JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY
DIT 0204 (DIT0205)
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Class notes DIT 0204 (DIT0205)
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DIT 0204 (DIT0205)
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JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY
This book, for students TVET and up, hits the biggest soft spots most of today's students have. The problem with the mathematics curriculum used by most schools today is that students are given formula after formula to memorize and blindly use in problem solving. In this way, the students never lea...
JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY
DIT 0204 (DIT0205)
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MINISTRY OF EDUCATION
DIPLOMA IN
INFORMATION COMMUNICATION
TECHNOLOGY
KENYA INSTITUTE OF CURRICULUM DEVELOPMENT
STUDY NOTES
Computational Mathematics
MODULE I: SUBJECT NO 5
Page 1 of 199
,Contents
CHAPTER 1: INTRODUCTION TO COMPUTATIONAL MATHEMATICS .................................. 6
Equations .................................................................................................................................................. 6
Algebraic equation .................................................................................................................................... 6
An introduction to MATRICES .............................................................................................................. 19
Definition of Matrix............................................................................................................................. 19
Types of Matrices ................................................................................................................................ 20
Operation of matrices ......................................................................................................................... 22
Determinant of a Matrix ..................................................................................................................... 28
Inverse of a Matrix .............................................................................................................................. 30
Algebraic Properties of Matrix Operations ......................................................................................... 38
Applications of Matrix Mathematics .................................................................................................. 42
CHAPTER 2: NUMBER SYSTEM AND BINARY ARITHMETIC................................................... 43
Introduction to Number System .............................................................................................................. 43
Bits & Bytes: ........................................................................................................................................... 43
Binary Number System: .......................................................................................................................... 43
Other Number System............................................................................................................................. 45
Conversion between Number System ..................................................................................................... 46
Introduction to Binary Arithmetic........................................................................................................... 49
Representation of negative numbers ....................................................................................................... 56
Computer data formats/coding ................................................................................................................ 58
CHAPTER 3: LOGIC GATES AND BOOLEAN ALGEBRA............................................................. 64
Introduction to Logic Mathematics ......................................................................................................... 64
Types of Sets ....................................................................................................................................... 64
Operation of a Set ............................................................................................................................... 70
Venn Diagrams ................................................................................................................................... 83
Boolean Algebra ..................................................................................................................................... 91
Terminologies in Boolean Algebra ..................................................................................................... 91
Logic Functions gates and circuitry .................................................................................................... 92
Theorems of Boolean Algebra ............................................................................................................ 95
Karnaugh maps (K-maps) ................................................................................................................... 98
CHAPTER 4: DISCRETE COUNTING .............................................................................................. 103
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, The Basic Rules/Principles of Counting ............................................................................................... 103
The Rules of Sum and Product .......................................................................................................... 103
Pigeonhole Principle ......................................................................................................................... 103
Examples ........................................................................................................................................... 104
The Inclusion-Exclusion principle ...................................................................................................... 104
Counting Techniques ............................................................................................................................ 105
Permutations..................................................................................................................................... 105
Combinations .................................................................................................................................... 107
Pascal's Identity................................................................................................................................. 108
Binomial Theorem ................................................................................................................................ 108
Exponents.......................................................................................................................................... 109
The Pattern ....................................................................................................................................... 110
Coefficients ....................................................................................................................................... 111
Formula ............................................................................................................................................. 113
Geometry .......................................................................................................................................... 116
Pascal's Triangle ................................................................................................................................ 118
CHAPTER 5: PROBABILITY .............................................................................................................. 122
Introduction to probability .................................................................................................................... 122
Probability Models ................................................................................................................................ 122
Equally likely outcomes ........................................................................................................................ 123
The Sum Rule ....................................................................................................................................... 125
Random Variables................................................................................................................................. 126
The Mean (Expected Value) of a Probability model ............................................................................ 126
The Law of Large Numbers .................................................................................................................. 127
Probability of Single or Combined Events ........................................................................................... 127
Independent and Dependent Events ...................................................................................................... 127
Conditional Probability ......................................................................................................................... 128
Probability Tree Diagrams .................................................................................................................... 129
Set Theory in Probability ...................................................................................................................... 132
Probability Distribution ........................................................................................................................ 135
CHAPTER 6: GRAPHS OF FUNCTIONS .......................................................................................... 137
Defining the Graph of a Function ..................................................................................................... 137
Page 3 of 199
, Vertical Line Test ................................................................................................................................. 138
Characteristics of Graphs ...................................................................................................................... 139
Continuous Functions ........................................................................................................................... 142
Interpolation and Extrapolation ............................................................................................................ 144
Area under a Curve ............................................................................................................................... 144
Inequality .............................................................................................................................................. 147
Common Graph Construction Errors .................................................................................................... 149
CHAPTER 7: DATA COLLECTION METHODS ............................................................................. 152
Introduction to Data Collection Methods.............................................................................................. 152
Data Edition: ......................................................................................................................................... 152
Types of Data Collection Methods ....................................................................................................... 152
Selecting Appropriate Data Collection Method .................................................................................... 153
Classification of Data ............................................................................................................................ 153
Data Tabulation and Presentation ......................................................................................................... 154
CHAPTER 8: MEASURES OF CENTRAL TENDENCY ................................................................. 162
Introduction to central tendency ........................................................................................................... 162
The significance property of measures of central tendency .................................................................. 162
Types and measures of central tendency............................................................................................... 162
Calculation in central tendency ............................................................................................................. 162
CHAPTER 9: MEASURES OF DISPERSION.................................................................................... 166
Introduction to measure of Dispersion .................................................................................................. 166
Properties of a good measure of Dispersion ......................................................................................... 166
Types of Dispersion .............................................................................................................................. 166
Methods of Dispersion and Calculations .............................................................................................. 167
Quartiles, deciles, percentiles and S.I.R. ............................................................................................... 167
Skewness and kurtosis in Dispersion interplatation .............................................................................. 170
CHAPTER 10: NUMERICAL ANALYSIS ......................................................................................... 172
Introduction to Numerical analysis ....................................................................................................... 172
General introduction ............................................................................................................................. 172
Approximation theory ........................................................................................................................... 172
Numerical methods ............................................................................................................................... 173
Direct and iterative methods ................................................................................................................. 173
Page 4 of 199
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