1. Getting Started

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Null

Setup

\(Clear["Global`*`"]; 
Off[General::spell]; 
Off[General::spell1]; 
    \)

1.0   Differences between Mathematica v.3.0.1 (used here) and v.2.x (used in the textbook)

1.  Mathematica v.3.0.1 permits use of Greek letters, superscripts, subscripts, and mathematical notation.

fn  =   
      Sqrt[x]  - z^(1/3) +  Cos[ω t  +  ϕ]  +  
        Sin[Θ]

2.  The Simplify operation is more extensive in Mathematica v.3.0.1,  and the new operation FullSimplify is even more powerful.
See also Section 1.2.3 for examples.

y1 = 
      (√(
              (a^4) - 2 (a^6) + (a^8) - 2 (a^2) (b^2) - 6 (a^4) (b^2) + 
                4 (a^6) (b^2) + (b^4) - 6 (a^2) (b^4) + 6 (a^4) (b^4) - 
                2 (b^6) + 4 (a^2) (b^6) + (b^8) - 8 (a^5) b c + 
                8 (a^7) b c - 16 (a^3) (b^3) c + 24 (a^5) (b^3) c - 
                8 a (b^5) c + 24 (a^3) (b^5) c + 8 a (b^7) c - 
                8 (a^4) (b^2) (c^2) + 24 (a^6) (b^2) (c^2) - 
                8 (a^2) (b^4) (c^2) + 48 (a^4) (b^4) (c^2) + 
                24 (a^2) (b^6) (c^2) + 32 (a^5) (b^3) (c^3) + 
                32 (a^3) (b^5) (c^3) + 16 (a^4) (b^4) (c^4)))/
        (√(
              (a^4) - 2 (a^6) + (a^8) - 2 (a^2) (b^2) - 2 (a^4) (b^2) + 
                4 (a^6) (b^2) + (b^4) + 2 (a^2) (b^4) + 6 (a^4) (b^4) + 
                2 (b^6) + 4 (a^2) (b^6) + (b^8) - 8 (a^5) b c + 
                8 (a^7) b c + 24 (a^5) (b^3) c + 8 a (b^5) c + 
                24 (a^3) (b^5) c + 8 a (b^7) c - 8 (a^4) (b^2) (c^2) + 
                24 (a^6) (b^2) (c^2) + 8 (a^2) (b^4) (c^2) + 
                48 (a^4) (b^4) (c^2) + 24 (a^2) (b^6) (c^2) + 
                32 (a^5) (b^3) (c^3) + 32 (a^3) (b^5) (c^3) + 
                16 (a^4) (b^4) (c^4)));

y1 // Simplify

y1 // FullSimplify

3.  The packages "Algebra`Trigonometry`" and "Algebra`SymbolicSum`" are obsolete, their functionality is already present in Mathematica v.3.0.1, and they should NOT be loaded,

Needs["Algebra`Trigonometry`"]

Needs["Algebra`SymbolicSum`"]

4.   In Mathematica v.3.0.1 the operations TrigToComplex and ComplexToTrig are obsolete and have been replaced by TrigToExp and ExpToTrig.  These include hyperbolic functions, so the routines defined on p.147 of the text are also obsolete.

fn1  =  Cos[x]  +  I Sin[x]  +  Cosh[z]

fn1 // TrigToComplex

fn1 // TrigToExp

fn2  =  
      Exp[I ω t]  +  Exp[2 I ω t]  +  
        Exp[-z t]

fn2 // ComplexToTrig

fn2 // ExpToTrig

5.   In Mathematica v.3.0.1 the 3-D graphics option Graphics`VectorPlot`ScaleFunction
has been replaced by Graphics`Common`GraphicsCommon`ScaleFunction.  Use the latter designation when setting a scale function in vector plots.  See Section 1.6.3.

Context[ScaleFunction]

Needs["Graphics`PlotField`"]

Context[ScaleFunction]

Context[Graphics`Common`GraphicsCommon`ScaleFunction]

Options[PlotGradientField]

6.  Mathematica v.3.0.1 is quite stable but is NOT immune to crashes (usually from insuffient memory) and to aberrant behavior.
Therefore:
(1) SAVE YOUR WORK FREQUENTLY,

(2) Do a program Exit/Restart at the first observation of a "glitch" or unexpected response.

(3)  When starting a new problem, always do a program Exit/Restart to avoid conflicts with variables already defined or initialized.