. Introduction to units and measurement in Mathematica.
Propagation of error.
Deriving formulas.
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Kinematics. Forces and mass. Dynamics. Conservation laws.
Projectiles. Oscillations. Collisions. Introduction to mechanics in Mathematica.
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Conduct a calculation or derivation.
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Vector analysis. Electric fields. Magnetic fields. Induction.
DC circuits. AC circuits. Maxwell's equations and waves. Introduction to electrodynamics in Mathematica.
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Conduct a calculation or derivation.
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Waves. Uncertainty. The Schrödinger equation. Bound states.
The photoelectric effect. The Compton effect. The quantum structure of matter. Introduction to quantum physics in Mathematica.
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Conduct a calculation or derivation.
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Thermodynamic properties. Thermodynamic laws. Kinetic theory. Statistical mechanics.
States of matter. The ideal gas. Quantum statistics. Introduction to thermal physics in Mathematica.
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Conduct a calculation or derivation.
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The periodic table of the elements. Chemical reactions. Stoichiometry. Chemical bonding.
Aqueous reactions. Solutions. Chemical equilibrium. Introduction to chemistry in Mathematica.
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Conduct a calculation or derivation.
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