# Fundamentals of Technical Mathematics

###### Sarhan M. Musa
Publisher:
Publication Date:
2016
Number of Pages:
394
Format:
Paperback
Price:
100.00
ISBN:
9780128019870
Category:
Textbook
[Reviewed by
Tom Schulte
, on
12/21/2016
]

Fundamentals of Technical Mathematics introduces basic mathematics from fractions, decimals, percentages, order of operations, and more to fundamentals of algebra, equations, inequalities, vectors, modelling, graphs and functions, geometry, and trigonometry. The theme of applied mathematics for engineering technologists and technicians comes out through strategically placed story problems drawn from such areas as circuit design, astrophysics, measurement systems, and more. This is the minority of the largely general content. About once per chapter there are samples in MATLAB and Maple.

The material is appropriate for secondary education or even the first year of higher education. The text includes plenty of examples and chapter exercises backed up by, for all exercises, detailed solutions. Also at the back of the book are fairly complete primers for MATLAB and Maple, which I both appreciate and find unusual considering comparable texts.

Like many textbooks at this level, the chapters feature highlighted definitions and key points. In my experience, even students unwilling to invest in reading an entire chapter will pay attention to these, so when they are present care should be taken with them. Consider the definition here of a quadratic equation: “A quadratic equation is a second order equation written as $ax^2+bx+c=0$…” This definition is too restrictive, really; it should have ended at word eight. On the other extreme, some definitions are incomplete to the point of seeming ill-conceived or hastily assembled: “A determinant of a matrix is a scalar number that replaces the bracket with vertical lines.” I cannot recommend this text for independent study. It requires a guided presentation with amplification of key details and, in some cases, important clarifications.

The scope of content is ambitious in several ways for a textbook at this level. The author has brought in much material not in comparable textbooks. But this makes more glaring a key exception: there is a nearly complete absence of a set theoretic basis or motivation at any point. For instance, it seems that this awkward wording is the result of this avoidance: for the “Definition of the solution of equation” [sic], the author says that “A solution of equation is the numbers that produce true statement for the equation [sic].”

This is one of the rare textbooks I see that, especially at this level, introduces the complex plane along with complex numbers. Why, however, this is done a chapter ahead of introducing the rectangular coordinate system based on the reals I find elusive. In that chapter on the Cartesian coordinate system, distance formula makes an appearance, a chapter ahead of the Pythagorean Theorem. In my experience, going the other way around succeeds better with students.

Tom Schulte presents carefully curated classroom capsules to community college students outside of Detroit, Michigan.

• Dedication
• Preface
• Acknowledgments
• Chapter 1. Basic Concepts in Arithmetic
• Introduction
• 1.1. Basic arithmetic
• 1.1. Exercises
• 1.2. Decimals
• 1.2. Exercises
• 1.3. Percents (%)
• 1.3. Exercises
• Chapter 1 Review exercises
• Chapter 2. Introduction to Algebra
• Introduction
• 2.1. Introduction to algebra
• 2.1. Exercises
• 2.2. Addition, subtraction, multiplication, and division of monomials
• 2.2. Exercises
• 2.3. Ratio, proportion, and variation
• 2.3. Exercises
• Chapter 2 Review exercises
• Chapter 3. Equations, Inequalities, and Modeling
• Introduction
• 3.1. Equations
• 3.1. Exercises
• 3.2. Inequality equations and intervals
• 3.2. Exercises
• 3.3. Complex numbers
• 3.3. Exercises
• Chapter 3 Review exercises
• Chapter 4. Graphs and Functions
• Introduction
• 4.1. Graphs
• 4.1. Exercises
• 4.2. Functions
• 4.2. Exercises
• Chapter 4 Review exercises
• Chapter 5. Measurement
• Introduction
• 5.1. Length measurements
• 5.1. Exercises
• 5.2. Mass and weight measurements
• 5.2. Exercises
• 5.3. Capacity measurements of liquid
• 5.3. Exercises
• 5.4. Time measurements
• 5.4. Exercises
• 5.5. Temperature (T) measurement
• 5.5. Exercises
• 5.6. Derived units
• 5.6. Exercises
• Chapter 5 Review exercises
• Chapter 6. Geometry
• Introduction
• 6.1. Basic concepts in geometry
• 6.1. Exercises
• 6.2. Angle measurement and triangles
• 6.2. Exercises
• 6.3. Perimeter and circumference in geometry
• 6.3. Exercises
• 6.4. Area in geometry
• 6.4. Exercises
• 6.5. Volume in geometry
• 6.5. Exercises
• Chapter 6 Review exercises
• Chapter 7. Trigonometry
• Introduction
• 7.1. Units of angles
• 7.1. Exercises
• 7.2. Types of angles and right triangle
• 7.2. Exercises
• 7.3. Trigonometric functions
• 7.3. Exercises
• 7.4. Unit circle and oblique triangles
• 7.4. Exercises
• Chapter 7 Review exercises
• Chapter 8. Matrices, Determinants, and Vectors
• Introduction
• 8.1. Matrices
• 8.1. Exercises
• 8.2. Determinants
• 8.2. Exercises
• 8.3. Vectors
• 8.3. Exercises
• Chapter 8 Review exercises
• Appendix A. Maple
• Appendix B. MATLAB
• Appendix C. Solution Manual
• Glossary
• Index