Basic Technical Mathematics with Calculus, 11th edition
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Overview
Basic Technical Mathematics with Calculus builds your understanding of mathematical methods without requiring formulas. Featuring applications from technical and preengineering fields, it starts by establishing a solid background in algebra and trigonometry to give you a foundation for solving applied problems.
Published by Pearson (July 14th 2021)  Copyright © 2018
ISBN13: 9780137554843
Subject: Technical, Trade, & Business Mathematics
Category: Technical Math
Table of contents
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 Alternatingcurrent (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 Higherorder 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 DoubleAngle Formulas
 20.4 HalfAngle 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 Seconddegree 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: Nonrepeated 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 Firstorder Equations
 31.6 Elementary Applications
 31.7 Higherorder Homogeneous Equations
 31.8 Auxiliary Equation with Repeated or Complex Roots
 31.9 Solutions of Nonhomogeneous Equations
 31.10 Applications of Higherorder 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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