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Calculus: Resequenced for Students in STEM, Enhanced eText, Preliminary Edition

ISBN: 978-1-119-32159-0
1120 pages
December 2017, ©2018
Calculus: Resequenced for Students in STEM, Enhanced eText, Preliminary Edition (111932159X) cover image

Description

Dwyer and Gruenwald’s Calculus Resequenced for Students in STEM, Preliminary Edition highlights a new approach to calculus and is devoted to improving the calculus sequence for students in STEM majors. The text introduces a new standard for order and choice of topics for the 3-semester sequence.  Resequencing topics in the calculus sequence allows for front-loading material for upper-level STEM majors into the first two semesters, ensuring Calculus 2 is an attractive jumping-off point for students in biology and chemistry. The topical ordering was developed in consultation with advisory boards consisting of educators in mathematics, biology, chemistry, physics, engineering and economics at diverse institutions.

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Table of Contents

Chapter 1 - Functions
    1.1 Functions and Their Graphs
    1.2 Library of Functions
    1.3 Implicit Functions and Conic Sections
    1.4 Polar Functions
    1.5 Parametric Functions

Chapter 2 - Limits
    2.1 Limits in Calculus
    2.2 Limits: Numerical and Graphical Approaches
    2.3 Calculating Limits Using Limit Laws
    2.4 Limits at Infinity and Horizontal Asymptotes
    2.5 Continuity and the Intermediate Value Theorem
    2.6 Formal Definition of Limit

Chapter 3 - The Derivative
    3.1 Tangents,Velocities,and Other Rates of Change
    3.2 Derivatives
    3.3 Rules for Differentiation
    3.4 Product and Quotient Rules
    3.5 Trigonometric Functions and Their Derivatives
    3.6 Chain Rule
    3.7 Tangents to Parametric and Polar Curves
    3.8 Implicit Differentiation
    3.9 Inverse Functions and Their Derivatives
    3.10 Logarithmic Functions and Their Derivatives

Chapter 4 - Applications of the Derivative
    4.1 Maximum and Minimum Values
    4.2 The Mean Value Theorem
    4.3 Derivatives and Graphs
    4.4 Optimization
    4.5 Applications to Rates of Change
    4.6 Indeterminate Limits and L Hôpital s Rule
    4.7 Polynomial Approximations
    4.8 Tangent Line Approximations: Differentials and Newton s Method

Chapter 5 - The Integral
    5.1 Antiderivatives and Indefinite Integrals
    5.2 Area Under a Curve and Total Change
    5.3 The Definite Integral
    5.4 The Fundamental Theorem of Calculus
    5.5 Integration by Substitution

Chapter 6 - Techniques of Integration
    6.1 Advanced Substitution techniques
    6.2 Integration by Parts
    6.3 Trigonometric Substitution
    6.4 Integrating Rational Functions
    6.5 Improper Integrals
    6.6 Approximating Definite Integrals

Chapter 7 - Applications of Integration
    7.1 Average Value and Area Between Curves
    7.2 Arc Length
    7.3 Volumes
    7.4 Solids of Revolution
    7.5 Work

Chapter 8 - Vectors and Matrices
    8.1 Vectors
    8.2 Dot Product
    8.3 Matrices
    8.4 Determinants and Inverse Matrices
    8.5 Cross Product
    8.6 Lines and Planes in Space

Chapter 9 - Functions of Several Variables
    9.1 Introduction to Functions of Several Variables
    9.2 Limits and Continuity
    9.3 Partial Derivatives
    9.4 Chain Rule
    9.5 Directional Derivatives and Gradients
    9.6 Tangent Planes and Linear Approximations
    9.7 Extrema and the Second Partials Test
    9.8 Lagrange Multipliers

Chapter 10 - Double Integrals
    10.1 Double Integrals over Rectangles
    10.2 Double Integrals over Regions
    10.3 Double Integrals in Polar Coordinates
    10.4 Applications of Double Integrals

Chapter 11 - Differential Equations
    11.1 Introduction to Differential Equations
    11.2 Separable Differential Equations
    11.3 Graphical and Numerical Solutions to Differential Equations
    11.4 Linear First Order Differential Equations

Chapter 12 - Infinite Series
    12.1 Sequences
    12.2 Series
    12.3 Integral Test
    12.4 Comparison Tests
    12.5 Alternating Series
    12.6 Ratio and Root Tests
    12.7 Power Series
    12.8 Power Series Representations of Functions
    12.9 Taylor Series

Chapter 13 - Vector-Valued Functions
    13.1 Review of Vectors
    13.2 Vector-Valued Function
    13.3 Differentiation and Integration of Vector-Valued Functions
    13.4 Arc Length and Curvature
    13.5 Motion in Space
    13.6 Tangent, Normal, and Binormal Vectors

Chapter 14 - Surfaces, Solids, and Multiple Integrals
    14.1 Cylinders and Quadric Surfaces
    14.2 Review of Double Integrals
    14.3 Surface Area
    14.4 Integrals over Solids: Triple Integration
    14.5 Cylindrical and Spherical Coordinates
    14.6 Triple Integrals in Cylindrical and Spherical Coordinates
    14.7 Change of Variables: The Jacobian

Chapter 15 - Vector Analysis
    15.1 Vector Fields
    15.2 Line Integrals
    15.3 Conservative Vector Fields
    15.4 Green s Theorem
    15.5 Parametric Surfaces
    15.6 Surface Integrals
    15.7 Divergence Theorem
    15.8 Stokes Theorem

 

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