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Calculus with Early Transcendentals, 2nd Edition

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Calculus with Early Transcendentals, 2nd Edition

by Dr. Paul Sisson and Dr. Tibor Szarvas

A comprehensive, mathematically rigorous exposition, Calculus with Early Transcendentals blends precision and depth with a conversational tone to include the reader in developing the ideas and intuition of calculus. A consistent focus on historical context, theoretical discovery, and ample exercise sets provides insight into the many applications and inherent beauty of the subject.

This comprehensive calculus title offers over 9700 exercises to choose from. The extensive exercise sets progress in difficulty level to develop students' understanding of the content and include application-based practice opportunities and technology questions that underscore the role of modern tools in advanced computations. Each chapter concludes with two projects: one designed to expand students' conceptual understanding of calculus beyond the typical theories studied, and another that showcases a real-world application of calculus in action. Additionally, comprehensive review sections in the software summarize key concepts of each chapter and serve as a helpful guide during exam preparation.

The last five chapters of the text are a comprehensive treatment of multivariable calculus, covering analytic and differential geometry in three dimensions, partial derivatives, multiple integrals and alternate coordinate systems, and the deep extensions of single-variable theorems to three and higher dimensions.

Pair this title with Hawkes Learning's 3-step, mastery-based homework and testing software now with 36% more exercises. Built-in annotated solutions and step-by-step problem-solving tutorials provide immediate support for students, and a video walkthrough for each example helps to facilitate a genuine mastery of subject matter.

Formats: Software, Textbook, eBook

Product ISBN
Software + eBook 978-1-64277-593-8
Software + eBook + Textbook 978-1-64277-592-1
Textbook 978-1-64277-588-4
Student Solutions Manual eBook 978-1-64277-595-2

About the Authors:

Paul Sisson

Dr. Paul Sisson

Paul Sisson received his bachelor's degree in mathematics and physics from New Mexico Tech and his PhD from the University of South Carolina. Since then, he has taught a wide variety of math and computer science courses, including Intermediate Algebra, College Algebra, Discrete Mathematics, Calculus, Advanced Calculus, Differential Equations, Topology, Mathematical Art, History of Mathematics, Real Analysis, Complex Analysis, Linear Algebra, Abstract Algebra, Mathematica Programming, and Network Operating Systems. He is Professor of Mathematics and Provost Emeritus at Louisiana State University in Shreveport. He is also the author of Hawkes Learning's textbooks Algebra and Trigonometry, Precalculus, and College Algebra.


Tibor Szarvas

Dr. Tibor Szarvas

Tibor Szarvas received his master's degree in mathematics from the University of Szeged, Hungary, and his PhD from the University of South Carolina. His teaching experience in mathematics includes courses such as Intermediate Algebra, Liberal Arts Mathematics, Mathematics for Elementary Teachers, Precalculus, Calculus, Advanced Calculus, Discrete Mathematics, Differential Equations, College Geometry, Mathematical Modeling, Linear Algebra, Abstract Algebra, Topology, Real Analysis, Complex Variables, Number Theory, and Mathematical Logic. He is currently serving as Professor and Dean of the College of Arts & Sciences at Louisiana State University in Shreveport.


Table of Contents

  1. Chapter 1: A Review of Functions
    1. 1.1 Functions and How We Represent Them
    2. 1.2 Common Functions
    3. 1.3 Transforming and Combining Functions
    4. 1.4 Inverse Functions
    5. 1.5 Calculus, Calculators, and Computer Algebra Systems
    6. Chapter 1 Review

    Chapter 2: Limits and the Derivative
    1. 2.1 Rates of Change and Tangent Lines
    2. 2.2 Limits All around the Plane
    3. 2.3 The Mathematical Definition of Limit
    4. 2.4 Determining Limits of Functions
    5. 2.5 Continuity
    6. 2.6 Rate of Change Revisited: The Derivative
    7. Chapter 2 Review

    Chapter 3: Differentiation
    1. 3.1 Differentiation Notation and Consequences
    2. 3.2 Derivatives of Polynomials, Exponentials, Products, and Quotients
    3. 3.3 Derivatives of Trigonometric Functions
    4. 3.4 The Chain Rule
    5. 3.5 Implicit Differentiation
    6. 3.6 Derivatives of Inverse Functions
    7. 3.7 Rates of Change in Use
    8. 3.8 Related Rates
    9. 3.9 Linearization and Differentials
    10. Chapter 3 Review

    Chapter 4: Applications of Differentiation
    1. 4.1 Extreme Values of Functions
    2. 4.2 The Mean Value Theorem
    3. 4.3 The First and Second Derivative Tests
    4. 4.4 L'Hôpital's Rule
    5. 4.5 Calculus and Curve Sketching
    6. 4.6 Optimization Problems
    7. 4.7 Antiderivatives
    8. Chapter 4 Review

    Chapter 5: Integration
    1. 5.1 Area, Distance, and Riemann Sums
    2. 5.2 The Definite Integral
    3. 5.3 The Fundamental Theorem of Calculus
    4. 5.4 Indefinite Integrals and the Substitution Rule
    5. 5.5 The Substitution Rule and Definite Integration
    6. Chapter 5 Review

    Chapter 6: Applications of the Definite Integral
    1. 6.1 Finding Volumes Using Slices
    2. 6.2 Finding Volumes Using Cylindrical Shells
    3. 6.3 Arc Length and Surface Area
    4. 6.4 Moments and Centers of Mass
    5. 6.5 Force, Work, and Pressure
    6. 6.6 Hyperbolic Functions
    7. Chapter 6 Review

    Chapter 7: Techniques of Integration
    1. 7.1 Integration by Parts
    2. 7.2 The Partial Fractions Method
    3. 7.3 Trigonometric Integrals
    4. 7.4 Trigonometric Substitutions
    5. 7.5 Integration Summary and Integration Using Computer Algebra Systems
    6. 7.6 Numerical Integration
    7. 7.7 Improper Integrals
    8. Chapter 7 Review

    Chapter 8: Differential Equations
    1. 8.1 Separable Differential Equations
    2. 8.2 First-Order Linear Differential Equations
    3. 8.3 Autonomous Differential Equations and Slope Fields
    4. 8.4 Second-Order Linear Differential Equations
    5. Chapter 8 Review

    Chapter 9: Parametric Equations and Polar Coordinates
    1. 9.1 Parametric Equations
    2. 9.2 Calculus and Parametric Equations
    3. 9.3 Polar Coordinates
    4. 9.4 Calculus in Polar Coordinates
    5. 9.5 Conic Sections in Cartesian Coordinates
    6. 9.6 Conic Sections in Polar Coordinates
    7. Chapter 9 Review

    Chapter 10: Sequences and Series
    1. 10.1 Sequences
    2. 10.2 Infinite Series
    3. 10.3 The Integral Test
    4. 10.4 Comparison Tests
    5. 10.5 The Ratio and Root Tests
    6. 10.6 Absolute and Conditional Convergence
    7. 10.7 Power Series
    8. 10.8 Taylor and Maclaurin Series
    9. 10.9 Further Applications of Series
    10. Chapter 10 Review

    Chapter 11: Vectors and the Geometry of Space
    1. 11.1 Three-Dimensional Cartesian Space
    2. 11.2 Vectors and Vector Algebra
    3. 11.3 The Dot Product
    4. 11.4 The Cross Product
    5. 11.5 Describing Lines and Planes
    6. 11.6 Cylinders and Quadric Surfaces
    7. Chapter 11 Review

    Chapter 12: Vector Functions
    1. 12.1 Vector-Valued Functions
    2. 12.2 Arc Length and the Unit Tangent Vector
    3. 12.3 The Unit Normal and Binormal Vectors, Curvature, and Torsion
    4. 12.4 Planetary Motion and Kepler's Laws
    5. Chapter 12 Review

    Chapter 13: Partial Derivatives
    1. 13.1 Functions of Several Variables
    2. 13.2 Limits and Continuity of Multivariable Functions
    3. 13.3 Partial Derivatives
    4. 13.4 The Chain Rule for Multivariable Functions
    5. 13.5 Directional Derivatives and Gradient Vectors
    6. 13.6 Tangent Planes and Differentials
    7. 13.7 Extreme Values of Functions of Two Variables
    8. 13.8 Lagrange Multipliers
    9. Chapter 13 Review

    Chapter 14: Multiple Integrals
    1. 14.1 Double Integrals
    2. 14.2 Applications of Double Integrals
    3. 14.3 Double Integrals in Polar Coordinates
    4. 14.4 Triple Integrals
    5. 14.5 Triple Integrals in Cylindrical and Spherical Coordinates
    6. 14.6 Substitutions and Multiple Integrals
    7. Chapter 14 Review

    Chapter 15: Vector Calculus
    1. 15.1 Vector Fields
    2. 15.2 Line Integrals
    3. 15.3 The Fundamental Theorem for Line Integrals
    4. 15.4 Green's Theorem
    5. 15.5 Parametric Surfaces and Surface Area
    6. 15.6 Surface Integrals
    7. 15.7 Stokes' Theorem
    8. 15.8 The Divergence Theorem
    9. Chapter 15 Review