Calculus with Differential Equations

For freshman/sophomore-level courses treating calculus of both one and several variables with additional material on differential equations. Clear and Concise! Varberg focuses on the most critical concepts freeing you to teach the way you want! This popular calculus text remains the shortest mainstream calculus book available — yet covers all the material needed by, and at an appropriate level for, students in engineering, science, and mathematics. It’s conciseness and clarity helps students focus on, and understand, critical concepts in calculus without them getting bogged down and lost in excessive and unnecessary detail. It is accurate, without being excessively rigorous, up-to-date without being faddish. The authors make effective use of computing technology, graphics, and applications. Ideal for instructors who want a no-nonsense, concisely written treatment.

Features

• Calculus with Differential Equations, 9/e
• ISBN: 0-13-230633-6Dale Varberg/Edwin J. Purcell/Steve E. Rigdon
• 0 PRELIMINARIES
• 0.1
• Real Numbers, Estimation, and Logic
• 0.2
• Inequalities and Absolute Values
• 0.3
• The Rectangular Coordinate System
• 0.4
• Graphs of Equations
• 0.5
• Functions and Their Graphs
• 0.6
• Operations on Functions
• 0.7
• The Trigonometric Functions
• 0.8
• Chapter Review
• 1 LIMITS
• 1.1
• Introduction to Limits
• 1.2
• Rigorous Study of Limits
• 1.3
• Limit Theorems
• 1.4
• Limits Involving Trigonometric Functions
• 1.5
• Limits at Infinity; Infinite Limits
• 1.6
• Continuity of Functions
• 1.7
• Chapter Review
• 2 THE DERIVATIVE
• 2.1
• Two Problems with One Theme
• 2.2
• The Derivative
• 2.3
• Rules for Finding Derivatives
• 2.4
• Derivatives of Trigonometric Functions
• 2.5
• The Chain Rule
• 2.6
• Higher-Order Derivatives
• 2.7
• Implicit Differentiation
• 2.8
• Related Rates
• 2.9
• Differentials and Approximations
• 2.10
• Chapter Review
• 3 APPLICATIONS OF THE DERIVATIVE
• 3.1
• Maxima and Minima
• 3.2
• Monotonicity and Concavity
• 3.3
• Local Extrema and Extrema on Open Intervals
• 3.4
• Practical Problems
• 3.5
• Graphing Functions Using Calculus
• 3.6
• The Mean Value Theorem for Derivatives
• 3.7
• Solving Equations Numerically
• 3.8
• Antiderivatives
• 3.9
• Introduction to Differential Equations
• 3.10
• Chapter Review
• 4 THE DEFINITE INTEGRAL
• 4.1
• Introduction to Area
• 4.2
• The Definite Integral
• 4.3
• The 1st Fundamental Theorem of Calculus
• 4.4
• The 2nd Fundamental Theorem of Calculus and the Method of Substitution
• 4.5
• The Mean Value Theorem for Integrals & the Use of Symmetry
• 4.6
• Numerical Integration
• 4.7
• Chapter Review
• 5 APPLICATIONS OF THE INTEGRAL
• 5.1
• The Area of a Plane Region
• 5.2
• Volumes of Solids: Slabs, Disks, Washers
• 5.3
• Volumes of Solids of Revolution: Shells
• 5.4
• Length of a Plane Curve
• 5.5
• Work and Fluid Pressure
• 5.6
• Moments, Center of Mass
• 5.7
• Probability and Random Variables
• 5.8
• Chapter Review
• 6 TRANSCENDENTAL FUNCTIONS
• 6.1
• The Natural Logarithm Function
• 6.2
• Inverse Functions and Their Derivatives
• 6.3
• The Natural Exponential Function
• 6.4
• General Exponential & Logarithmic Functions
• 6.5
• Exponential Growth and Decay
• 6.6
• First-Order Linear Differential Equations
• 6.7
• Approximations for Differential Equations
• 6.8
• The Inverse Trig Functions & Their Derivatives
• 6.9
• The Hyperbolic Functions & Their Inverses
• 6.10
• Chapter Review
• 7 TECHNIQUES OF INTEGRATION
• 7.1
• Basic Integration Rules
• 7.2
• Integration by Parts
• 7.3
• Some Trigonometric Integrals
• 7.4
• Rationalizing Substitutions
• 7.5
• Integration of Rational Functions Using Partial Fractions
• 7.6
• Strategies for Integration
• 7.7
• Chapter Review
• 8 INDETERMINATE FORMS & IMPROPER INTEGRALS
• 8.1
• Indeterminate Forms of Type 0/0
• 8.2
• Other Indeterminate Forms
• 8.3
• Improper Integrals: Infinite Limits of Integration
• 8.4
• Improper Integrals: Infinite Integrands
• 8.5
• Chapter Review
• 9 INFINITE SERIES
• 9.1
• Infinite Sequences
• 9.2
• Infinite Series
• 9.3
• Positive Series: The Integral Test
• 9.4
• Positive Series: Other Tests
• 9.5
• Alternating Series, Absolute Convergence, and Conditional Convergence
• 9.6
• Power Series
• 9.7
• Operations on Power Series
• 9.8
• Taylor and Maclaurin Series
• 9.9
• The Taylor Approximation to a Function
• 9.10
• Chapter Review
• 10 CONICS AND POLAR COORDINATES
• 10.1
• The Parabola
• 10.2
• Ellipses and Hyperbolas
• 10.3
• Translation and Rotation of Axes
• 10.4
• Parametric Representation of Curves in the Plane
• 10.5
• The Polar Coordinate System
• 10.6
• Graphs of Polar Equations
• 10.7
• Calculus in Polar Coordinates
• 10.8
• Chapter Review
• 11 GEOMETRY IN SPACE AND VECTORS
• 11.1
• Cartesian Coordinates in Three-Space
• 11.2
• Vectors
• 11.3
• The Dot Product
• 11.4
• The Cross Product
• 11.5
• Vector Valued Functions & Curvilinear Motion
• 11.6
• Lines in Three-Space
• 11.7
• Curvature and Components of Acceleration
• 11.8
• Surfaces in Three Space
• 11.9
• Cylindrical and Spherical Coordinates
• 11.10
• Chapter Review
• 12 DERIVATIVES OF FUNCTIONS OF TWO OR MORE VARIABLES
• 12.1
• Functions of Two or More Variables
• 12.2
• Partial Derivatives
• 12.3
• Limits and Continuity
• 12.4
• Differentiability
• 12.5
• Directional Derivatives and Gradients
• 12.6
• The Chain Rule
• 12.7
• Tangent Planes and Approximations
• 12.8
• Maxima and Minima
• 12.9
• The Method of Lagrange Multipliers
• 12.10
• Chapter Review
• 13 MULTIPLE INTEGRATION
• 13.1
• Double Integrals over Rectangles
• 13.2
• Iterated Integrals
• 13.3
• Double Integrals over Nonrectangular Regions
• 13.4
• Double Integrals in Polar Coordinates
• 13.5
• Applications of Double Integrals
• 13.6
• Surface Area
• 13.7
• Triple Integrals in Cartesian Coordinates
• 13.8
• Triple Integrals in Cylindrical & Spherical Coordinates
• 13.9
• Change of Variables in Multiple Integrals
• 13.1
• Chapter Review
• 14 VECTOR CALCULUS
• 14.1
• Vector Fields
• 14.2
• Line Integrals
• 14.3
• Independence of Path
• 14.4
• Green’s Theorem in the Plane
• 14.5
• Surface Integrals
• 14.6
• Gauss’s Divergence Theorem
• 14.7
• Stokes’s Theorem
• 14.8
• Chapter Review
• 15 DIFFERENTIAL EQUATIONS
• 15.1
• Linear Homogeneous Equations
• 15.2
• Nonhomogeneous Equations
• 15.3
• Applications of Second-Order Equations
• APPENDIX
• A.1
• Mathematical Induction
• A.2
• Proofs of Several Theorems