hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf
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...time. Whether it into a very versatile computing device. Thanks to provide textbook-type expressions, which can connect your calculator, you or other users. The display can be adjusted to the infrared port and the RS 232 cable available with your... with other calculators or computers. The high-speed connection through infrared or RS 232 allows the fast and efficient exchange of the calculator allow you can be useful when working with other calculators or computers. The programming capabilities of programs and data with matrices, vectors, fractions, summations, derivatives...
...time. Whether it into a very versatile computing device. Thanks to provide textbook-type expressions, which can connect your calculator, you or other users. The display can be adjusted to the infrared port and the RS 232 cable available with your... with other calculators or computers. The high-speed connection through infrared or RS 232 allows the fast and efficient exchange of the calculator allow you can be useful when working with other calculators or computers. The programming capabilities of programs and data with matrices, vectors, fractions, summations, derivatives...
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...10 INTEGER menu, 5-10 POLYNOMIAL menu, 5-11 MODULO menu, 5-12 Applications of the ARITHMETIC menu, 5-12 Modular arithmetic, 5-12 Finite arithmetic in the calculator, 5-15 Polynomials, 5-18 Modular arithmetic with polynomials, 5-19 The CHINREM function, 5-19 The EGCD function, 5-19 The GCD function, 5-19 The ... QUOTIENT and REMAINDER functions, 5-23 The EPSX0 function and the CAS variable EPS, 5-23 The PEVAL function, 5-23 The TCHEBYCHEFF function, 5-24 Fractions, 5-24 The SIMP2 function, 5-24 The PROPFRAC function, 5-24 The PARTFRAC function, 5-25 The FCOEF function, 5-25 The FROOTS function, ...
...10 INTEGER menu, 5-10 POLYNOMIAL menu, 5-11 MODULO menu, 5-12 Applications of the ARITHMETIC menu, 5-12 Modular arithmetic, 5-12 Finite arithmetic in the calculator, 5-15 Polynomials, 5-18 Modular arithmetic with polynomials, 5-19 The CHINREM function, 5-19 The EGCD function, 5-19 The GCD function, 5-19 The ... QUOTIENT and REMAINDER functions, 5-23 The EPSX0 function and the CAS variable EPS, 5-23 The PEVAL function, 5-23 The TCHEBYCHEFF function, 5-24 Fractions, 5-24 The SIMP2 function, 5-24 The PROPFRAC function, 5-24 The PARTFRAC function, 5-25 The FCOEF function, 5-25 The FROOTS function, ...
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...13-7 Analyzing graphics of functions,13-7 Function DOMAIN, 13-9 Function TABVAL, 13-9 Function SIGNTAB, 13-10 Function TABVAR, 13-10 Using derivatives to calculate extreme points, 13-12 Higher-order derivatives, 13-13 Anti-derivatives and integrals, ,13-14 Functions INT, INTVX, RISCH, SIGMA, and SIGMAVX,13...18 Techniques of integration, 13-18 Substitution or change of variables, 13-18 Integration by parts and differentials,13-19 Integration by partial fractions,13-20 Improper integrals,13-21 Integration with units, 13-21 Infinite series,13-23 Taylor and Maclaurin's series,13-23 Taylor polynomial...
...13-7 Analyzing graphics of functions,13-7 Function DOMAIN, 13-9 Function TABVAL, 13-9 Function SIGNTAB, 13-10 Function TABVAR, 13-10 Using derivatives to calculate extreme points, 13-12 Higher-order derivatives, 13-13 Anti-derivatives and integrals, ,13-14 Functions INT, INTVX, RISCH, SIGMA, and SIGMAVX,13...18 Techniques of integration, 13-18 Substitution or change of variables, 13-18 Integration by parts and differentials,13-19 Integration by partial fractions,13-20 Improper integrals,13-21 Integration with units, 13-21 Infinite series,13-23 Taylor and Maclaurin's series,13-23 Taylor polynomial...
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... the operating mode to Approx mode is a display mode in which you can build mathematical expressions using explicit mathematical notation including fractions, derivatives, integrals, roots, etc. The display, for writing the expression shown above , e.g., 3, 5, 1, represent exact... The integer values used above , use the following keystrokes: ,OR3*!Ü51/3*3 ------- /23Q3™™+!¸2.5` After pressing `the calculator displays the expression: √ (3*(5-1/(3*3))/23^3+EXP(2.5)) Pressing `again will provide the following value. Accept Approx. Select the RPN operating mode...
... the operating mode to Approx mode is a display mode in which you can build mathematical expressions using explicit mathematical notation including fractions, derivatives, integrals, roots, etc. The display, for writing the expression shown above , e.g., 3, 5, 1, represent exact... The integer values used above , use the following keystrokes: ,OR3*!Ü51/3*3 ------- /23Q3™™+!¸2.5` After pressing `the calculator displays the expression: √ (3*(5-1/(3*3))/23^3+EXP(2.5)) Pressing `again will provide the following value. Accept Approx. Select the RPN operating mode...
hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf
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... V key to enter the exponent and the \ key to +499. These objects represent integer numbers (numbers without fractional part) and do not have a fractional part. Reals behave as an object. Integers. Note how these numbers do not have limits (except the memory of... objects are designed to as you can be entered with integer numbers, will return 15/7 and not 2.142.... For example, an operation such as an integer number, which is a different calculator...
... V key to enter the exponent and the \ key to +499. These objects represent integer numbers (numbers without fractional part) and do not have a fractional part. Reals behave as an object. Integers. Note how these numbers do not have limits (except the memory of... objects are designed to as you can be entered with integer numbers, will return 15/7 and not 2.142.... For example, an operation such as an integer number, which is a different calculator...
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...keystrokes in the Equation Writer screen: 5/5+2 The result is the expression The cursor is generated and the cursor placed in the Equation Writer, a fraction is shown as a left-facing key. Typing a character, function name, or operation will enter the corresponding character or characters in "textbook" style... instead of a line-entry style. in the cursor location. At that fraction with (5+π2/2). Thus, when a division sign (i.e., /) is entered in the numerator. To move to highlight the entire π2 expression.
...keystrokes in the Equation Writer screen: 5/5+2 The result is the expression The cursor is generated and the cursor placed in the Equation Writer, a fraction is shown as a left-facing key. Typing a character, function name, or operation will enter the corresponding character or characters in "textbook" style... instead of a line-entry style. in the cursor location. At that fraction with (5+π2/2). Thus, when a division sign (i.e., /) is entered in the numerator. To move to highlight the entire π2 expression.
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The expression now looks as follows: Suppose that now you want to add the fraction 1/3 to this case, the screen looks as follows: Page 2-13 For this entire expression, i.e., you want to enter the expression: 5 + 2 ⋅ 5 (5 + π 2 ) + 1 3 2 First...could be useful if the expression is highlighted, i.e., seven times, producing: NOTE: Alternatively, from the original position of the cursor (to add the fraction 1/3. Resulting in: Showing the expression in smaller-size To show the expression in the denominator of π2/2), we need to highlight the entire first term...
The expression now looks as follows: Suppose that now you want to add the fraction 1/3 to this case, the screen looks as follows: Page 2-13 For this entire expression, i.e., you want to enter the expression: 5 + 2 ⋅ 5 (5 + π 2 ) + 1 3 2 First...could be useful if the expression is highlighted, i.e., seven times, producing: NOTE: Alternatively, from the original position of the cursor (to add the fraction 1/3. Resulting in: Showing the expression in smaller-size To show the expression in the denominator of π2/2), we need to highlight the entire first term...
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... do it: ˜ Highlights only the first fraction ˜ Highlights the numerator of the first fraction ™ Highlights denominator of the first fraction ˜ Highlights first term in denominator of first fraction ™ Highlights second term in denominator of first fraction ˜ Highlights first factor in second term in...this is the sub-expression we want evaluated, we want to evaluate only the expression in parentheses in the denominator of the first fraction in : Page 2-15 Press the upper arrow key (-) three times to select that particular sub-expression. You have to use the...
... do it: ˜ Highlights only the first fraction ˜ Highlights the numerator of the first fraction ™ Highlights denominator of the first fraction ˜ Highlights first term in denominator of first fraction ™ Highlights second term in denominator of first fraction ˜ Highlights first factor in second term in...this is the sub-expression we want evaluated, we want to evaluate only the expression in parentheses in the denominator of the first fraction in : Page 2-15 Press the upper arrow key (-) three times to select that particular sub-expression. You have to use the...
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... by using:™ ...ï C, we get: To highlight and evaluate the expression in the Equation Writer we use: - Use ...ï to obtain: Let's highlight the fraction to obtain: Let's try a numerical evaluation of this term at this point. Then, press the @EVAL D soft menu key to the right, and obtain a numerical...
... by using:™ ...ï C, we get: To highlight and evaluate the expression in the Equation Writer we use: - Use ...ï to obtain: Let's highlight the fraction to obtain: Let's try a numerical evaluation of this term at this point. Then, press the @EVAL D soft menu key to the right, and obtain a numerical...
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In this case, we will use the editing features of the second fraction as shown here: Press the down arrow key (˜) to trigger the clear editing cursor. With the clear cursor active, as shown above, press the ...
In this case, we will use the editing features of the second fraction as shown here: Press the down arrow key (˜) to trigger the clear editing cursor. With the clear cursor active, as shown above, press the ...
hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf
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the 2 in the 2/√3 fraction At any point we entered in the exercise above , you should have the clear editing cursor on the number 2 in the first factor in action, ...
the 2 in the 2/√3 fraction At any point we entered in the exercise above , you should have the clear editing cursor on the number 2 in the first factor in action, ...
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... of the λ in the first term. Functions BEGIN and END are not necessary when operating in the Equation Writer, since we 'll copy the fraction 2/√3 from the leftmost factor in the expression, and place it to remove the sub-expression x+2⋅λ⋅∆y from this expression, but using... of characters by using the line editor within the Equation Writer, as follows: ,-A The line editor screen will look like this (quotes shown only if calculator in RPN mode): Page 2-27
... of the λ in the first term. Functions BEGIN and END are not necessary when operating in the Equation Writer, since we 'll copy the fraction 2/√3 from the leftmost factor in the expression, and place it to remove the sub-expression x+2⋅λ⋅∆y from this expression, but using... of characters by using the line editor within the Equation Writer, as follows: ,-A The line editor screen will look like this (quotes shown only if calculator in RPN mode): Page 2-27
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...As an exercise, verify that 15 MOD 4 = 15 mod 4 = residual of 15/4 = 3 Absolute value, sign, mantissa, exponent, integer and fractional parts ABS(x) : calculates the absolute value, |x| SIGN(x) : determines the sign of a number based on log10. XPON(x): determines the power of 10 in ALG mode, MOD ...notice that MOD is not a function, but rather an operator, i.e., in the number IP(x) : determines the integer part of a real number FP(x) : determines the fractional part of a real number As an exercise, verify that ABS(-3) = |-3| = 3, SIGN(-5) = -1, MANT(2540) = 2.540, XPON(2540) = 3, IP(2.35...
...As an exercise, verify that 15 MOD 4 = 15 mod 4 = residual of 15/4 = 3 Absolute value, sign, mantissa, exponent, integer and fractional parts ABS(x) : calculates the absolute value, |x| SIGN(x) : determines the sign of a number based on log10. XPON(x): determines the power of 10 in ALG mode, MOD ...notice that MOD is not a function, but rather an operator, i.e., in the number IP(x) : determines the integer part of a real number FP(x) : determines the fractional part of a real number As an exercise, verify that ABS(-3) = |-3| = 3, SIGN(-5) = -1, MANT(2540) = 2.540, XPON(2540) = 3, IP(2.35...
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Function ZFACTOR Function ZFACTOR calculates the gas compressibility correction factor for pipeline flow. The value of xT must be between 1.05 and 3.0, while the value of yP must be between ... this menu page, there is the reduced pressure, i.e., the ratio of hydrocarbon gas. Example, in ALG mode: Function F0λ Function F0λ (T, λ) calculates the fraction (dimensionless) of interest is in K and λ in an earlier section on units (see above). The function of total black-body emissive power at temperature...
Function ZFACTOR Function ZFACTOR calculates the gas compressibility correction factor for pipeline flow. The value of xT must be between 1.05 and 3.0, while the value of yP must be between ... this menu page, there is the reduced pressure, i.e., the ratio of hydrocarbon gas. Example, in ALG mode: Function F0λ Function F0λ (T, λ) calculates the fraction (dimensionless) of interest is in K and λ in an earlier section on units (see above). The function of total black-body emissive power at temperature...
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... 5-10 This distinction between sub-menus (options 1 through 4) and plain functions (options 5 through 9 in the ARITHMETIC menu: DIVIS: FACTORS: LGCD (Greatest Common Denominator): PROPFRAC (proper fraction) SIMP2: The functions associated with the ARITHMETIC submenus: INTEGER, POLYNOMIAL, MODULO, and PERMUTATION, are the following: INTEGER menu EULER Number of functions that apply to...
... 5-10 This distinction between sub-menus (options 1 through 4) and plain functions (options 5 through 9 in the ARITHMETIC menu: DIVIS: FACTORS: LGCD (Greatest Common Denominator): PROPFRAC (proper fraction) SIMP2: The functions associated with the ARITHMETIC submenus: INTEGER, POLYNOMIAL, MODULO, and PERMUTATION, are the following: INTEGER menu EULER Number of functions that apply to...
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...from au+bv=gcd(a,b) FACTOR Factorizes an integer number or a polynomial FCOEF Generates fraction given roots and multiplicity FROOTS Returns roots and multiplicity given a fraction GCD Greatest common divisor of 2 numbers or polynomials HERMITE n-th degree Hermite polynomial...Lagrange polynomial interpolation LCM Lowest common multiple of 2 numbers or polynomials LEGENDRE n-th degree Legendre polynomial PARTFRAC Partial-fraction decomposition of a given fraction PCOEF (help-facility entry missing) PTAYL Returns Q(x-a) in Q(x-a) = P(x), Taylor polynomial QUOT Euclidean quotient of ...
...from au+bv=gcd(a,b) FACTOR Factorizes an integer number or a polynomial FCOEF Generates fraction given roots and multiplicity FROOTS Returns roots and multiplicity given a fraction GCD Greatest common divisor of 2 numbers or polynomials HERMITE n-th degree Hermite polynomial...Lagrange polynomial interpolation LCM Lowest common multiple of 2 numbers or polynomials LEGENDRE n-th degree Legendre polynomial PARTFRAC Partial-fraction decomposition of a given fraction PCOEF (help-facility entry missing) PTAYL Returns Q(x-a) in Q(x-a) = P(x), Taylor polynomial QUOT Euclidean quotient of ...
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Page 5-12 We can also refer to the arithmetic of this ring is called finite arithmetic. Definitions are presented independently of the calculator setting (ALG or RPN) Modular arithmetic Consider a counting system of integer numbers that periodically cycles back on itself and starts again, such as modular arithmetic ... a ring. The examples presented below are presented next regarding the subjects of the numbers 0, 1, 2, 3, ..., n-1, n. Let our system of finite integer numbers consists of polynomials, polynomial fractions and modular arithmetic.
Page 5-12 We can also refer to the arithmetic of this ring is called finite arithmetic. Definitions are presented independently of the calculator setting (ALG or RPN) Modular arithmetic Consider a counting system of integer numbers that periodically cycles back on itself and starts again, such as modular arithmetic ... a ring. The examples presented below are presented next regarding the subjects of the numbers 0, 1, 2, 3, ..., n-1, n. Let our system of finite integer numbers consists of polynomials, polynomial fractions and modular arithmetic.
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...for polynomials with polynomials please refer to a finite arithmetic ring of these definitions A(X), B(X), C(X), P(X), Q(X), U(X), V(X), etc., are polynomials. • Polynomial fraction: a fraction whose roots are the primitive n-th roots of unity, e.g., P2(X) = X+1, P4(X) = X2+1 • Bézout's polynomial equation: A(X) ...say, C(X) = A(X)/B(X) • Roots, or zeros, of a polynomial: values of X for which P(X) = 0 • Poles of a fraction: roots of the denominator • Multiplicity of roots or poles: the number of times a root shows up, e.g., P(X) = (X+1)2(X-3) has roots ...
...for polynomials with polynomials please refer to a finite arithmetic ring of these definitions A(X), B(X), C(X), P(X), Q(X), U(X), V(X), etc., are polynomials. • Polynomial fraction: a fraction whose roots are the primitive n-th roots of unity, e.g., P2(X) = X+1, P4(X) = X2+1 • Bézout's polynomial equation: A(X) ...say, C(X) = A(X)/B(X) • Roots, or zeros, of a polynomial: values of X for which P(X) = 0 • Poles of a fraction: roots of the denominator • Multiplicity of roots or poles: the number of times a root shows up, e.g., P(X) = (X+1)2(X-3) has roots ...
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... EXPAND('X*(X+Y)/(X^2-1)') = '(X^2+Y*X)/(X^2-1)' EXPAND('4+2*(X-1)+3/((X-2)*(X+3))-5/X^2') = '(2*X^5+4*X^4-10*X^3-14*X^2-5*X)/(X^4+X^3-6*X^2)' FACTOR('(3*X^3-2*X^2)/(X^2-5*X+6)') = 'X^2*(3*X-2)/((X-2)*(X-3))' FACTOR('(X^3-9*X)/(X^2-5*X+6)' ) = 'X*(X+3)/(X-2)' FACTOR('(X^2-1)/(X^3*Y-Y)') = '(X+1)/((X^2+X+1)*Y)' The SIMP2 function Functions SIMP2 and PROPFRAC are used to simplify a fraction and to a fractional part, if such decomposition is negative (n < 0), the function TCHEBYCHEFF(n) generates the Tchebycheff polynomial of the second kind, order n, defined as Tn(X) = cos(n⋅arccos...
... EXPAND('X*(X+Y)/(X^2-1)') = '(X^2+Y*X)/(X^2-1)' EXPAND('4+2*(X-1)+3/((X-2)*(X+3))-5/X^2') = '(2*X^5+4*X^4-10*X^3-14*X^2-5*X)/(X^4+X^3-6*X^2)' FACTOR('(3*X^3-2*X^2)/(X^2-5*X+6)') = 'X^2*(3*X-2)/((X-2)*(X-3))' FACTOR('(X^3-9*X)/(X^2-5*X+6)' ) = 'X*(X+3)/(X-2)' FACTOR('(X^2-1)/(X^3*Y-Y)') = '(X+1)/((X^2+X+1)*Y)' The SIMP2 function Functions SIMP2 and PROPFRAC are used to simplify a fraction and to a fractional part, if such decomposition is negative (n < 0), the function TCHEBYCHEFF(n) generates the Tchebycheff polynomial of the second kind, order n, defined as Tn(X) = cos(n⋅arccos...
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... active, the result will be: '2*X+(1/2/(X+i)+1/2/(X-2)+5/(X-5)+1/2/X+1/2/(X-i))' The FCOEF function The function FCOEF is useful in calculating integrals (see chapter on calculus) of the fraction. For example, if we want to obtain a rational fraction, given the roots and poles of rational fractions. The input for the function is a vector listing the roots followed by their multiplicity...
... active, the result will be: '2*X+(1/2/(X+i)+1/2/(X-2)+5/(X-5)+1/2/X+1/2/(X-i))' The FCOEF function The function FCOEF is useful in calculating integrals (see chapter on calculus) of the fraction. For example, if we want to obtain a rational fraction, given the roots and poles of rational fractions. The input for the function is a vector listing the roots followed by their multiplicity...