Essential Calculus

by D. Franklin Wright, Spencer P. Hurd, and Bill D. New

Essential Calculus introduces students to basic concepts in the field of calculus. Each chapter section provides examples including graphs, tables, and diagrams.

Because of the multitude of real-world applications, students from different fields and majors will be able to connect with the material.

Formats: Software, Textbook, eBook

Product ISBN
Courseware + eBook 978-1-944894-45-0
Courseware + eBook + Textbook 978-1-944894-46-7

Table of Contents

  1. Chapter 1: Functions, Models and Graphs
    1. 1.1 Real Numbers and Number Lines
    2. 1.2 Integer Exponents
    3. 1.3 Fractional Exponents and Radicals
    4. 1.4 Polynomials
    5. 1.5 Lines and Their Graphs
    6. 1.6a An Introduction to Functions
    7. 1.6b Operations with Functions
    8. 1.7 Functions and Their Graphs: A Calculator Section
    9. 1.8 Functions and Models
  2. Chapter 2: Limits, Slopes, and the Derivative
    1. 2.1a Left and Right Hand Limits
    2. 2.1b Limits
    3. 2.2a Average Rate of Change
    4. 2.2b Instantaneous Rate of Change and Interpreting Graphs
    5. 2.3a Definition of the Derivative and Power Rule
    6. 2.3b Slope and Rate of Change Considered Algebraically
    7. 2.4 Applications: Marginal Analysis
    8. 2.5a More About Limits
    9. 2.5b More About Continuity
  3. Chapter 3: Algebraic Differentiation Rules
    1. 3.1 Product and Quotient Rules
    2. 3.2 The Chain Rule and the General Power Rule
    3. 3.3 Implicit Differentiation and Related Rates
    4. 3.4a Increasing and Decreasing Intervals
    5. 3.4b Critical Points and the First Derivative Test
    6. 3.5 Absolute Maximum and Minimum
  4. Chapter 4: Applications of the Derivative
    1. 4.1a Higher Order Derivatives and Concavity
    2. 4.1b Higher Order Derivatives: the Second Derivative Test
    3. 4.2 Curve Sketching: Polynomial Functions
    4. 4.3 Curve Sketching: Rational Functions
    5. 4.4 Business Applications
    6. 4.5 Other Applications
    7. 4.6 Differentials
  5. Chapter 5: Exponential and Logarithmic Functions
    1. 5.1 Exponential Functions
    2. 5.2 The Algebra of the Natural Logarithm Function
    3. 5.3 Differentiation of Logarithmic Functions
    4. 5.4 Differentiation of Exponential Functions
    5. 5.5a Applications of Exponential Functions: Growth and Decay
    6. 5.5b Logarithmic Differentiation and Elasticity of Demand
  6. Chapter 6: Integration with Applications
    1. 6.1 The Indefinite Integral
    2. 6.2 Integration by Substitution
    3. 6.3a The Fundamental Theorem of Calculus
    4. 6.3b The Definite Integral
    5. 6.4 Area (with Applications)
    6. 6.5 Area Between Two Curves (with Applications)
    7. 6.6 Differential Equations
  7. Chapter 7: Additional Integration Topics
    1. 7.1 Integration by Parts
    2. 7.2 Annuities and Income Streams
    3. 7.3 Tables of Integrals
    4. 7.4 Improper Integrals
    5. 7.5 Probability
    6. 7.6 Volume
  8. Chapter 8: Multivariable Calculus
    1. 8.1 Functions of Several Variables
    2. 8.2 Partial Derivatives
    3. 8.3 Local Extrema for Functions of Two Variables
    4. 8.4 Lagrange Multipliers
    5. 8.5 The Method of Least Squares
    6. 8.6 Double Integrals
  9. Chapter 9: The Trigonometric Functions
    1. 9.1 The Trigonometric Functions
    2. 9.2 Derivatives of the Trigonometric Functions
    3. 9.3 Integration of the Trigonometric Functions
    4. 9.4 Inverse Trigonometric Functions
  10. Chapter 10: Sequences, Taylor Polynomials, and Power Series
    1. 10.1 Infinite Sequences
    2. 10.2 Taylor Polynomials
    3. 10.3 Taylor Series, Infinite Expressions, and Their Applications
  11. Appendix
    1. A.1 Linear Equations
    2. A.2 Quadratic Equations
    3. A.3 Rational and Radical Equations