Chapter 01 Calculating Numbers and Expressions
1.1 Basic Operations ························································································· 1
1.2 Operations on Irrational Numbers and Irrational Expressions ··············································· 10
1.3 Ratios and Proportions ·································································· 13
Practice Problems ······················································································· 19 Chapter 02 Equations and Inequalities
2.1 First and Second Degree Equations ··························································· 21
2.2 Systems of Equations ······································································· 25
2.3 First and second order inequalities ··························································· 31
2.4 Simultaneous Inequalities ······································································· 38
Practice Problems ·························································································· 41 Chapter 03 Exponential and Logarithmic Functions
3.1 Exponents and Logarithms ·································································· 45
3.2 Function Movement ·································································· 49
3.3 Exponential Functions ······································································· 52
3.4 Logarithmic Function ······································································· 57
Practice Problems ·························································································· 62 Chapter 04 Trigonometric Functions
4.1 Trigonometric Ratios ············································································· 67
4.2 Sexagesimal and Hodo Methods ················································································· 71
4.3 Definition of Trigonometric Functions ··························································· 75
4.4 Graphs of Trigonometric Functions ······················································· 80
4.5 Addition theorem and formulas for trigonometric functions ······································ 84
Practice Problems ······················································································· 88 Chapter 05 Matrices and Determinants
5.1 Matrix ··························································································· 93
5.2 Various operations on matrices ················································ 95
5.3 Various Matrices ········································································· 99
Practice Problems ·················································································· 106 Chapter 06 Vectors
6.1 Definition of vectors and basic operations ················································ 109
6.2 Dot and cross products of vectors ································································· 114
Practice Problems ·················································································· 118 Chapter 07 Differential Calculus
7.1 Differentiation and Derivatives ························································· 121
7.2 Differentiation of Transcendental Functions ································································· 125
7.3 Various Formulas of Differentiation ································· 127
Practice Problems ·················································································· 132 Chapter 08 Integration
8.1 Indefinite Integrals ········································································ 135
8.2 Definite Integrals ························································································· 139
8.3 Applications of Integration ································································ 146
Practice Problems ·················································································· 151 Chapter 09 Complex Numbers
9.1 Complex Numbers ························································································· 155
9.2 Complex Plane ·················································································· 160
9.3 Various Theorems and Applications ·························································· 166
Practice Problems ·················································································· 174 Chapter 10 Spatial Figures and Spatial Coordinates
10.1 Spatial Figures ······································································· 177
10.2 Orthographic projection ·········································································· 182
10.3 Spatial Coordinates ······································································· 184
Practice Problems ················································································· 190
Search ················································································ 193