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Calculus with Early Transcendentals Plus Integrated Review, 2nd Edition

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Calculus with Early Transcendentals Plus Integrated Review, 2nd Edition

by Dr. Paul Sisson and Dr. Tibor Szarvas

Calculus with Early Transcendentals Plus Integrated Review seamlessly combines a comprehensive and rigorous calculus curriculum with targeted prerequisite support in a single course. This versatile title is suitable for both traditional calculus courses and co-requisite programs, featuring curriculum-level content alongside just-in-time algebra and trigonometry review.

Students build foundational knowledge and confidence through carefully selected topics and extensive practice opportunities, progressing from limits and derivatives to vector calculus with essential prerequisite remediation along the way.

The 3-step, mastery-based homework and testing software provides immediate support through built-in annotated solutions and step-by-step problem-solving tutorials and video walkthroughs. Additionally, the review content within the student software offers flexible implementation to suit individual course goals and student needs, allowing instructors to assign individual lessons throughout the course as needed or bundle multiple topics into comprehensive review assignments.

Formats: Software

Product ISBN
Software + Calculus with Early Transcendentals 2nd Edition eBook 978-1-64277-889-2
Software + Calculus with Early Transcendentals 2nd Edition eBook + Calculus with Early Transcendentals 2nd Edition Textbook 978-1-64277-890-8

Table of Contents

  1. Chapter 0: Strategies for Academic Success
    1. 0.1 Understanding and Reducing Stress
    2. 0.2 Staying Organized
    3. 0.3 Managing Your Time Effectively
    4. 0.4 Reading a Textbook and Note-Taking
    5. 0.5 Using Effective Study Strategies
    6. 0.6 Reducing Test Anxiety

    Chapter F: Fundamental Concepts of Algebra
    1. F.1 Real Numbers
    2. F.2 Simplifying and Evaluating Algebraic Expressions
    3. F.3 Properties of Exponents
    4. F.4 Properties of Radicals
    5. F.5 Rational Number Exponents
    6. F.6 Adding, Subtracting, and Multiplying Polynomials
    7. F.7 Division with Polynomials
    8. F.8 Factoring Polynomials and Polynomial-Like Expressions

    Chapter 1.R: Integrated Review
    1. 1.R.1 The Cartesian Coordinate System
    2. 1.R.2 Circles
    3. 1.R.3 Lines
    4. 1.R.4 Relations and Functions
    5. 1.R.5 Linear and Quadratic Functions
    6. 1.R.6 Power Functions and Other Common Functions
    7. 1.R.7 Polynomial Functions
    8. 1.R.8 Rational Functions
    9. 1.R.9 Introduction to Exponential and Logarithmic Functions
    10. 1.R.10 Introduction to Trigonometric Functions

    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.R: Integrated Review
    1. 2.R.1 Simplifying Radical Expressions by Rationalizing
    2. 2.R.2 Rational Expressions
    3. 2.R.3 Simplifying Complex Rational Expressions and Algebraic Expressions
    4. 2.R.4 Linear Equations in One Variable
    5. 2.R.5 Linear Inequalities in One Variable

    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.R: Integrated Review
    1. 3.R.1 Exponential Functions
    2. 3.R.2 Logarithmic Functions
    3. 3.R.3 Properties of Logarithms
    4. 3.R.4 Exponential and Logarithmic Equations
    5. 3.R.5 Trigonometric Functions
    6. 3.R.6 Trigonometric Identities
    7. 3.R.7 Trigonometric Equations

    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.R: Integrated Review
    1. 4.R.1 Polynomial and Polynomial-Like Equations in One Variable
    2. 4.R.2 Rational Equations in One Variable
    3. 4.R.3 Radical Equations in One Variable
    4. 4.R.4 Polynomial and Rational Inequalities
    5. 4.R.5 Solving Systems of Linear Equations by Substitution and Addition

    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.R: Integrated Review
    1. 9.R.1 Ellipses
    2. 9.R.2 Parabolas
    3. 9.R.3 Hyperbolas

    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