Book description
A thorough revision of the classic tutorial of scientific and engineering mathematics
For more than fifteen years, Mastering Technical Mathematics has been the definitive self-teaching guide for those wishing to boost their career by learning the principles of mathematics as they apply to science and engineering. Featuring the same user-friendly pedagogy, practical examples, and detailed illustrations that have made this resource a favorite of the scientific and technical communities, the new third edition delivers four entirely new chapters and expanded treatment of cutting-edge topics.
Table of contents
- Cover
- Half Title
- Title
- Copyright
- Dedication
- Contents
- Introduction
-
Part 1: Working with Numbers
-
1. From Counting to Addition
- Numbers and Numerals
- Counting in Tens and Dozens
- Writing Numerals Greater Than 10
- Why Zero Is Used in Counting
- By Tens and Hundreds to Thousands
- Don’t Forget the Zeros
- Millions and More
- What About Infinity?
- Addition Is Counting on
- Adding Three or More Numbers
- Adding Larger Numbers
- Carrying
- Checking Answers
- Weights
- Using the Grocer’s Balance
- Questions and Problems
- 2. Subtraction
- 3. Multiplication
-
4. Division
- Let’s Think Like a Calculator
- Division “Undoes” Multiplication
- Alternative Notation
- Dividing into Longer Numbers
- Multiplication Checks Division
- More About How a Calculator Does It
- Dividing by Larger Numbers (The People Way)
- Division by Factors
- When a Remainder Is Left
- How a Calculator Handles Fractions
- Decimal Equivalents of Fractions
- More Difficult Fractions
- Where Groups of Digits Repeat
- Converting Recurring Decimals to Fractions
- Questions and Problems
-
5. Fractions
- Slicing up a Pie
- Factors Help Simplify Fractions
- Spotting the Factors
- Prime Numbers
- Factoring into Primes
- Prime Factors of 139
- Prime Factors of 493
- Prime Factors of 546
- Adding and Subtracting Fractions
- Finding the Common Denominator
- Significant Figures
- Approximate Division and Multiplication
- Approximate Addition and Subtraction
- Questions and Problems
- 6. Plane Polygons
- 7. Time, Percentages, and Graphs
-
1. From Counting to Addition
-
Part 2: Algebra, Geometry, and Trigonometry
-
8. First Notions in Algebra
- Shortcuts for Long Problems
- Graphs Help You Find Errors and Solutions
- Manipulating Equations
- Writing It as Algebra
- Italics—or Not?
- Grouping Symbols
- Solving Problems with Grouping Symbols
- Putting a Problem into Algebra
- Magic by Algebra
- A Boat-in-the-River Problem
- Number Problems
- Questions and Problems
- 9. Some “School” Algebra
- 10. Quadratic Equations
- 11. Some Useful Shortcuts
-
12. Mechanical Mathematics
- What Is Force?
- Units of Force
- Acceleration, Speed, and Distance
- Force and Work
- Work and Energy
- Energy and Power
- Gravity as a Source of Energy
- Weight as Force
- Gravitational Measure of Work
- Energy for Constant Acceleration
- Potential and Kinetic Energy
- Kinetic Energy and Speed
- Acceleration at Constant Power
- How a Spring Stores Energy
- How a Spring Transfers Energy
- Resonance Cycle
- Travel and Speed in Resonant System
- Questions and Problems
-
13. Ratio and Proportion
- Fractions, Projections, Extremes, and Means
- Proportions in Practice
- Shape and Size
- About Angles in Triangles
- Use of Right Triangles
- Angles Identified by Ratios
- Theorem of Pythagoras
- Names for Angle Ratios
- Spotting the Triangle
- Degree Measure of Angles
- Three Applications of Trigonometry
- Questions and Problems
-
14. Trigonometric and Geometric Calculations
- Ratios for Sum Angles
- Finding Tan (A + B)
- An Example: Ratios for 75°
- Ratios for Angles Greater Than 90°
- Ratios for Difference Angles
- Ratios Through the Four Quadrants
- Pythagoras in Trigonometry
- Double Angles
- Higher Multiple Angles
- Properties of the Isosceles Triangle
- Angles in a Circle
- Angles in a Semicircle
- Definitions
- Questions and Problems
-
8. First Notions in Algebra
-
Part 3: Analysis and Calculus
-
15. Systems of Counting
- Mechanical Counters
- Duodecimal Numbers
- Conversion from Decimal to Duodecimal
- Conversion from Duodecimal to Decimal
- Octal Numbers
- Hexadecimal numbers
- Binary Numbers
- Comparing the Values
- Converting Decimal to Binary
- Binary Multiplication
- Binary Division
- Indices
- Negative and Fractional Exponents
- Surds
- Questions and Problems
- 16. Progressions, Permutations, and Combinations
- 17. Introduction to Derivatives
-
18. More About Differentiation
- Frequency and Period of a Sine Wave
- Sinusoidal Motion
- Harmonic Motion
- Linear and Nonlinear Relationships
- Multiples and Powers
- Functions
- Derivative of Constant
- Derivative of Sum of Two Functions
- Derivative of Difference of Two Functions
- Derivative of Function Multiplied by a Constant
- Derivative of Product of Two Functions
- Derivative of Product of Three Functions
- Derivative of Quotient of Two Functions
- Reciprocal Derivatives
- Derivative of Function Raised to a Power
- Chain Rule
- Questions and Problems
-
19. Introduction to Integrals
- Adding up the Pieces
- The Antiderivative
- Patterns in Calculations
- The Constant of Integration
- Definite Integrals
- Finding Area by Integration
- Area of a Circle
- Curved Areas of Cylinders and Cones
- Surface Area of a Sphere
- Volumes of Wedges and Pyramids
- Volumes of Cones and Spheres
- Questions and Problems
-
20. Combining Calculus with Other Tools
- Local Maximum and Minimum
- Point of Inflection
- Maximum and Minimum Slope
- Maximum Area with Constant Perimeter
- Box with Minimum Surface Area
- Cylinder with Minimum Surface Area
- Cone with Minimum Surface Area
- Equations for Circles, Ellipses, and Parabolas
- Directrix, Focus, and Eccentricity
- The Ellipse and the Circle
- Relationships Between Focus, Directrix, and Eccentricity
- Focus Property of Parabola
- Focus Property of Ellipse
- Hyperbola: Eccentricity Greater Than 1
- Geometry of Conic Sections
- Questions and Problems
-
21. Alternative Coordinate Systems
- Mathematician’s Polar Coordinates
- Some Examples
- Compressed Polar Coordinates
- Mathematician’s Polar vs. Cartesian Coordinates
- Navigator’s Polar Coordinates
- Mathematician’s Vs. Navigator’s Polar Coordinates
- Navigator’s Polar Vs. Cartesian Coordinates
- Latitude and Longitude
- Celestial Coordinates
- Cartesian Three-Space
- Cylindrical Coordinates
- Spherical Coordinates
- Questions and Problems
- 22. Complex Numbers
-
15. Systems of Counting
-
Part 4: Tools of Applied Mathematics
- 23. Trigonometry in the Real World
-
24. Logarithms and Exponentials
- The Logarithm Base
- Common Logarithms
- Natural Logarithms
- Basic Properties of Logarithms
- Conversion of Log Functions
- Logarithm Comparisons
- The Exponential Base
- Common Exponentials
- Natural Exponentials
- Alternative Expressions
- Logarithms Vs. Exponentials
- Basic Properties of Exponentials
- Exponential Comparisons
- Numerical Orders of Magnitude
- Questions and Problems
-
25. Scientific Notation Tutorial
- Standard Form
- Alternative Form
- The “Times” Sign
- Plain-Text Exponents
- Orders of Magnitude
- When to Use Scientific Notation
- Prefix Multipliers
- Multiplication
- Division
- Raising to a Power
- Taking a Root
- Addition
- Subtraction
- Significant Figures
- How Accurate Are You?
- What About 0?
- What About Exact Values?
- More About Addition and Subtraction
- Questions and Problems
-
26. Vectors
- Magnitude and Direction
- Sum of Two Vectors
- Multiplication of a Vector by a Scalar
- Dot Product of Two Vectors
- Magnitude and Direction in the Polar Plane
- Sum of Two Vectors in the Polar Plane
- Multiplication of a Vector by a Scalar in the Polar Plane
- Dot Product of Two Vectors in Polar Plane
- Magnitude in XYZ Space
- Direction in XYZ Space
- Sum of two Vectors in XYZ Space
- Multiplication of a Vector by a Scalar in XYZ Space
- Dot Product of Two Vectors in XYZ Space
- Cross Product of Two Vectors
- Negative Vector Magnitudes
- Questions and Problems
-
27. Logic and Truth Tables
- Sentences
- Negation (Not)
- Conjunction (And)
- Disjunction (Or)
- Implication (If/Then)
- Logical Equivalence (Iff)
- Truth Tables
- Tables for Basic Logic Functions
- The Equals Sign
- Q.E.D.
- Precedence
- Contradiction and Double Negation
- Commutative Laws
- Associative Laws
- Law of Implication Reversal
- De Morgan’s Laws
- Distributive Law
- Truth Table Proofs
- Proofs Without Tables
- Questions and Problems
-
28. Beyond Three Dimensions
- Imagine That!
- Time-Space
- Position and Motion
- Time as Displacement
- Universal Speed
- The Four-Cube
- The Rectangular Four-Prism
- Impossible Paths
- General Time-Space Hypervolume
- Cartesian N-Space
- Distance Formulas
- Vertices of a Tesseract
- Hypervolume of a Four-Prism
- Euclid’s Axioms
- The Parallel Postulate
- Geodesics
- Modified Parallel Postulate
- No Parallel Geodesics
- More Than One Parallel Geodesic
- Curved Space
- The “Hyperfunnel”
- Questions and Problems
- 29. A Statistics Primer
-
30. Probability Basics
- Sets and Set Notation
- Event Vs. Outcome
- Sample Space
- Mathematical Probability
- Empirical Probability
- Law of Large Numbers
- Independent Outcomes
- Mutually Exclusive Outcomes
- Complementary Outcomes
- Nondisjoint Outcomes
- Multiple Outcomes
- The Density Function
- Expressing the Pattern
- Area under the Curve
- Uniform Distribution
- Normal Distribution
- The Empirical Rule
- Questions and Problems
- Final Exam
- Appendices
- Suggested Additional Reading
- Index
Product information
- Title: Mastering Technical Mathematics, Third Edition, 3rd Edition
- Author(s):
- Release date: October 2007
- Publisher(s): McGraw-Hill Education TAB
- ISBN: 9780071595421
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