Index
Note: Page numbers followed by “f”, “t” and “b” indicates figures, tables and boxes respectively.
Absolute values, 84–85
equation, 77
Acute angle, 189
Acute triangle, 210
Additive inverse matrix, 226
Algebra, 37
basic principles
example, 38–39
exercises, 298–299
exponent, 45–47
expression, 38
polynomial, 52
proportion, 56–59
radicals, 45–47
ratio, 55–56
shortened rules, 38
variation, 59
Angle, 151
Arc, 157
Arcfunction, 202
Area, 173
of circular ring, 176
in geometry, 173–177
exercises, 177–178
of rectangle, 173
of sector, 177
of square, 173
of trapezoid, 174
of triangle, 175
Arithmetic numbers, 1–2
decimals, 20
addition, 23
division, 25–26
multiplication, 24–25
rules to rounding off decimals, 22–23
subtraction, 24
exercises, 289–298
operations, 2
adding or subtracting of fractions, 10
addition, 2
dividing fractions, 11–14
division, 5–6
fractions, 6–9
multiplication, 3–5
multiplying fractions, 11
subtraction, 2–3
percents (%), 28–30
Associative property of matrix addition, 226–227
Base, 49
Binomial, 51–52
Capacity measurements of liquid, 135–137
Cartesian coordinates, See Rectangular coordinates
Celsius (C), 140
Center, 156
Central angle, 190
Chord, 157
Circle, 156
Close interval, 80
Coefficient, 38
Column matrix, 222
Column vector, See Column matrix
Common denominator, 10
Commutative property of matrix addition, 226
Complementary angles, 190
Complex numbers, 87–90
Constant of variation, 59
Data visualization, 97
Decagon, 155
Decimals, 20
addition, 23
division, 25–26
multiplication, 24–25
rules to rounding off decimals, 22–23
subtraction, 24
Degree, 152
Denominator, 6
Derived units, 143–145
base and supplementary units, 143t
derived units with special names, 144t
exercises, 145–146
quantities of units having special names, 143t
Determinants, 235
Diagonal matrix, 222
Diameter, 157
Direct proportion, 59
Direct variation, 59b
Distance between points, 99b
Distance points, 99–100
Dividing fractions, 11–14
Division, 5–6
Domain, 108b
Dot product, 248
Elements of matrix, 222
Entries of matrix, See Elements of matrix
Equality of matrices, 224
Equations, 68
absolute value equation, 77
constructing models to solve problems with one variable, 69–71
example, 68
exercises, 77–80
quadratic equations, 72–73
radical equation, 75–76
rational equation, 73–75
with two variables, 71–72
Equilateral polygon, 167
Equilateral triangle, 169
Even and odd functions, 110
Expand commands, 266
Exponent, 45–47
Expression, 38
Factor commands, 266
Fahrenheit (F), 140
Fractions, 6–9
Functions, 108–119
Geometry, 149–157
angle measurement and triangles, 160–163
area in, 173–177
exercises, 157–160
perimeter and circumference in, 166–170
volume in, 179–182
Gram, 133
Graphs, 98–105
Half-closed interval, 81
Half-open interval, 81
Hexagon, 154
Horizontal line test, 112b
Inequality equations, 80–85
linear inequality, 83–85
Inner product, See Dot product
Inscribed angle, 190
Integer numbers, 2
International System of Units (SI) Prefixes, 129t
Intervals, 80–85
Inverse
Irrational numbers, 2
Isosceles triangle, 169
Joint variation, 60
Kite, 156
Law of cosines, 211–212
Law of sines, 210–211
LCD, See Lowest common denominator (LCD)
Length measurements, 126–129
Like terms, 50
Line, 150
Linear inequality, 83–85
absolute values, 84–85
Lowest common denominator (LCD), 10
Lowest term, 7
assignments, 266
default environment, 262f
help system, 264f
plots with, 268–269
solving equations, 267
started and windows of, 261
symbolic computation, 266
working with output, 267
worksheet mode, 263f
Mass, 133
Mass and weight measurements, 133–134
exercises, 134–135
metric system and U.S. system of weight, 133t
metric units of weight, 133t
U.S. customary units of weight, 133t
Mathematical models, 69
arithmetic operations on arrays, 278t
arithmetic operators, 273t
default environment, 272f
elementary math functions, 274t
getting started and windows, 271
in calculations, 271–279
Line Color Types, 280t
Line Styles, 279t
matrix operations, 275t
named constants, 277t
plotting, 279–286
Point Styles, 279t
software, 271
symbolic computation, 287
windows, 273t
Matrices, 222
example, 223–224
exercises, 230–234
location of element in matrix, 222
operations, 224
addition of matrices, 224
additive identity matrix, 226
additive inverse matrix, 226
associative property of matrix addition, 226–227
commutative property of matrix addition, 226
equality of matrices, 224
multiplicative identity matrix, 228
multiplicative inverse matrix, 228–229
product of constant and matrix, 227
product of matrices, 227–228
subtraction of matrices, 224–225
symmetric matrix, 230
transpose of matrix, 229–230
size determination, 223
types, 222
Measure, 125
Measurement, 125
capacity measurements of liquid, 135–137
derived units, 143–145
length, 126–129
mass and weight, 133–134
temperature, 140–142
Meter, 126
Metric units of length, 126t
Minutes, 161
Mixed number, 8
Multiplicative identity matrix, 228
Multiplicative inverse matrix, 228–229
Multiplying fractions, 11
Negative angle, 205–206
Negative exponents, 45b–46b
Negative matrix, See Additive inverse matrix
Null matrix, See Additive identity matrix
Number line, 81
Numerator, 6
Oblique triangle, 210
Obtuse angle, 189
Obtuse triangle, 210
Octagon, 155
Open interval, 80
Order of operations, 12
Origin, 98
Orthogonal vectors, 250
Parallel and perpendicular lines, 104
Parallel lines, 153
Parallel vectors, 250–251
Pentagon, 154
Percents (%), 28–30
Perimeter, 166
Perimeter and circumference in geometry, 166–173
Perpendicular lines, 153
Plane, 151
Plot functions, 276
Plotting, 279
two-dimensional, 279–286
Point, 150
of tangent, 157
Polygon, 154–155
Polynomial, 52
Positive angle, 205–206
Product of constant and matrix, 227
Product of matrices, 227–228
Proportion, 56–59
Protractor, 160–161
Quadratic equations, 72–73
Quadratic formula, 72
Quadrilateral, 154
Radicals, 45–47
equation, 75–76
Radius, 157
Range, 108b
Ratio, 55–56
Rational equation, 73–75
Rational numbers, 2
Ray, 151
Real numbers, 2
Reciprocal identities, 200
Rectangular coordinates, 98–99
Reference angle, 208–209
Rhombus, 156
Right angle, 189
Right triangle, 191–192
Row matrix, 222
Row vector, See Row matrix
Scalar, 242b
Scalar product, See Dot product
Secant, 157
Second, 161
Sector, 157
Segment, 157
Set, 81
Sides, 151
Simplify command, 266
Singular matrix, 238
matrix, 222
Standard International Metric system (SI), 125
Standard position, 206
Standard unit vectors, 246–248
Straight angle, 189
Subtracting of fractions, 10
Subtraction, 2–3
of matrices, 224–225
Supplementary angles, 190
Symbolic computation, 287
simplifying symbolic expressions, 287
Symbolic math, 287
Symmetric matrix, 230
Systems analysis, 221
Tangent, point of, 157
Temperature measurement, 140–142
Time measurements, 138–140
Transpose of matrix, 229–230
Trapezoid, 155
Triangle, 154
Trigonometric functions, 197
complementary functions, 201
example, 198–199
inverse trigonometric functions, 202–203
reciprocal identities, 200
supplementary functions, 201–202
Trigonometry, 187–188
angles types, 189
complementary functions, 201
supplementary functions, 201–202
trigonometric functions, 197–203
unit circle, 205–212
units of angles, 188
Trigonometry cofunction identities functions, See Trigonometry—complementary functions
Trinomial, 52
Two-dimensional plotting, 279
axis commands, 283t
example, 282
fplot function, 280
Greek characters, 284t
Line Color Types, 280t
MATLAB plots with graphics, 286t
plots in MATLAB, 282–283
Unit circle, 205
law of cosines, 211–212
law of sines, 210–211
oblique triangle, 210
Pythagorean theorem, 207
reference angle, 208–209
standard position, 206
unit circle diagram, 206
Unlike terms, 50
Variables, 38
Variation, 59
constant of variation, 59
direct variation, 59b
example, 59–61
inverse variation, 61b
joint variation, 60
See also Scalar
addition, 244
component form of vector, 243
dot product, 248–251
examples, 242–243
operations, 244–246
standard unit vectors, 246–248
zero vector, 243
Vertex, 151
Vertical line test, 108–113
Volume, 179
of cone, 180
of cube, 179
of cylinder, 180
in geometry, 179–183
of pyramid, 181
of rectangular solid, 179
of sphere, 181
Weight, 133
Weight measurements, See Mass and weight measurements
Whole numbers, 2
Work (W), 252–253
x-axis, 98
y-axis, 98
y-intercept, 101
Zero angle, 189
Zero exponents, 45b–46b
Zero matrix, See Additive identity matrix
Zero vector, 243
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