- #1
- 19,464
- 10,073
- Author: Howard Anton
- Amazon Link:
https://www.amazon.com/dp/0470647698/?tag=pfamazon01-20
https://www.amazon.com/dp/0470647728/?tag=pfamazon01-20
https://www.amazon.com/dp/0471153060/?tag=pfamazon01-20
https://www.amazon.com/dp/0470183497/?tag=pfamazon01-20
https://www.amazon.com/dp/0470183462/?tag=pfamazon01-20 - Prerequisities: High-School Mathematics
Table of Contents:
Code:
[LIST]
[*] Before Calculus
[LIST]
[*] Functions
[*] New Functions from Old
[*] Families of Functions
[*] Inverse Functions; Inverse Trigonometric Functions
[*] Exponential and Logarithmic Functions
[/LIST]
[*] Limits and Continuity
[LIST]
[*] Limits (An Intuitive Approach)
[*] Computing Limits
[*] Limits at Infinity; End Behavior of a Function
[*] Limits (Discussed More Rigorously)
[*] Continuity
[*] Continuity of Trigonometric, Exponential, and Inverse Functions
[/LIST]
[*] The Derivative
[LIST]
[*] Tangent Lines and Rates of Change
[*] The Derivative Function
[*] Introduction to Techniques of Differentiation
[*] The Product and Quotient Rules
[*] Derivatives of Trigonometric Functions
[*] The Chain Rule
[/LIST]
[*] Topics in Differentiation
[LIST]
[*]Implicit Differentiation
[*] Derivatives of Logarithmic Functions
[*] Derivatives of Exponential and Inverse Trigonometric Functions
[*] Related Rates
[*] Local Linear Approximation; Differentials
[*] L’Hôpital’s Rule; Indeterminate Forms
[/LIST]
[*] The derivative in Graphing and Applications
[LIST]
[*] Analysis of Functions I: Increase, Decrease, and Concavity
[*] Analysis of Functions II: Relative Extrema; Graphing Polynomials
[*] Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents
[*] Absolute Maxima and Minima
[*] Applied Maximum and Minimum Problems
[*] Rectilinear Motion
[*] Newton’s Method
[*] Rolle’s Theorem; Mean-Value Theorem
[/LIST]
[*] Integration
[LIST]
[*] An Overview of the Area Problem
[*] The Indefinite Integral
[*] Integration by Substitution
[*] The Definition of Area as a Limit; Sigma Notation
[*] The Definite Integral
[*] The Fundamental Theorem of Calculus
[*] Rectilinear Motion Revisited Using Integration
[*] Average Value of a Function and its Applications
[*] Evaluating Definite Integrals by Substitution
[*] Logarithmic and Other Functions Defined by Integrals
[/LIST]
[*] Applications of the Definite Integral in Geometry, Science, and Engineering
[LIST]
[*] Area Between Two Curves
[*] Volumes by Slicing; Disks and Washers
[*] Volumes by Cylindrical Shells
[*] Length of a Plane Curve
[*] Area of a Surface of Revolution
[*] Work
[*] Moments, Centers of Gravity, and Centroids
[*] Fluid Pressure and Force
[*] Hyperbolic Functions and Hanging Cables
[/LIST]
[*] Principles of Integral Evaluation
[LIST]
[*] An Overview of Integration Methods
[*] Integration by Parts
[*] Integrating Trigonometric Functions
[*] Trigonometric Substitutions
[*] Integrating Rational Functions by Partial Fractions
[*] Using Computer Algebra Systems and Tables of Integrals
[*] Numerical Integration; Simpson’s Rule
[*] Improper Integrals
[/LIST]
[*] Mathematical Modeling with Differential Equations
[LIST]
[*] Modeling with Differential Equations
[*] Separation of Variables
[*] Slope Fields; Euler’s Method
[*] First-Order Differential Equations and Applications
[/LIST]
[*] Infinite Series
[LIST]
[*] Sequences
[*] Monotone Sequences
[*] Infinite Series
[*] Convergence Tests
[*] The Comparison, Ratio, and Root Tests
[*] Alternating Series; Absolute and Conditional Convergence
[*] Maclaurin and Taylor Polynomials
[*] Maclaurin and Taylor Series; Power Series
[*] Convergence of Taylor Series
[*] Differentiating and Integrating Power Series; Modeling with Taylor Series
[/LIST]
[*] Parametric and Polar Curves; Conic Sections
[LIST]
[*] Parametric Equations; Tangent Lines and Arc Length for Parametric Curves
[*] Polar Coordinates
[*] Tangent Lines, Arc Length, and Area for Polar Curves
[*] Conic Sections
[*] Rotation of Axes; Second-Degree Equations
[*] Conic Sections in Polar Coordinates
[/LIST]
[*] Three-dimensional Space; Vectors
[LIST]
[*] Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces
[*] Vectors
[*] Dot Product; Projections
[*] Cross Product
[*] Parametric Equations of Lines
[*] Planes in 3-Space
[*] Quadric Surfaces
[*] Cylindrical and Spherical Coordinates
[/LIST]
[*] Vector-Valued Functions
[LIST]
[*] Introduction to Vector-Valued Functions
[*] Calculus of Vector-Valued Functions
[*] Change of Parameter; Arc Length
[*] Unit Tangent, Normal, and Binormal Vectors
[*] Curvature
[*] Motion Along a Curve
[*] Kepler’s Laws of Planetary Motion
[/LIST]
[*] Partial Derivatives
[LIST]
[*] Functions of Two or More Variables
[*] Limits and Continuity
[*] Partial Derivatives
[*] Differentiability, Differentials, and Local Linearity
[*] The Chain Rule
[*] Directional Derivatives and Gradients
[*] Tangent Planes and Normal Vectors
[*] Maxima and Minima of Functions of Two Variables
[*] Lagrange Multipliers
[/LIST]
[*] Multiple Integrals
[LIST]
[*] Double Integrals
[*] Double Integrals over Nonrectangular Regions
[*] Double Integrals in Polar Coordinates
[*] Surface Area; Parametric Surfaces
[*] Triple Integrals
[*] Triple Integrals in Cylindrical and Spherical Coordinates
[*] Change of Variables in Multiple Integrals; Jacobians
[*] Centers of Gravity Using Multiple Integrals
[/LIST]
[*] Topics in Vector Calculus
[LIST]
[*] Vector Fields
[*] Line Integrals
[*] Independence of Path; Conservative Vector Fields
[*] Green’s Theorem
[*] Surface Integrals
[*] Applications of Surface Integrals; Flux
[*] The Divergence Theorem
[*] Stokes’ Theorem
[/LIST]
[*] Appendices
[LIST]
[*] Graphing Functions Using Calculators and Computer Algebra Systems
[*] Trigonometry Review
[*] Solving Polynomial Equations
[*] Selected Proofs
[/LIST]
[*] Answers to Odd-Numbered Exercises
[*] Index
[*] Web Appendices (Available for download at [url]www.wiley.com/college/anton[/url] or at [url]www.howardanton.com[/url] and in WileyPLUS.)
[LIST]
[*] Real Numbers, Intervals, and Inequalities
[*] Absolute Value
[*] Coordinate Planes, Lines, and Linear Functions
[*] Distance, Circles, and Quadratic Equations
[*] Early Parametric Equations Option
[*] Mathematical Models
[*] The Discriminant
[*] Second-Order Linear Homogeneous Differential Equations
[/LIST]
[*] Web Projects: Expanding the Calculus Horizon (online only) (Available for download at [url]www.wiley.com/college/anton[/url] or at [url]www.howardanton.com[/url] and in WileyPLUS)
[LIST]
[*] Blammo The Human Cannonball
[*] Comet Collision
[*] Hurricane Modeling
[*] Iteration and Dynamical Systems
[*] Railroad Design
[*] Robotics
[/LIST]
[/LIST]
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