13/14 Semester 1
Computer Programming
(TKK-2144)
Instructor: Rama Oktavian
Email: rama.oktavian@ub.ac.id
Office Hr.: M.13-15, W. 13-15 Th. 13-15, F. 13-15
Outlines
1. Microsoft Excel basic function
2. Matrix (basic theory)
3. Matrix operation in excel
4. The application of Matrix in Chem. Eng
Basic function
Using Relative References
Cell references are used in formulas, functions, charts , and other Excel
commands.
By default, a spreadsheet cell reference is relative. What this means is that
as a formula or function is copied and pasted to other cells, the cell
references in the formula or function change to reflect the function's new
location.
Basic function
Using Absolute References
an absolute cell reference identifies the location a cell or group of cells.
An absolute cell reference consists of the column letter and row number
surrounded by dollar signs ( $ ).
An absolute cell reference is used when you want a cell reference to stay
fixed on a specific cell.
Basic function
Using Mixed references
Basic function
Entering Relative, Absolute, and Mixed References
 To enter a relative reference, type the cell reference


as it appears in the worksheet. For example, enter
B2 for cell B2
To enter an absolute reference, type $ (a dollar
sign) before both the row and column references.
For example, enter $B$2
To enter a mixed reference, type $ before either the
row or column reference. For example, enter $B2 or
B$2
or
 Select the cell reference you want to change
 Press the F4 key to cycle the reference from relative
to absolute to mixed and then back to relative
Basic function
-Mathematics function
- Statistical function
- Logical function
- etc
Basic function
Mathematics functions
abs(CELL): Absolute value of CELL
sqrt(CELL): Square root of CELL [to do nth roots, use CELL^(1/n)]
ln(CELL): Natural log of CELL
log10(CELL): Log of CELL to base 10
log(CELL, NUM): Log of CELL to the base NUM (use for all bases except e
and 10)
exp(CELL): Exponential(e^x) of CELL. Use since Excel doesn't have a builtin constant "e".
sin(CELL), cos(CELL), tan(CELL): Trigonometric functions sine, cosine, and
tangent of CELL. CELL must be in radians
asin(CELL), acos(CELL), atan(CELL): Inverse trigonometric functions
(returns values in radians)
sinh(CELL), cosh(CELL), tanh(CELL): Hyperbolic functions
asinh(CELL), acosh(CELL), atanh(CELL): Inverse hyperbolic functions
Basic function
Statistical functions
average(CELL1, CELL2, ...) OR average(GROUP): Computes the arithmetic
average of all inputs
intercept(GROUP1, GROUP2): Calculates the y-intercept (b) of the regression
line where y = GROUP1 and x = GROUP2
slope(GROUP1, GROUP2): Calculates the slope (m) of the regression line
where y = GROUP1 and x = GROUP2.
“if” function
Working with Logical Functions
 A logical function is a function that works with
values that are either true or false
 The IF function is a logical function that returns
one value if the statement is true and returns a
different value if the statement is false
 IF(logical_test, value_if_true, [value_if_false])
“if” function
Working with Logical Functions
A comparison operator is a symbol that indicates the relationship
between two values
“if” function
Working with Logical Functions
 =IF(A1="YES", "DONE", "RESTART")
 =IF(A1="MAXIMUM", MAX(B1:B10), MIN(B1:B10))
 =IF(D33>0, $K$10, 0)
“if” function
Working with Logical Functions
Matrix (basic theory)
Matrix Mathematics
 Matrices are very useful in engineering calculations. For
example, matrices are used to:
- Efficiently store a large number of values
-Solve systems of linear simultaneous equations
 Several mathematical operations involving matrices are
important
Matrix (basic theory)
Review: Properties of Matrices
• An element of a matrix is usually written in lower case, with
its row number and column number as subscripts:
• The dimension (size) of a matrix is defined by the number
of rows and number of columns
• Examples:
3 × 3:
2×4:
Matrix (basic theory)
Matrix Operations
•
•
•
•
•
•
Matrix Addition
Multiplication of a Matrix by a Scalar
Matrix Multiplication
Matrix Transposition
Finding the Determinate of a Matrix
Matrix Inversion
Matrix (basic theory)
Matrix Addition
• Vectors must be the same size in order to add
• To add two vectors, add the individual elements:
• Matrix addition is commutative:
A+B=B+A
Matrix (basic theory)
Multiplication of Matrices
• To multiple two matrices together, the matrices must have
compatible sizes:
This multiplication is possible only if the number of columns in A
is the same as the number of rows in B
• The resultant matrix C will have the same number of rows as
A and the same number of columns as B
Matrix (basic theory)
Multiplication of Matrices
• Consider these matrices:
•
Can we find this product?
Yes, 3 columns of A = 3 rows of B
• What will be the size of C?
2 X 2: 2 rows in A, 2 columns in B
Matrix (basic theory)
Example – Matrix Multiplication
•
Solution:
In general, matrix multiplication
is not commutative:
AB ≠ BA
Matrix (basic theory)
Transpose of a Matrix
• The transpose of a matrix by switching its row and columns
The transpose of a matrix is designated by a superscript T:
Matrix (basic theory)
Determinant of a Matrix
• The determinant of a square matrix is a scalar quantity that
has some uses in matrix algebra. Finding the determinate
of 2 × 2 and 3 × 3 matrices can be done relatively easily:
• The determinate is designated as |A| or det(A)
• 2 × 2:
Matrix (basic theory)
Determinant of a Matrix
• 3 × 3:
Matrix (basic theory)
Inverse of Matrix
• The inverse of a 2X2 matrix is easy to find:
Matrix (basic theory)
The identity matrix
• a square matrix with 1’s as the diagonal elements and 0’s as
the other elements
• Find A-1, check that A A-1 = I
Matrix Operations in Excel
• Excel has commands for:
•
•
•
•
Multiplication (mmult)
Transpose (transpose)
Determinate (mdeterm)
Inverse (minverse)
• Important to remember that these commands apply to an
array of cells instead of to a single cell
• When entering the command, you must identify the entire
array where the answer will be displayed
• Using the Enter key with an array command only returns an
answer in a single cell. Instead, use Ctrl + Shift + Enter keys
with array functions
Matrix Operations in Excel
Excel Matrix Multiplication
Matrix Operations in Excel
Excel Matrix Multiplication
The MMULT function has two arguments: the ranges of cells to be
multiplied. Remember that the order of multiplication is
important.
Matrix Operations in Excel
Excel Transpose
Matrix Operations in Excel
Excel Determinate
Matrix Operations in Excel
Excel Matrix Inversion
Remember that only square matrices can have inverses
Matrix Operations in Excel
Excel Matrix Inversion
A X A-1 = I, the identity matrix:
The application of Matrix
Solving linear simultaneous equation
• If equations contain only linear terms of the independent
variables – that is, only constants multiplied by each variable
– and constants, then the equation is linear
• If the equation contains any terms such as x2, cos(x), ex,
etc., then the equation is non-linear
Linear simultaneous equation
The application of Matrix
Solution to Simultaneous Equations
• Graphical solution
• Substitution method
• Elimination method
The application of Matrix
Equations in Matrix Form
• The first step in using matrix methods to solve a series of linear
simultaneous equations is to write them in matrix form
• For n simultaneous equations and n unknowns:
where A is the coefficient matrix (n × n); X is the matrix of
unknowns (n × 1), and C is the constant matrix (n × 1)
The application of Matrix
Solution of System of Linear Equations
 Multiply both sides of the equation by the inverse of the
coefficient matrix. Remember that the order of
multiplication is important.
 Since the inverse of a matrix times that matrix is equal to
the identity matrix,
The application of Matrix
Solution of System of Linear Equations
 Since the identity matrix times another matrix is equal to
that matrix,
 Therefore, we can find the unknown variables by
multiplying the inverse of the coefficient matrix by the
constant matrix
The application of Matrix
Example – 3 Equations
Write these equations in matrix form:
The application of Matrix
Excel Solution
Enter coefficient and constant matrices:
The application of Matrix
Excel Solution
Enter formula to invert A matrix and multiply the result by the C
matrix. This can be done in two steps or with nested commands as
shown here:
The application of Matrix
Chem. Eng Problem
Steady state material balances on a separation train
Xylene, styrene, toluene and benzene are to be separated with
the array of distillation columns that is shown below where F, D,
B, D1, B1, D2 and B2 are the molar flow rates in mol/min.
The application of Matrix
Chem. Eng Problem
Solution
Material balances on individual components on the overall
separation train yield the equation set
The application of Matrix