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This text is written for today's technology student, with an accessible, intuitive approach and an emphasis on applications of calculus to technology. The text's presentation of concepts is clear and concise, with examples worked in great detail, enhanced by marginal annotations, and supported with step-by-step procedures whenever possible. Another powerful enhancement is the use of a functional second color to help explain steps. Differential and integral calculus are introduced in the first five chapters, while more advanced topics, such as differential equations and LaPlace transforms, are covered in later chapters. This organization allows the text to be used in a variety of technology programs.
1. INTRODUCTION TO ANALYTIC GEOMETRY.
The Cartesian Coordinate System. The Slope. The Straight Line. Curve Sketching. Discussion of Curves with Graphing Utilities. The Conics. The Circle. The Parabola. The Ellipse. The Hyperbola. Translation of Axes; Standard Equations of the Conics. Review Exercises.
2. INTRODUCTION TO CALCULUS: THE DERIVATIVE.
Functions and Intervals. Limits. The Derivative. The Derivative by the Four-Step Process. Derivatives of Polynomials. Instantaneous Rates of Change. Differentiation Formulas. Implicit Differentiation. Higher Derivatives. Review Exercises.
3. APPLICATIONS OF THE DERIVATIVE.
The First-Derivative Test. The Second-Derivative Test. Exploring with Graphing Utilities. Applications of Minima and Maxima. Related rates. Differentials. Review Exercises.
4. THE INTEGRAL.
Antiderivatives. The Area Problem. The Fundamental Theorem of Calculus. The Integral: Notation and General Definition. Basic Integration Formulas. Area Between Curves. Improper Integrals. The Constant of Integration. Numerical Integration. Review Exercises.
5. APPLICATION OF THE INTEGRAL.
Means of Root Mean Squares. Volumes of Revolution: Disk and Washer Methods. Volumes of Revolution: Shell Method. Centroids. Moments of Inertia. Work and Fluid Pressure. Review Exercises.
6. DERIVATIVES OF TRANSCENDENTAL FUNCTIONS.
Review of Trigonometry. Derivatives of Sine and Cosine Functions. Other Trigonometric Functions. Inverse Trigonometric Functions. Derivatives of Inverse Trigonometric Functions. Exponential and Logarithmic Functions. Derivative of the Logarithmic Function. Derivative of the Exponential Function. L'Hospital's rule. Applications. Newton's Method. Review Exercises.
7. INTEGRATION TECHNIQUES.
The Power Formula Again. The Logarithmic and Exponentials Forms. Trigonometric Forms. Further Trigonometric Forms. Inverse Trigonometric Forms. Integration by Trigonometric Substitution. Integration by Parts. Integration of Rational Functions. Integration by Use of Tables. Additional Remarks. Review Exercises.
8. PARAMETIC EQUATIONS, VECTORS, AND POLAR COORDINATES.
Vectors and Parametric Equations. Arc Length. Polar Coordinates. Curves in Polar Coordinates. Areas in Polar Coordinates. Review Exercises.
9. THREE-DIMENSIONAL SPACE; PARTIAL DERIVATIVES; MULTIPLE INTEGRALS.
Surfaces in Three Dimensions. Partial Derivatives. Applications of Partial Derivatives. Curve Fitting. Integrated Integrals. Volumes by Double Integration. Mass, Centroids, and Moments of Inertia. Volumes in Cylindrical Coordinates. Review Exercises.
10. INFINITE SERIES.
Introduction to Infinite Series. Tests for Convergence. Maclaurin Series. Operations with Series. Computations with Series; Applications. Fourier Series. Review Exercises.
11. FIRST-ORDER DIFFERETIAL EQUATIONS.
What is Differential Equation? Separation of Variables. First-Order Linear Differential Equations. Applications of First-Order Differential Equations. Numerical Solutions. Review Exercises.
12. HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS.
Higher-Order Homogeneous Differential Equations. Auxiliary Equations with Repeating or Complex Roots. Nonhomogeneous Equations. Applications of Second-Order Equations. Review Exercises.
13. THE LAPLACE TRANSFORM.
Introduction and Basic Properties. Inverse Laplace Transforms. Partial Fractions. Solutions of Linear Equations by Laplace Transforms. Review Exercises.
Appendix A: Tables.
Common Units of Measure. A Short Table of Integrals.
Appendix B: Answers to Selected Exercises.
Index.
This text is written for today's technology student, with an accessible, intuitive approach and an emphasis on applications of calculus to technology. The text's presentation of concepts is clear and concise, with examples worked in great detail, enhanced by marginal annotations, and supported with step-by-step procedures whenever possible. Another powerful enhancement is the use of a functional second color to help explain steps. Differential and integral calculus are introduced in the first five chapters, while more advanced topics, such as differential equations and LaPlace transforms, are covered in later chapters. This organization allows the text to be used in a variety of technology programs.
Table of Contents
1. INTRODUCTION TO ANALYTIC GEOMETRY.
The Cartesian Coordinate System. The Slope. The Straight Line. Curve Sketching. Discussion of Curves with Graphing Utilities. The Conics. The Circle. The Parabola. The Ellipse. The Hyperbola. Translation of Axes; Standard Equations of the Conics. Review Exercises.
2. INTRODUCTION TO CALCULUS: THE DERIVATIVE.
Functions and Intervals. Limits. The Derivative. The Derivative by the Four-Step Process. Derivatives of Polynomials. Instantaneous Rates of Change. Differentiation Formulas. Implicit Differentiation. Higher Derivatives. Review Exercises.
3. APPLICATIONS OF THE DERIVATIVE.
The First-Derivative Test. The Second-Derivative Test. Exploring with Graphing Utilities. Applications of Minima and Maxima. Related rates. Differentials. Review Exercises.
4. THE INTEGRAL.
Antiderivatives. The Area Problem. The Fundamental Theorem of Calculus. The Integral: Notation and General Definition. Basic Integration Formulas. Area Between Curves. Improper Integrals. The Constant of Integration. Numerical Integration. Review Exercises.
5. APPLICATION OF THE INTEGRAL.
Means of Root Mean Squares. Volumes of Revolution: Disk and Washer Methods. Volumes of Revolution: Shell Method. Centroids. Moments of Inertia. Work and Fluid Pressure. Review Exercises.
6. DERIVATIVES OF TRANSCENDENTAL FUNCTIONS.
Review of Trigonometry. Derivatives of Sine and Cosine Functions. Other Trigonometric Functions. Inverse Trigonometric Functions. Derivatives of Inverse Trigonometric Functions. Exponential and Logarithmic Functions. Derivative of the Logarithmic Function. Derivative of the Exponential Function. L'Hospital's rule. Applications. Newton's Method. Review Exercises.
7. INTEGRATION TECHNIQUES.
The Power Formula Again. The Logarithmic and Exponentials Forms. Trigonometric Forms. Further Trigonometric Forms. Inverse Trigonometric Forms. Integration by Trigonometric Substitution. Integration by Parts. Integration of Rational Functions. Integration by Use of Tables. Additional Remarks. Review Exercises.
8. PARAMETIC EQUATIONS, VECTORS, AND POLAR COORDINATES.
Vectors and Parametric Equations. Arc Length. Polar Coordinates. Curves in Polar Coordinates. Areas in Polar Coordinates. Review Exercises.
9. THREE-DIMENSIONAL SPACE; PARTIAL DERIVATIVES; MULTIPLE INTEGRALS.
Surfaces in Three Dimensions. Partial Derivatives. Applications of Partial Derivatives. Curve Fitting. Integrated Integrals. Volumes by Double Integration. Mass, Centroids, and Moments of Inertia. Volumes in Cylindrical Coordinates. Review Exercises.
10. INFINITE SERIES.
Introduction to Infinite Series. Tests for Convergence. Maclaurin Series. Operations with Series. Computations with Series; Applications. Fourier Series. Review Exercises.
11. FIRST-ORDER DIFFERETIAL EQUATIONS.
What is Differential Equation? Separation of Variables. First-Order Linear Differential Equations. Applications of First-Order Differential Equations. Numerical Solutions. Review Exercises.
12. HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS.
Higher-Order Homogeneous Differential Equations. Auxiliary Equations with Repeating or Complex Roots. Nonhomogeneous Equations. Applications of Second-Order Equations. Review Exercises.
13. THE LAPLACE TRANSFORM.
Introduction and Basic Properties. Inverse Laplace Transforms. Partial Fractions. Solutions of Linear Equations by Laplace Transforms. Review Exercises.
Appendix A: Tables.
Common Units of Measure. A Short Table of Integrals.
Appendix B: Answers to Selected Exercises.
Index.