ASCOT Library Zabali Campus

1 Sets and the numbers systems –
1.1 Sets –
1.2 Number sets –
1.3 Algebra of the real numbers R –
1.4 Order in R –
1.5 Algebra of complex numbers –
Chapter 1 summary –
2 Algebraic expressions –
2.1 Polynomials –
2.2 Addition and subtraction of algebraic expressions –
2.3 Laws of exponents –
2.4 Multiplication of polynomials –
2.5 Special products –
2.6 Binomial expansion –
2.7 Division of polynomials –
2.8 Factoring –
2.9 Rational or fractional expressions –
2.10 Simplification of rational expressions –
2.11 Multiplication and division of rational expressions –
2.12 Addition and subtraction of rational expressions –
2.13 Complex fractions –
2.14 Zero and negative exponents –
2.15 Irrational expressions –
2.16 Simplification of radicals –
2.17 Addition and subtraction of radicals –
2.18 Multiplication and division of radicals –
Chapter 2 summary –
3 Functions and graphs –
3.1 The two-dimensional coordinate system –
3.2 Relations and functions –
3.3 Graphs of functions and relations –
3.4 Operations on functions –
3.5 Types of functions –
Chapter 3 summary –
4 Equations and inequalities –
4.1 The linear function and its graphs –
4.2 The straight line –
4.3 Solution of a linear equation in one variable –
4.4 The quadratic function and its graph –
4.5 Solutions of a quadratic function and its graph –
4.6 nature of the roots of a quadratic equation –
4.7 Equations involving radicals –
4.8 Equations in quadratic form –
4.9 Word problems –
4.10 Variation –
4.11 Polynomial equations in one variable –
4.12 Inequalities –
Chapter 4 summary –
5 Systems of equations and inequalities –
5.1 System of two linear equations in two variables –
5.2 System of two non-linear equations in two variables –
5.3 System of three linear equations in three variables –
5.4 Solutions of systems of linear equations –
5.5 Systems of inequalities in two variables –
Chapter 5 summary –
6 Circular functions –
6.1 The point function –
6.2 The circular functions –
6.3 Identities of the circular functions –
6.4 Angles –
6.5 Trigonometric functions of angles –
6.6 Graph of the circular functions –
6.7 Identities, equations and inequalities –
Chapter 6 summary
7 Inverse functions –
7.1 Inverse of a function –
7.2 Inverse circular or inverse trigonometric relations –
7.3 Inverse circular or inverse trigonometric functions –
7.4 Identities and equations involving inverse circular –
Chapter 7 summary –
8 Applications of trigonometric functions –
8.1 Trigonometric functions of an angle of a right triangle –
8.2 Right triangle solution –
8.3 Oblique triangle solution –
8.4 Vectors –
8.5 Complex numbers –
8.6 Multiplication and division of complex numbers in polar form –
8.7 Powers and roots of complex numbers in polar form –
Chapter 8 summary –
9 The exponential and logarithmic functions –
9.1 The exponential function –
9.2 The logarithmic function –
9.3 Common logarithms –
Chapter 9 summary –
10 Sequences, series, mathematical induction...
10.1 Sequences –
10.2 Series –
10.3 The arithmetic sequence or arithmetic progression –
10.4 The geometric sequence or geometric progression –
10.5 Mathematical induction –
10.6 The binomial theorem –
10.7 Counting principle –
10.8 Permutations –
10.9 Combinations –
10.10 Sets and counting –
Chapter 10 summary.

"The authors, faculty members from the UP Mathematics Department, envision the book College Algebra and Trigonometry to be readable and mathematically sound.
This book unifies the subjects of algebra and trigonometry and is intended to serve as a textbook for a course which is prerequisite to other mathematical courses. Hence, one of the aims of this book is to develop in a student the necessary skills and attitudes to effectively learn succeeding courses. A long-range objective is to enable the student to appreciate the logical nature of mathematics. To this end, the student must be exposed to mathematical thoughts and processes through a rigorous exposition of the subject matter.
The notion of sets is introduced in Chapter 1. Also in this chapter are all the important properties of real numbers, which are clearly stated and proved. The one-dimensional coordinate system is presented in the ordering of real numbers. A discussion of the algebra of complex numbers is included as an extension of the real number system.
Chapter 2 provides for the development of skills in algebraic processes of mathematical expressions. In Chapter 3, the concept of a function and a relation is presented both as correspondence (mapping) and as a set of ordered pairs. The two-dimensional coordinate system is then introduced with the use of the Cartesian product R x R. A comprehensive discussion of functions includes operations, types, transformations, and graphs.
In the solution of equations and systems of equations in Chapters 4 and 5, emphasis is placed on equivalent equations and systems. Geometric methods and determinant methods are used to solve equations.
An unusual feature of the book can be found in Chapter 6, which is a discussion of the point function. This function associates real numbers to a point P(x, y) on the Cartesian plane. From this, the six circular functions are defined. The analytic, rather than the computational part of trigonometry, is emphasized. Eventually, the real number is considered as a measure of an angle. Inverse functions are discussed in Chapter 7. The trigonometric functions of angles followed by the computational aspect of trigonometry become tools in solving problems involving triangles. These are discussed in detail in Chapter 8 where vectors and the polar form of a complex number are also taken up.
In Chapter 9, the logarithmic and exponential functions are fully discussed. Chapter 10 includes other topics not covered by the previous chapters, such as sequences, series, mathematical induction, the binomial theorem, and permutations and combinations.
The authors believe that, at the level of a freshman college student, learning can best be attained by example. Thus, to clarify concepts and show models of procedure, a variety of solved examples are provided in every section of the book. Proofs of theorems within the student's capability of understanding are presented.
In addition to the standard and traditional topics of algebra and trigonometry, we have included vectors, matrices and determinants, sequences, mathematical induction, permutations and combinations Thus, the student should be adequately equipped to study finite mathematics, probability and statistics, analytic geometry and calculus.
Each chapter opens with a quotation from one among several remarkable men of mathematics. A brief historical sketch pertinent to some chapters is given. All sections in each chapter end with exercises and all chapters conclude with summary and review tests.
We acknowledge the invaluable assistance of Gilbert Abueg, Maria Carmen Amarra, Romar dela Cruz, Marc Anthony Gonzales, Michael Gutierrez, Manuel Joseph Loquias, Mia Rosales, Christopher Santos and Gino Angelo Velasco for the typing and layout of the book.
We shall appreciate feedback, comments and suggestions from teachers and students of mathematics who use this book." - Leticia L. Castillo, Fe N. Reyes, Flor V. Cejalvo, Jesusa T. Tangco