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Students who have used Smith/Minton's Calculus say it was easier to read than any other math book they've used. That testimony underscores the success of the authors' approach which combines the most reliable aspects of mainstream Calculus teaching with the best elements of reform, resulting in a motivating, challenging book. Smith/Minton wrote the book for the students who will use it, in a language that they understand, and with the expectation that their backgrounds may have some gaps. Smith/Minton provide exceptional, reality-based applications that appeal to students' interests and demonstrate the elegance of math in the world around us. New features include: • Many new exercises and examples (for a total of 7,000 exercises and 1000 examples throughout the book) provide a careful balance of routine, intermediate and challenging exercises • New exploratory exercises in every section that challenge students to make connections to previous introduced material. • New commentaries (''Beyond Formulas'') that encourage students to think mathematically beyond the procedures they learn. • New counterpoints to the historical notes, ''Today in Mathematics,'' stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present. • An enhanced discussion of differential equations and additional applications of vector calculus. • Exceptional Media Resources: Within MathZone, instructors and students have access to a series of unique Conceptual Videos that help students understand key Calculus concepts proven to be most difficult to comprehend, 248 Interactive Applets that help students master concepts and procedures and functions, 1600 algorithms , and 113 e-Professors.
Chapter 0: Preliminaries 0.1 The Real Numbers and the Cartesian Plane 0.2 Lines and Functions 0.3 Graphing Calculators and Computer Algebra Systems 0.4 Trigonometric Functions 0.5 Transformations of Functions
Chapter 1: Limits and Continuity 1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve 1.2 The Concept of Limit 1.3 Computation of Limits 1.4 Continuity and its Consequences The Method of Bisections 1.5 Limits Involving Infinity Asysmptotes 1.6 The Formal Definition of the Limit 1.7 Limits and Loss-of-Significance Errors Computer Representation or Real Numbers Chaper 2: Differentiation 2.1 Tangent Lines and Velocity 2.2 The Derivative Alternative Derivative Notations Numerical Differentiation 2.3 Computation of Derivatives: The Power Rule Higher Order Derivatives Acceleration 2.4 The Product and Quotient Rules 2.5 The Chain Rule 2.6 Derivatives of the Trigonometric Functions 2.7 Implicit Differentiation 2.8 The Mean Value Theorem
Chapter 3: Applications of Differentiation 3.1 Linear Approximations and Newton's Method 3.2 Maximum and Minimum Values 3.3 Increasing and Decreasing Functions 3.4 Concavity and the Second Derivative Test 3.5Overview of Curve Sketching 3.6Optimization 3.8Related Rates 3.8Rates of Change in Economics and the Sciences
Chapter 4: Integration 4.1 Antiderivatives 4.2 Sums and Sigma Notation Principle of Mathematical Induction 4.3 Area under a Curve 4.4 The Definite Integral Average Value of a Function 4.5 The Fundamental Theorem of Calculus 4.6 Integration by Substitution 4.7 Numerical Integration Error bounds for Numerical Integration
Chapter 5: Applications of the Definite Integral 5.1 Area Between Curves 5.2 Volume: Slicing, Disks, and Washers 5.3 Volumes by Cylindrical Shells 5.4 Arc Length and Srface Area 5.5 Projectile Motion 5.6 Applications of Integration to Physics and Engineering
Chapter 6: Exponentials, Logarithms and other Transcendental Functions 6.1 The Natural Logarithm 6.2 Inverse Functions 6.3 Exponentials 6.4 The Inverse Trigonometric Functions 6.5 The Calculus of the Inverse Trigonometric Functions 6.6 The Hyperbolic Function
Chapter 7: First-Order Differential Equations 7.1 Modeling with Differential Equations Growth and Decay Problems Compound Interest 7.2 Separable Differential Equations Logistic Growth 7.3 Direction Fields and Euler's Method 7.4 Systems of First-Order Differential Equations Predator-Prey Systems 7.6 Indeterminate Forms and L'Hopital's Rule Improper Integrals A Comparison Test 7.8 Probability
Chapter 8: First-Order Differential Equations 8.1 modeling with Differential Equations Growth and Decay Problems Compound Interest 8.2 Separable Differential Equations Logistic Growth 8.3 Direction Fields and Euler's Method Systems of First Order Equations
Chapter 9: Infinite Series 9.1 Sequences of Real Numbers 9.2 Infinite Series 9.3 The Integral Test and Comparison Tests 9.4 Alternating Series Estimating the Sum of an Alternating Series 9.5 Absolute Convergence and the Ratio Test The Root Test Summary of Convergence Test 9.6 Power Series 9.7 Taylor Series Representations of Functions as Series Proof of Taylor's Theorem 9.8 Applications of Taylor Series The Binomial Series 9.9 Fourier Series
Chapter 10: Parametric Equations and Polar Coordinates 10.1 Plane Curves and Parametric Equations 10.2 Calculus and Parametric Equations 10.3 Arc Length and Surface Area in Parametric Equations 10.4 Polar Coordinates 10.5 Calculus and Polar Coordinates 10.6 Conic Sections 10.7 Conic Sections in Polar Coordinates
Chapter 11: Vectors and the Geometry of Space 11.1 Vectors in the Plane 11.2 Vectors in Space 11.3 The Dot Product Compo
Robert T Smith and Roland B. Minton
ISBN13: 978-0073312705Students who have used Smith/Minton's Calculus say it was easier to read than any other math book they've used. That testimony underscores the success of the authors' approach which combines the most reliable aspects of mainstream Calculus teaching with the best elements of reform, resulting in a motivating, challenging book. Smith/Minton wrote the book for the students who will use it, in a language that they understand, and with the expectation that their backgrounds may have some gaps. Smith/Minton provide exceptional, reality-based applications that appeal to students' interests and demonstrate the elegance of math in the world around us. New features include: • Many new exercises and examples (for a total of 7,000 exercises and 1000 examples throughout the book) provide a careful balance of routine, intermediate and challenging exercises • New exploratory exercises in every section that challenge students to make connections to previous introduced material. • New commentaries (''Beyond Formulas'') that encourage students to think mathematically beyond the procedures they learn. • New counterpoints to the historical notes, ''Today in Mathematics,'' stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present. • An enhanced discussion of differential equations and additional applications of vector calculus. • Exceptional Media Resources: Within MathZone, instructors and students have access to a series of unique Conceptual Videos that help students understand key Calculus concepts proven to be most difficult to comprehend, 248 Interactive Applets that help students master concepts and procedures and functions, 1600 algorithms , and 113 e-Professors.
Table of Contents
Chapter 0: Preliminaries 0.1 The Real Numbers and the Cartesian Plane 0.2 Lines and Functions 0.3 Graphing Calculators and Computer Algebra Systems 0.4 Trigonometric Functions 0.5 Transformations of Functions
Chapter 1: Limits and Continuity 1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve 1.2 The Concept of Limit 1.3 Computation of Limits 1.4 Continuity and its Consequences The Method of Bisections 1.5 Limits Involving Infinity Asysmptotes 1.6 The Formal Definition of the Limit 1.7 Limits and Loss-of-Significance Errors Computer Representation or Real Numbers Chaper 2: Differentiation 2.1 Tangent Lines and Velocity 2.2 The Derivative Alternative Derivative Notations Numerical Differentiation 2.3 Computation of Derivatives: The Power Rule Higher Order Derivatives Acceleration 2.4 The Product and Quotient Rules 2.5 The Chain Rule 2.6 Derivatives of the Trigonometric Functions 2.7 Implicit Differentiation 2.8 The Mean Value Theorem
Chapter 3: Applications of Differentiation 3.1 Linear Approximations and Newton's Method 3.2 Maximum and Minimum Values 3.3 Increasing and Decreasing Functions 3.4 Concavity and the Second Derivative Test 3.5Overview of Curve Sketching 3.6Optimization 3.8Related Rates 3.8Rates of Change in Economics and the Sciences
Chapter 4: Integration 4.1 Antiderivatives 4.2 Sums and Sigma Notation Principle of Mathematical Induction 4.3 Area under a Curve 4.4 The Definite Integral Average Value of a Function 4.5 The Fundamental Theorem of Calculus 4.6 Integration by Substitution 4.7 Numerical Integration Error bounds for Numerical Integration
Chapter 5: Applications of the Definite Integral 5.1 Area Between Curves 5.2 Volume: Slicing, Disks, and Washers 5.3 Volumes by Cylindrical Shells 5.4 Arc Length and Srface Area 5.5 Projectile Motion 5.6 Applications of Integration to Physics and Engineering
Chapter 6: Exponentials, Logarithms and other Transcendental Functions 6.1 The Natural Logarithm 6.2 Inverse Functions 6.3 Exponentials 6.4 The Inverse Trigonometric Functions 6.5 The Calculus of the Inverse Trigonometric Functions 6.6 The Hyperbolic Function
Chapter 7: First-Order Differential Equations 7.1 Modeling with Differential Equations Growth and Decay Problems Compound Interest 7.2 Separable Differential Equations Logistic Growth 7.3 Direction Fields and Euler's Method 7.4 Systems of First-Order Differential Equations Predator-Prey Systems 7.6 Indeterminate Forms and L'Hopital's Rule Improper Integrals A Comparison Test 7.8 Probability
Chapter 8: First-Order Differential Equations 8.1 modeling with Differential Equations Growth and Decay Problems Compound Interest 8.2 Separable Differential Equations Logistic Growth 8.3 Direction Fields and Euler's Method Systems of First Order Equations
Chapter 9: Infinite Series 9.1 Sequences of Real Numbers 9.2 Infinite Series 9.3 The Integral Test and Comparison Tests 9.4 Alternating Series Estimating the Sum of an Alternating Series 9.5 Absolute Convergence and the Ratio Test The Root Test Summary of Convergence Test 9.6 Power Series 9.7 Taylor Series Representations of Functions as Series Proof of Taylor's Theorem 9.8 Applications of Taylor Series The Binomial Series 9.9 Fourier Series
Chapter 10: Parametric Equations and Polar Coordinates 10.1 Plane Curves and Parametric Equations 10.2 Calculus and Parametric Equations 10.3 Arc Length and Surface Area in Parametric Equations 10.4 Polar Coordinates 10.5 Calculus and Polar Coordinates 10.6 Conic Sections 10.7 Conic Sections in Polar Coordinates
Chapter 11: Vectors and the Geometry of Space 11.1 Vectors in the Plane 11.2 Vectors in Space 11.3 The Dot Product Compo