Quick Start Tips for MathematicaüWe will be using a very small subset of Mathematica's capabilities. Mathematica is very powerful, and is different from a graphing calculator in that it can actually do symbolic manipulation. Mathematica can solve algebraic equations, perform definite and indefinite integerals, take derivatives, solve differential equations, manipulate special functions (bessel, hyperconfluent geometric, etc), perform sums, solve for eignenvalues and eigenvectors, and also perform numerical solutions to most of the above. MENUES AND PALETTES:Help>>Documentation Center Window Mathematica has a gazzillion useful functions that can be searched for using this help function.Window>Basic Math Input Palette Very basic "clickable"pallete for entering forumulasWindow>Basic Math Assistant Palette Basic "clickable" pallete for entering forumulasUSER INTERFACE TIPS:MATHEMATICA IS CASE SENSITIVE!The RETURN key means "new line".The ENTER key means "evaluate this expression".For keyboards without an ENTER key, use SHIFT-RETURN instead.Use arrow keys to navigate cursor through complex expressions. You can also use your mouse toclick on an expression or cell in order to modify it.BASIC MATH FUNCTIONS:Multiplication: x*y*z = x y z = (x) (y)(z)Division: y/(x z ) = yx z... can also use key sequence CNTRL êScientific Notation: 1.234*^4 = 1.234 *104 THIS DOES NOT WORK: 1.234E4Numerical Ouput: 11/2 //N returns 5.5 OR 11. /2 returns 5.5Constants: E = 2.718...P = p =3.14159 ... can also use key sequence: ESC pi ESC I = ‰ =-1 ... can also use key sequence ESC ii ESCExponentiation: x^y = xy ... can also use key sequence x CNTRL^ ySquare Root: Sqrt[x] = Sqrt@xD ... can also use use key sequence CNTRL ûTrig and Other Functions: All trig functions assume radians--NOT degrees!Cos[x]Sin[x]Tan[x]ArcCos[x] ArcSin[x]ArcTan[x]Log[b, x] returns "log base b of x"Complex Numbers:Abs[x+‰ y] = x2+ y2Arg[x+‰ y] = ArcTan[x,y]Exp[‰ x] = e‰ xArg[ Exp[i f] ] = fRe[x+ ‰ y] = xIm[x + ‰ y] = yConjugate[x + ‰ y] = x - ‰ yEXPORTING GRAPHICS: Option 1: Right click on graph and use "Copy Graphics Selection" to put in clipboard for pasting into other files directly. This does not seem to work with Microsoft Word, but it does with many other text editors. Option 2: To save graph to file: (a) select graph by clicking on it (b) File>Save Selection As... (c) Follow file dialog. The file formats pdf and png tend to interact well with many text editors, and also print well.MORE ADVANCED FUNCTIONS:Substitution: x*q /. {x -> a*b , q-> z} returns a*b*zLists/Arrays: Arrays are called lists and have the format x={a, b, c, d, e, f} To index elements from a list use: x[[1]] returns a x[[2]] returns bMultidimensional List/Array:A multi-dimensional array could be of the form x = {{a, b}, {c, d}, {e, f}} To index elements from a multidimensional list use: x[[1,1]] returns a x[[1,2]] returns b x[[3, 2]] returns f Length[x] returns the number of elements in the array x MatrixForm[x] displays the array x as: a bc de f TableForm[x, TableHeadings Æ {{"Row 1", "Row 2", "Row 3"}, {"x value", "y value"}}] displays the array x as: "x value" "y value""Row 1" a b"Row 2" c d"Row 3" e f Table comand allows you to create arrays or lists: x = TableA9a, a2=, 8a, 1, 4, 0.5<E returns x= {{1., 1.}, {1.5, 2.25}, {2., 4.}, {2.5, 6.25}, {3., 9.}, {3.5, 12.25}, {4., 16.}}üWe will be using a very small subset of Mathematica's capabilities. Mathematica is very powerful, and is different from a graphing calculator in that it can actually do symbolic manipulation. Mathematica can solve algebraic equations, perform definite and indefinite integerals, take derivatives, solve differential equations, manipulate special functions (bessel, hyperconfluent geometric, etc), perform sums, solve for eignenvalues and eigenvectors, and also perform numerical solutions to most of the above. MENUES AND PALETTES:Help>>Documentation Center Window Mathematica has a gazzillion useful functions that can be searched for using this help function.Window>Basic Math Input Palette Very basic "clickable"pallete for entering forumulasWindow>Basic Math Assistant Palette Basic "clickable" pallete for entering forumulasUSER INTERFACE TIPS:MATHEMATICA IS CASE SENSITIVE!The RETURN key means "new line".The ENTER key means "evaluate this expression".For keyboards without an ENTER key, use SHIFT-RETURN instead.Use arrow keys to navigate cursor through complex expressions. You can also use your mouse toclick on an expression or cell in order to modify it.BASIC MATH FUNCTIONS:Multiplication: x*y*z = x y z = (x) (y)(z)Division: y/(x z ) = yx z... can also use key sequence CNTRL êScientific Notation: 1.234*^4 = 1.234 *104 THIS DOES NOT WORK: 1.234E4Numerical Ouput: 11/2 //N returns 5.5 OR 11. /2 returns 5.5Constants: E = 2.718...P = p =3.14159 ... can also use key sequence: ESC pi ESC I = ‰ =-1 ... can also use key sequence ESC ii ESCExponentiation: x^y = xy ... can also use key sequence x CNTRL^ ySquare Root: Sqrt[x] = Sqrt@xD ... can also use use key sequence CNTRL ûTrig and Other Functions: All trig functions assume radians--NOT degrees!Cos[x]Sin[x]Tan[x]ArcCos[x] ArcSin[x]ArcTan[x]Log[b, x] returns "log base b of x"Complex Numbers:Abs[x+‰ y] = x2+ y2Arg[x+‰ y] = ArcTan[x,y]Exp[‰ x] = e‰ xArg[ Exp[i f] ] = fRe[x+ ‰ y] = xIm[x + ‰ y] = yConjugate[x + ‰ y] = x - ‰ yEXPORTING GRAPHICS: Option 1: Right click on graph and use "Copy Graphics Selection" to put in clipboard for pasting into other files directly. This does not seem to work with Microsoft Word, but it does with many other text editors. Option 2: To save graph to file: (a) select graph by clicking on it (b) File>Save Selection As... (c) Follow file dialog. The file formats pdf and png tend to interact well with many text editors, and also print well.MORE ADVANCED FUNCTIONS:Substitution: x*q /. {x -> a*b , q-> z} returns a*b*zLists/Arrays: Arrays are called lists and have the format x={a, b, c, d, e, f} To index elements from a list use: x[[1]] returns a x[[2]]