Calculus with Early Transcendentals
by Paul Sisson and 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 extensive exercise sets provides insight into the many applications and inherent beauty of the subject.
Formats: Textbook, Software (Beta)
Product  ISBN 

Textbook  9781935782216 
Courseware (Beta)  9781941552308 
Textbook + Courseware (Beta)  9781946158444 
About the Authors:
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, Calculus, Topology, Mathematical Art, History of Mathematics, Real Analysis, Mathematica Programming, and Network Operating Systems. He is Professor of Mathematics and Provost Emeritus at Louisiana State University in Shreveport.
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 Chair of Mathematics at Louisiana State University in Shreveport.
Resources
 Formulas – Algebra, Geometry, Conic Sections, Limits, Derivatives, Integration, Sequences and Series
 Table of Integrals
 Appendices
 Fundamentals of Mathematica
 Properties of Exponents and Logarithms, Graphs of Exponential and Logarithmic Functions
 Trigonometric and Hyperbolic Functions
 Complex Numbers
 Proofs of Selected Theorems
Table of Contents

A Function Primer
 Functions and How We Represent Them
 A Function Repertory
 Transforming and Combining Functions
 Inverse Functions
 Calculus, Calculators, and Computer Algebra Systems

Limits and the Derivative
 Rates of Change and Tangents
 Limits All Around the Plane
 The Mathematical Definition of Limit
 Determining Limits of Functions
 Continuity
 Rate of Change Revisited: The Derivative

Differentiation
 Differentiation Notation and Consequences
 Derivatives of Polynomials, Exponentials, Products, and Quotients
 Derivatives of Trigonometric Functions
 The Chain Rule
 Implicit Differentiation
 Derivatives of Inverse Functions
 Rates of Change in Use
 Related Rates
 Linearization and Differentials

Applications of Differentiation
 Extreme Values of Functions
 The Mean Value Theorem
 The First and Second Derivative Tests
 L'Hôpital's Rule
 Calculus and Curve Sketching
 Optimization Problems
 Antiderivatives

Integration
 Area, Distance, and Riemann Sums
 The Definite Integral
 The Fundamental Theorem of Calculus
 Indefinite Integrals and the Substitution Rule
 The Substitution Rule and Definite Integration

Applications of the Definite Integral
 Finding Volumes Using Slices
 Finding Volumes Using Cylindrical Shells
 Arc Length and Surface Area
 Moments and Centers of Mass
 Force, Work, and Pressure
 Hyperbolic Functions

Techniques of Integration
 Integration by Parts
 The Partial Fractions Method
 Trigonometric Integrals
 Trigonometric Substitutions
 Integration Summary and Integration Using Computer Algebra Systems
 Numerical Integration
 Improper Integrals

Differential Equations
 Separable Differential Equations
 FirstOrder Linear Differential Equations
 Autonomous Differential Equations and Slope Fields
 SecondOrder Differential Equations

Parametric Equations and Polar Coordinates
 Parametric Equations
 Calculus and Parametric Equations
 Polar Coordinates
 Calculus in Polar Coordinates
 Conic Sections in Cartesian Coordinates
 Conic Sections in Polar Coordinates

Sequences and Series
 Sequences
 Infinite Series
 The Integral Test
 Comparison Tests
 The Ratio and Root Tests
 Absolute and Conditional Convergence
 Power Series
 Taylor and Maclaurin Series
 Further Applications of Series

Chapter 11: Vectors and the Geometry of Space
 ThreeDimensional Cartesian Space
 Vectors and Vector Algebra
 The Dot Product
 The Cross Product
 Describing Lines and Planes
 Cylinders and Quadric Surfaces

Chapter 12: Vector Functions
 VectorValued Functions
 Arc Length and the Unit Tangent Vector
 The Unit Normal and Binormal Vectors, Curvature, and Torsion
 Planetary Motion and Kepler's Laws

Chapter 13: Partial Derivatives
 Functions of Several Variables
 Limits and Continuity of Multivariable Functions
 Partial Derivatives
 The Chain Rule
 Directional Derivatives and Gradient Vectors
 Tangent Planes and Differentials
 Extreme Values of Multivariable Functions
 Lagrange Multipliers

Chapter 14: Multiple Integrals
 Double Integrals
 Applications of Double Integrals
 Double Integrals in Polar Coordinates
 Triple Integrals
 Triple Integrals in Cylindrical and Spherical Coordinates
 Substitutions and Multiple Integrals

Chapter 15: Vector Calculus
 Vector Fields
 Line Integrals
 The Fundamental Theorem for Line Integrals
 Green's Theorem
 Parametric Surfaces and Surface Area
 Surface Integrals
 Stokes' Theorem
 The Divergence Theorem