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Basic Technical Mathematics with Calculus, 11th edition
Published by Pearson (July 14, 2021) © 2018
- Allyn J. Washington Dutchess Community College
- Richard Evans Corning Community College
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Basic Technical Mathematics with Calculus builds your understanding of mathematical methods without requiring formulas. Featuring applications from technical and pre-engineering fields, it starts by establishing a solid background in algebra and trigonometry to give you a foundation for solving applied problems.
Table of Contents
- Basic Algebraic Operations
- 1.1 Numbers
- 1.2 Fundamental Operations of Algebra
- 1.3 Calculators and Approximate Numbers
- 1.4 Exponents and Unit Conversions
- 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
- 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
- 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
- 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
- Systems of Linear Equations Determinants
- 5.1 Linear Equations and Graphs of Linear Functions
- 5.2 Systems of Equations and Graphical Solutions
- 5.3 Solving Systems of Two Linear Equations in Two Unknowns Algebraically
- 5.4 Solving Systems of Two Linear Equations in Two Unknowns by Determinants
- 5.5 Solving Systems of Three Linear Equations in Three Unknowns Algebraically
- 5.6 Solving Systems of Three Linear Equations in Three Unknowns by Determinants
- Factoring and Fractions
- 6.1 Factoring: Greatest Common Factor and Difference of Squares
- 6.2 Factoring Trinomials
- 6.3 The Sum and Difference of Cubes
- 6.4 Equivalent Fractions
- 6.5 Multiplication and Division of Fractions
- 6.6 Addition and Subtraction of Fractions
- 6.7 Equations Involving Fractions
- 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
- 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
- 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
- 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 Trigonometric Curves
- Exponents and Radicals
- 11.1 Simplifying Expressions with Integer Exponents
- 11.2 Fractional Exponents
- 11.3 Simplest Radical Form
- 11.4 Addition and Subtraction of Radicals
- 11.5 Multiplication and Division of Radicals
- 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
- 12.6 Products, Quotients, Powers, and Roots of Complex Numbers
- 12.7 An Application to Alternating-current (ac) Circuits
- Exponential and Logarithmic Functions
- 13.1 Exponential Functions
- 13.2 Logarithmic Functions
- 13.3 Properties of Logarithms
- 13.4 Logarithms to the Base
- 13.5 Natural Logarithms
- 13.6 Exponential and Logarithmic Equations
- 13.7 Graphs on Logarithmic and Semilogarithmic Paper
- Additional Types of Equations and Systems of Equations
- 14.1 Graphical Solution of Systems of Equations
- 14.2 Algebraic Solution of Systems of Equations
- 14.3 Equations in Quadratic Form
- 14.4 Equations with Radicals
- Equations of Higher Degree
- 15.1 The Remainder and Factor Theorems; Synthetic Division
- 15.2 The Roots of an Equation
- 15.3 Rational and Irrational Roots
- Matrices; Systems of Linear Equations
- 16.1 Matrices: Definitions and Basic Operations
- 16.2 Multiplication of Matrices
- 16.3 Finding the Inverse of a Matrix
- 16.4 Matrices and Linear Equations
- 16.5 Gaussian Elimination
- 16.6 Higher-order Determinants
- Inequalities
- 17.1 Properties of Inequalities
- 17.2 Solving Linear Inequalities
- 17.3 Solving Nonlinear Inequalities
- 17.4 Inequalities Involving Absolute Values
- 17.5 Graphical Solution of Inequalities with Two Variables
- 17.6 Linear Programming
- Variation
- 18.1 Ratio and Proportion
- 18.2 Variation
- Sequences and the Binomial Theorem
- 19.1 Arithmetic Sequences
- 19.2 Geometric Sequences
- 19.3 Infinite Geometric Series
- 19.4 The Binomial Theorem
- Additional Topics in Trigonometry
- 20.1 Fundamental Trigonometric Identities
- 20.2 The Sum and Difference Formulas
- 20.3 Double-Angle Formulas
- 20.4 Half-Angle Formulas
- 20.5 Solving Trigonometric Equations
- 20.6 The Inverse Trigonometric Functions
- Plane Analytic Geometry
- 21.1 Basic Definitions
- 21.2 The Straight Line
- 21.3 The Circle
- 21.4 The Parabola
- 21.5 The Ellipse
- 21.6 The Hyperbola
- 21.7 Translation of Axes
- 21.8 The Second-degree Equation
- 21.9 Rotation of Axes
- 21.10 Polar Coordinates
- 21.11 Curves in Polar Coordinates
- Introduction to Statistics
- 22.1 Graphical Displays of Data
- 22.2 Measures of Central Tendency
- 22.3 Standard Deviation
- 22.4 Normal Distributions
- 22.5 Statistical Process Control
- 22.6 Linear Regression
- 22.7 Nonlinear Regression
- The Derivative
- 23.1 Limits
- 23.2 The Slope of a Tangent to a Curve
- 23.3 The Derivative
- 23.4 The Derivative as an Instantaneous Rate of Change
- 23.5 Derivatives of Polynomials
- 23.6 Derivatives of Products and Quotients of Functions
- 23.7 The Derivative of a Power of a Function
- 23.8 Differentiation of Implicit Functions
- 23.9 Higher Derivatives
- Applications of the Derivative
- 24.1 Tangents and Normals
- 24.2 Newton’s Method for Solving Equations
- 24.3 Curvilinear Motion
- 24.4 Related Rates
- 24.5 Using Derivatives in Curve Sketching
- 24.6 More on Curve Sketching
- 24.7 Applied Maximum and Minimum Problems
- 24.8 Differentials and Linear Approximations
- Integration
- 25.1 Antiderivatives
- 25.2 The Indefinite Integral
- 25.3 The Area Under a Curve
- 25.4 The Definite Integral
- 25.5 Numerical Integration: The Trapezoidal Rule
- 25.6 Simpson's Rule
- Applications of Integration
- 26.1 Applications of the Indefinite Integral
- 26.2 Areas by Integration
- 26.3 Volumes by Integration
- 26.4 Centroids
- 26.5 Moments of Inertia
- 26.6 Other Applications
- Differentiation of Transcendental Functions
- 27.1 Derivatives of the Sine and Cosine Functions
- 27.2 Derivatives of the Other Trigonometric Functions
- 27.3 Derivatives of the Inverse Trigonometric Functions
- 27.4 Applications
- 27.5 Derivative of the Logarithmic Function
- 27.6 Derivative of the Exponential Function
- 27.7 L’Hospital’s Rule
- 27.8 Applications
- Methods of Integration
- 28.1 The Power Rule for Integration
- 28.2 The Basic Logarithmic Form
- 28.3 The Exponential Form
- 28.4 Basic Trigonometric Forms
- 28.5 Other Trigonometric Forms
- 28.6 Inverse Trigonometric Forms
- 28.7 Integration by Parts
- 28.8 Integration by Trigonometric Substitution
- 28.9 Integration by Partial Fractions: Non-repeated Linear Factors
- 28.10 Integration by Partial Fractions: Other Cases
- 28.11 Integration by Use of Tables
- Partial Derivatives and Double Integrals
- 29.1 Functions of Two Variables
- 29.2 Curves and Surfaces in Three Dimensions
- 29.3 Partial Derivatives
- 29.4 Double Integrals
- Expansion of Functions in Series
- 30.1 Infinite Series
- 30.2 Maclaurin Series
- 30.3 Operations with Series
- 30.4 Computations by Use of Series Expansions
- 30.5 Taylor Series
- 30.6 Introduction to Fourier Series
- 30.7 More About Fourier Series
- Differential Equations
- 31.1 Solutions of Differential Equations
- 31.2 Separation of Variables
- 31.3 Integrating Combinations
- 31.4 The Linear Differential Equation of the First Order
- 31.5 Numerical Solutions of First-order Equations
- 31.6 Elementary Applications
- 31.7 Higher-order Homogeneous Equations
- 31.8 Auxiliary Equation with Repeated or Complex Roots
- 31.9 Solutions of Nonhomogeneous Equations
- 31.10 Applications of Higher-order Equations
- 31.11 Laplace Transforms
- 31.12 Solving Differential Equations by Laplace Transforms
Appendix A Solving Word Problems
Appendix B Units of Measurement
Appendix C Newton’s Method
Appendix D A Table of Integrals
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