Basic Technical Mathematics with Calculus

Each chapter contains: Equations, Quick Chapter Review, Review Exercises, Practice Test



1. Basic Algebraic Operations

1.1 Numbers

1.2 Fundamental Operations of Algebra

1.3 Calculators and Approximate Numbers

1.4 Exponents

1.5 Scientific Notation

1.6 Roots and Radicals

1.7 Addition and Subtraction of Algebraic Expressions

1.8 Multiplication of Algebraic Expressions

1.9 Division of Algebraic Expressions

1.10 Solving Equations

1.11 Formulas and Literal Equations

1.12 Applied Word Problems

2. Geometry

2.1 Lines and Angles

2.2 Triangles

2.3 Quadrilaterals

2.4 Circles

2.5 Measurement of Irregular Areas

2.6 Solid Geometric Figures

3. Functions and Graphs

3.1 Introduction to Functions

3.2 More about Functions

3.3 Rectangular Coordinates

3.4 The Graph of a Function

3.5 Graphs on the Graphing Calculator

3.6 Graphs of Functions Defined by Tables of Data

4. The Trigonometric Functions

4.1 Angles

4.2 Defining the Trigonometric Functions

4.3 Values of the Trigonometric Functions

4.4 The Right Triangle

4.5 Applications of Right Triangles

5. Systems of Linear Equations; Determinants

5.1 Linear Equations

5.2 Graphs of Linear Functions

5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

6. Factoring and Fractions

6.1 Special Products

6.2 Factoring: Common Factor and Difference of Squares

6.3 Factoring Trinomials

6.4 The Sum and Difference of Cubes

6.5 Equivalent Fractions

6.6 Multiplication and Division of Fractions

6.7 Addition and Subtraction of Fractions

6.8 Equations Involving Fractions

7. Quadratic Equations

7.1 Quadratic Equations; Solution by Factoring

7.2 Completing the Square

7.3 The Quadratic Formula

7.4 The Graph of the Quadratic Function

8. Trigonometric Functions of Any Angle

8.1 Signs of the Trigonometric Functions

8.2 Trigonometric Functions of Any Angle

8.3 Radians

8.4 Applications of Radian Measure

9. Vectors and Oblique Triangles

9.1 Introduction to Vectors

9.2 Components of Vectors

9.3 Vector Addition by Components

9.4 Applications of Vectors

9.5 Oblique Triangles, the Law of Sines

9.6 The Law of Cosines

10. Graphs of the Trigonometric Functions

10.1 Graphs of y = a sin x and y = a cos x

10.2 Graphs of y = a sin bx and y = a cos bx

10.3 Graphs of y = a sin (bx + c ) and y = a cos (bx + c )

10.4 Graphs of y = tan x,y = cot x, y = sec x, y = csc x

10.5 Applications of the Trigonometric Graphs

10.6 Composite Trignometric Curves

11. Exponents and Radicals

11.1 Simplifying Expressions with Integral Exponents

11.2 Fractional Exponents

11.3 Simplest Radical Form

11.3 Addition and Subtraction of Radicals

11.5 Multiplication and Division of Radicals

12. Complex Numbers

12.1 Basic Definitions

12.2 Basic Operations with Complex Numbers

12.3 Graphical Representation of Complex Numbers

12.4 Polar Form of a Complex Number

12.5 Exponential Form of a Complex Number