Overview

The study of Calculus enables us to solve problems and articulate abstract concepts far beyond the theoretical reach of Algebra. The power of Calculus derives from the ingenuity and simplicity of its notation. This mathematical language allows the mathematician the freedom and immense versatility to accurately describe physical problems and the tools to solve them. This book consists of lectures on all the topics of a 3-course series on Calculus: Calculus I, II, and III. It can be used as a textbook, or as a supplement to other texts. Both students and instructors will find it helpful in elucidating the ideas and methods of Calculus.

Full Product Details

Author:   Deborah C Arangno
Publisher:   Kendall/Hunt Publishing Co ,U.S.
Imprint:   Kendall/Hunt Publishing Co ,U.S.
Edition:   2nd Revised edition
ISBN:  

9781792463259

ISBN 10:   1792463251
Pages:   277
Publication Date:   30 May 2021
Audience:   College/higher education ,  Tertiary & Higher Education
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable  
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Table of Contents

Preface About the Author Formulas Introduction Part 1 Calculus I Chapter 1 Functions and Limits 1.1 Functions, Transformations 1.2 Tangent and Velocity Functions 1.3 Limit of a Function, Limit Laws 1.4 Formal Definition of a Limit 1.5 Limit Laws 1.6 Continuity Chapter 2 Derivatives 2.1 Derivatives and Rates of Change 2.2 Derivative as a Function, Differentiation Formulas 2.3 Derivatives of Trigonometric Functions 2.4 Linear Approximations and Differentials 2.5 Chain Rule 2.6 Implicit Differentiation 2.7 Related Rates Chapter 3 Applications of Differentiation 3.1 Mean Value Theorem 3.2 Maximum and Minimum Values 3.3 Optimization Problems 3.4 Derivatives and Curve Sketching 3.5 Limits at Infinity 3.6 Newton's Method Chapter 4 Integrals 4.1 Antiderivatives 4.2 Areas and Distances 4.3 Definite Integral 4.4 Fundamental Theorem of Calculus Chapter 5 Applications of Integration 5.1 Areas Between Curves 5.2 Volumes of Solids of Revolution: Slices 5.3 Volumes of Solids of Revolution: Cylindrical Shells 5.4 Average Value of a Function 5.5 Improper Integrals Part 2 Calculus II Chapter 6 Special Functions, Indeterminate Forms 6.1 Logs and Exponents 6.2 Exponential Growth and Decay 6.3 Inverse Trig Functions 6.4 L'Hospital's Rule Chapter 7 Techniques of Integration 7.1 U-Substitution 7.2 Integration by Parts 7.3 Trig Integrals 7.4 Trigonometric Substitution 7.5 Partial Fractions 7.6 Numerical Integration Chapter 8 Applications of the Integral 8.1 Arclength 8.2 Surface Areas of Revolution 8.3 Mass, Work Chapter 9 Introduction to Differential Equations 9.1 Direction Fields and Euler's Method 9.2 Separable Differential Equations 9.3 Linear Differential Equations Chapter 10 Conics, Polar Coordinates, and Parametric Equations 10.1 Conics 10.2 Polar Coordinates 10.3 Parametric Equations Chapter 11 Sequences and Series 11.1 Sequences 11.2 Series 11.3 Convergence Tests 11.4 Power Series Part 3 Calculus III Chapter 12 Geometry in 3 Dimensions 12.1 3D coordinates 12.2 Vectors 12.3 The Dot Product 12.4 The Cross Product 12.5 Vector Equations of Lines, Planes 12.6 Vector Valued Functions 12.7 Calculus of Vector Valued Functions 12.8 Arclength 12.9 Tangent, Normal, and Binormal Vectors 12.10 Curvature 12.11 Motion in Space: Velocity and Acceleration Chapter 13 Functions of Several Variables 13.1 Introduction 13.2 Quadratic & Cylindrical Surfaces 13.3 Limits, Continuity 13.4 Partial Derivatives 13.5 Chain Rule 13.6 Directional Derivatives, Gradients 13.7 Tangent Planes, Normal Lines 13.8 Local Maxima, Local Minima, Saddle Points 13.9 Global Maxima and Minima 13.10 Lagrange Multipliers Chapter 14 Multiple Integrals 14.1 Double Integrals 14.2 Double Integrals in Polar Coordinates 14.3 Triple Integrals 14.4 Triple Integrals in Cylindrical Coordinates 14.5 Triple Integrals in Spherical Coordinates Chapter 15 Vector Calculus 15.1 Vector Fields 15.2 Line Integrals 15.3 Fundamental Theorem of Line Integrals 15.4 Green's Theorem 15.5 Line Integrals Made Easy 15.6 Surface Integrals 15.7 Flux Integrals 15.8 Stokes Theorem 15.9 Divergence Theorem Appendix Derivatives and Integrals

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