1Preface
783.5.3 Basis and its Properties
21.Functions and Relations
793.5.4 Span over the Basis
31.1 The Rectangular Coordinate System and Graphing Utilities
80Exercise Set 3.5
41.1.1 Plot points on a Rectangular Coordinate System
813.6 Vector Subspace : 3.6.1 Operations under Vector Subspace
51.1.2 The Distance and Midpoint Formulas
82Exercise Set 3.6
61.1.3 Graph Equations by Plotting Points
83References
71.1.4 Identify -x and y-Intercepts
844.Linear and Non-linear Functions
81.2 Circles
854.1 Straight Lines
91.2.1 Write an Equation of a Circle in Standard Form
864.1.1 Introduction
101.2.2 Write the General Form of an Equation of a Circle
874.1.2 Slope of Straight Line
111.3 Functions and Relations
884.1.3 Angle between two Straight Lines
121.3.1 Determine Whether a Relation is a Function
894.1.4 Collinearity of three Points
131.3.2 Apply Function Notation
904.1.5 Different forms of Line
141.3.3 Determine the x and y-intercepts of a Function Defined by y = f(x)
914.1.6 Distance
151.3.4 Determine Domain and Range of a Function
924.1.7 Section Formula
161.4 Linear Equations in Two Variables and Linear Functions
934.1.7 Shifting of Axis
171.4.1 Graph Linear Equations in Two Variables
944.1.8 Rotation of Axis
181.4.2 Determine the Slope of a Line
95Exercise Set 4.1
191.4.3 Apply the Slope – Intercept Form of a Line
964.2 Lines in pair
201.4.4 Compute Average Rate of Change
974.2.1 Family of Lines
211.5 Applications of Linear Equations and Modeling
984.2.2 Homogeneous Equation of Second Degree
221.5.1 Apply the Point – Slope Formula
994.2.3 Angle Bisector
231.5.2 Determine the Slopes of Parallel and Perpendicular Lines
100Exercise Set 4.2
241.5.3 Create a Linear Function in an Application
1014.3 Non-linear Function
251.6 Transformations of Graphs
1024.3.1 Introduction
261.6.1 Recognize Basic Functions
1034.3.2 Exponential Function
271.6.2 Apply Vertical and Horizontal Translations
1044.3.3 Logarithmic Functions
281.6.3 Apply Vertical and Horizontal Shrinking and Stretching
1054.3.4 Conversion between Exponential & Logarithmic Functions
291.6.4 Apply Reflections across the x and y-Axes
106Exercise Set 4.3
301.6.6 Summarize Transformations of Graphs
107References
311.7 Analyzing Graphs of Functions and Piecewise – Defined Functions
1085.Binomial Expansion, Sequence and Series
321.7.1 Test for Symmetry
1095.1 Binomial Expansion
331.7.2 Identify Even and Odd Functions
1105.1.1 Pascal’s Triangle
341.7.3 Graph Piecewise – Defined Functions
1115.1.2 Factorial Notation
351.7.4 Investigate Increasing, Decreasing, and Constant Behavior of a Function
1125.1.3 Binomial Theorem
361.7.5 Determine Relative Minima and Maxima of a Function
1135.2 Sequence
371.8 Algebra of Functions and Function Composition
1145.2.1 Finite and Infinite Sequences
381.8.1 Perform Operations on Functions
1155.2.2 Increasing and Decreasing Sequence
391.8.2 Evaluate a Difference Quotient
1165.3 Series: 5.3.1 Partial Sum
401.8.3 Compose and Decompose Functions
117Exercise Set 5.3
41References
1185.4 Arithmetic Sequence or Arithmetic Progression
422.Linear Programming
1195.4.1 General term (or nth term) of an Arithmetic Sequence
432.1 Linear inequalities
1205.4.2 Sum of an Arithmetic Sequence
44Exercise Set 2.1
1215.4.3 Arithmetic Mean
452.2 Properties associated with Linear Inequalities
1225.4.4 Real life examples of Arithmetic Sequence
46Exercise Set 2.2
123Exercise Set 5.4
472.3 Graphing Linear Inequalities
1245.5 Geometric Sequence or Geometric Progression
48Exercise Set 2.3
1255.5.1 General term (or nth term) of a Geometric Sequence
492.4 Linear Programming Practical Problems
1265.5.2 Sum of a Geometric Sequence
502.4.1 Furniture Manufacturing Problem
1275.5.3 Geometric Mean ( G. M. )
512.4.2 People’s Nutrition Problems
1285.5.4 Real life examples of Geometric Sequence
522.4.3 Packaging Problems
129Exercise Set 5.5
532.4.4 Investments and Funds Problems
1305.6 Relation between Arithmetic Mean and Geometric Mean
542.4.4 Transportation and Shipping Problems
131Exercise Set 5.6
55References
1325.7 Convergence and Divergence of Series
563.Vectors
1335.7.1 Limit of a Sequence
573.1 Scalars and vectors: Introduction
1345.7.2 Determining the Convergence and Divergence of a Sequence
583.1.1 Magnitude of the Vector
1355.7.3 nth term test for the Divergence of an Infinite Sequence
593.1.2 Algebraic Properties
1365.7.4 Test for the Convergence of Geometric Sequence
603.1.3 Classifications of the Vectors
1375.8 The p-Series and the Ratio Test for the convergence or divergence of series
613.2 Properties of vector
1385.8.1 The Harmonic Series
623.2.1 Associative Property
1395.8.2 The p- Series
633.2.2 Commutative Property
1405.8.3 Test for the Convergence of a p- Series
643.2.3 Plane of a Vector
1415.8.4 Ratio Test for the Convergence and Divergence of Series
653.2.4 Conditional Vectors
1425.8.5 Radius of Convergence
66Exercise Set 3.2
143Exercise Set 5.8
673.3 Coplanar Vectors
144References
683.3.1 Laws in Vectors
1456.Permutations and Combinations
693.3.2 Direction Cosines and their Ratios
1466.1 Permutations
703.3.3 Laws of Cosines and Sines
1476.1.1 Permutation of n Different Objects
713.3.4 Projection of the Vector
1486.1.2 Permutation of n Different Objects when Repetition is Allowed
72Exercise Set 3.3
1496.1.3 Permutation when the objects are not Distinct
733.4 Section formula
150Exercise 6.1
74Exercise Set 3.4
1516.2 Combinations: 6.2.1 Combination Formulas
753.5 Standard basis of R2 and R3
152Exercise Set 6.2
763.5.1 Linear Combination of the R2 and R3
153References
773.5.2 Test for Dependency
154Index
