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Learn Calculus with Examples, Exercises, and Projects from Calculus by Strauss, Bradley and Smith (5th Edition)


- Overview: What are the main features and benefits of this textbook? - Summary: How can this textbook help you learn and master calculus? H2: The Structure and Content of Calculus by Strauss, Bradley and Smith - Part 1: Single Variable Calculus - Part 2: Multivariable Calculus - Part 3: Vector Calculus - Part 4: Differential Equations - Part 5: Appendices and Index H3: Part 1: Single Variable Calculus - Chapter 1: Functions and Limits - Chapter 2: The Derivative - Chapter 3: Applications of the Derivative - Chapter 4: The Integral - Chapter 5: Applications of the Integral - Chapter 6: Transcendental Functions - Chapter 7: Techniques of Integration H3: Part 2: Multivariable Calculus - Chapter 8: Infinite Series - Chapter 9: Vectors and Matrices - Chapter 10: Partial Differentiation - Chapter 11: Multiple Integrals - Chapter 12: Vector Analysis H3: Part 3: Vector Calculus - Chapter 13: Line Integrals and Surface Integrals - Chapter 14: Theorems of Green, Gauss and Stokes H3: Part 4: Differential Equations - Chapter 15: First-Order Differential Equations - Chapter 16: Second-Order Linear Differential Equations - Chapter 17: Systems of Differential Equations - Chapter 18: Power Series Solutions of Differential Equations H3: Part 5: Appendices and Index - Appendix A: Review of Algebra and Trigonometry - Appendix B: Tables of Integrals - Appendix C: Answers to Selected Exercises - Index Table 2: Article with HTML formatting ```html Calculus by Strauss, Bradley and Smith:A Comprehensive Textbook for Students and Teachers




Calculus is one of the most important branches of mathematics, with applications in science, engineering, economics, and many other fields. It deals with the study of change, motion, rates, limits, functions, derivatives, integrals, and more. Whether you are a student who wants to learn calculus for the first time or a teacher who wants to improve your teaching skills, you need a reliable and comprehensive textbook that covers all the topics you need to know. In this article, we will introduce you to one such textbook:Calculus by Strauss, Bradley and Smith, a classic work that has been revised and updated for the fifth edition. We will give you an overview of what this textbook offers, how it is structured and organized, and how it can help you achieve your learning goals.




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The Structure and Content of Calculus by Strauss, Bradley and Smith




Calculus by Strauss, Bradley and Smith is divided into five parts, each consisting of several chapters. The parts are:


  • Part 1:Single Variable Calculus, which covers the basics of calculus for functions of one variable.



  • Part 2:Multivariable Calculus, which extends the concepts of calculus to functions of several variables.



  • Part 3:Vector Calculus, which explores the applications of calculus to vector fields and surfaces.



  • Part 4:Differential Equations, which introduces the methods and techniques for solving ordinary and partial differential equations.



  • Part 5:Appendices and Index, which provide useful reference materials and answers to selected exercises.



Each chapter in the textbook follows a consistent format, which includes:


  • Objectives:A list of the main goals and outcomes of the chapter.



  • Introduction:A brief overview of the topic and its motivation.



  • Definitions and Theorems:A clear and rigorous presentation of the key concepts and results of the chapter, with examples and proofs.



  • Examples:A variety of solved problems that illustrate and apply the definitions and theorems.



  • Exercises:A large collection of exercises that test your understanding and skills, ranging from routine to challenging.



  • Projects:A set of open-ended questions that encourage you to explore further aspects of the topic, using technology, research, or creativity.



  • Summary:A concise review of the main points and formulas of the chapter.



The textbook also features several pedagogical tools that enhance your learning experience, such as:


  • Marginal Notes:Helpful hints, tips, reminders, and warnings that appear in the margins of the pages.



  • Graphs and Figures:High-quality illustrations that visualize and explain the concepts and examples.



  • Cross-References:Links that direct you to related topics or sections within the textbook.



  • Historical Notes:Brief anecdotes that highlight the historical background and context of the topics.



  • Technology Notes:Suggestions on how to use calculators, computers, or software to enhance your understanding and problem-solving.



Part 1: Single Variable Calculus




The first part of the textbook covers the fundamentals of calculus for functions of one variable. It consists of seven chapters, which are:


Chapter 1: Functions and Limits




This chapter introduces you to the concept of a function, which is a rule that assigns a unique output to each input. You will learn how to represent functions using graphs, tables, formulas, or words. You will also learn how to manipulate functions using operations, compositions, inverses, transformations, and models. You will then study the concept of a limit, which is a way of describing the behavior of a function near a certain point or at infinity. You will learn how to calculate limits using algebraic techniques, graphical methods, or numerical approximations. You will also learn how to apply limits to find asymptotes, continuity, and end behavior of functions.


Chapter 2: The Derivative




This chapter introduces you to the concept of a derivative, which is a measure of how fast a function changes at a given point. You will learn how to find derivatives using the definition, rules, formulas, or shortcuts. You will also learn how to interpret derivatives as slopes, rates of change, tangents, or linear approximations. You will then study the concept of differentiability, which is a condition for a function to have a derivative at a point. You will learn how to determine if a function is differentiable using graphs or tests. You will also learn how to apply differentiability to find extrema, concavity, inflection points, or optimization problems.


Chapter 3: Applications of the Derivative




This chapter explores some of the applications of derivatives in various fields and contexts. You will learn how to use derivatives to analyze graphs, curves, motion, related rates, implicit differentiation, logarithmic differentiation, or differentials. You will also learn how to use derivatives to solve problems involving optimization, linearization, Newton's method, L'Hopital's rule, or mean value theorem.


Chapter 4: The Integral




This chapter introduces you to the concept of an integral, which is a way of finding the total amount or net change of a function over an interval. You will learn how to find integrals using antiderivatives, indefinite integrals, or definite integrals. You will also learn how to interpret integrals as areas, accumulations, or averages. You will then study the concept of integration techniques, which are methods for finding integrals that are not straightforward or simple. You will learn how to use integration techniques such as substitution, integration by parts, partial fractions, or trigonometric integrals. ```html Chapter 5: Applications of the Integral




This chapter explores some of the applications of integrals in various fields and contexts. You will learn how to use integrals to find areas between curves, volumes of solids, work done by forces, average value of functions, or probability and statistics. You will also learn how to use integrals to solve problems involving centroids, moments of inertia, hydrostatic pressure, or improper integrals.


Chapter 6: Transcendental Functions




This chapter introduces you to some of the most important and useful functions that are not algebraic, but rather transcendental. These include exponential functions, logarithmic functions, inverse trigonometric functions, and hyperbolic functions. You will learn how to define, graph, differentiate, and integrate these functions. You will also learn how to apply these functions to model growth and decay, compound interest, logarithmic scales, inverse functions, or trigonometric identities.


Chapter 7: Techniques of Integration




This chapter reviews and extends some of the techniques of integration that you learned in previous chapters. You will learn how to use integration by parts, trigonometric substitution, partial fractions, or numerical integration to find integrals that are more complicated or challenging. You will also learn how to use tables of integrals or computer algebra systems to find integrals that are not easily solvable by hand.


Part 2: Multivariable Calculus




The second part of the textbook covers the extension of calculus to functions of several variables. It consists of five chapters, which are:


Chapter 8: Infinite Series




This chapter introduces you to the concept of an infinite series, which is a sum of infinitely many terms. You will learn how to represent functions using power series, Taylor series, or Maclaurin series. You will also learn how to test for convergence or divergence of infinite series using various criteria or tests. You will then study the concept of sequences and series of functions, which are collections of functions that depend on a parameter. You will learn how to determine if a sequence or series of functions converges pointwise or uniformly using graphs or tests. You will also learn how to apply sequences and series of functions to find Fourier series or orthogonal functions.


Chapter 9: Vectors and Matrices




This chapter introduces you to the concept of a vector, which is a quantity that has both magnitude and direction. You will learn how to represent vectors using coordinates, components, or matrices. You will also learn how to manipulate vectors using operations, dot products, cross products, or determinants. You will then study the concept of a matrix, which is a rectangular array of numbers or symbols. You will learn how to represent matrices using rows, columns, or entries. You will also learn how to manipulate matrices using operations, multiplication, inverses, ```html Chapter 10: Partial Differentiation




This chapter introduces you to the concept of a partial derivative, which is a measure of how fast a function of several variables changes with respect to one of its variables. You will learn how to find partial derivatives using the definition, rules, formulas, or shortcuts. You will also learn how to interpret partial derivatives as slopes, rates of change, tangents, or linear approximations. You will then study the concept of higher-order partial derivatives, which are derivatives of partial derivatives. You will learn how to find higher-order partial derivatives using the notation, rules, or formulas. You will also learn how to apply higher-order partial derivatives to find extrema, concavity, inflection points, or optimization problems for functions of several variables.


Chapter 11: Multiple Integrals




This chapter introduces you to the concept of a multiple integral, which is a way of finding the total amount or net change of a function of several variables over a region. You will learn how to find multiple integrals using double integrals, triple integrals, or iterated integrals. You will also learn how to interpret multiple integrals as volumes, masses, moments, or averages. You will then study the concept of change of variables, which is a method for transforming multiple integrals into simpler or more convenient forms. You will learn how to use change of variables using substitutions, Jacobians, or polar, cylindrical, or spherical coordinates. You will also learn how to apply change of variables to find areas, volumes, or integrals in different coordinate systems.


Chapter 12: Vector Analysis




This chapter introduces you to the concept of a vector function, which is a function that assigns a vector to each point in a domain. You will learn how to represent vector functions using graphs, tables, formulas, or words. You will also learn how to manipulate vector functions using operations, compositions, inverses, transformations, or models. You will then study the concept of vector calculus, which is the application of calculus to vector functions. You will learn how to find limits, derivatives, and integrals of vector functions using the definition, rules, formulas, or shortcuts. You will also learn how to apply vector calculus to find arc length, curvature, torsion, or motion of curves and surfaces.


Part 3: Vector Calculus




The third part of the textbook covers the applications of calculus to vector fields and surfaces. It consists of two chapters, which are:


Chapter 13: Line Integrals and Surface Integrals




This chapter introduces you to the concept of a line integral and a surface integral, which are ways of finding the total amount or net change of a scalar or vector field along a curve or over a surface. You will learn how to find line integrals and surface integrals using parametrizations, orientations, or projections. You will also learn how to interpret line integrals and surface integrals as work, flux, circulation, or divergence. You will then study the concept of conservative fields and potential functions, which are special types of vector fields that have certain properties or relations. You will learn how to determine if a vector field is conservative or not using graphs or tests. You will also learn how to find potential functions for conservative fields using gradients or integrals.


Chapter 14: Theorems of Green, Gauss and Stokes




This chapter introduces you to some of the most important and powerful theorems in vector calculus: Green's theorem, Gauss's theorem (also known as the divergence theorem), and Stokes' theorem. These theorems establish connections between line integrals and surface integrals, or between surface integrals and volume integrals, for certain types of scalar or vector fields over certain types of regions. You will learn how to state and prove these theorems using geometry, algebra, or calculus. You will also learn how to apply these theorems to simplify calculations, solve problems, or verify results involving line integrals, surface integrals, or volume integrals.


Part 4: Differential Equations




The fourth part of the textbook covers the methods and techniques for solving ordinary and partial differential equations. It consists of four chapters, which are:


Chapter 15: First-Order Differential Equations




This chapter introduces you to the concept of a first-order differential equation, which is an equation that relates a function and its first derivative. You will learn how to classify, solve, and interpret first-order differential equations using various methods, such as separation of variables, integrating factors, exact equations, linear equations, or Bernoulli equations. You will also learn how to apply first-order differential equations to model population growth, radioactive decay, mixing problems, or cooling problems.


Chapter 16: Second-Order Linear Differential Equations




This chapter introduces you to the concept of a second-order linear differential equation, which is an equation that relates a function and its second derivative, and has the form $$a(x)y''+b(x)y'+c(x)y=d(x)$$ You will learn how to find the general solution and the particular solution of a second-order linear differential equation using various methods, such as characteristic equations, undetermined coefficients, variation of parameters, or reduction of order. You will also learn how to apply second-order linear differential equations to model harmonic motion, spring-mass systems, electrical circuits, or mechanical vibrations.


Chapter 17: Systems of Differential Equations




This chapter introduces you to the concept of a system of differential equations, which is a set of two or more differential equations that involve two or more unknown functions. You will learn how to represent, solve, and interpret systems of differential equations using various methods, such as elimination, substitution, matrices, or eigenvalues and eigenvectors. You will also learn how to apply systems of differential equations to model predator-prey systems, competing species, coupled oscillators, or chemical reactions.


Chapter 18: Power Series Solutions of Differential Equations




This chapter introduces you to the concept of a power series solution of a differential equation, which is a solution that has the form of an infinite series of powers of a variable. You will learn how to find power series solutions of differential equations using various methods, such as Frobenius method, Bessel's equation, or Legendre's equation. You will also learn how to apply power series solutions of differential equations to find special functions, such as Bessel functions, Legendre polynomials, or Chebyshev polynomials.


Part 5: Appendices and Index




The fifth part of the textbook provides useful reference materials and answers to selected exercises. It consists of three appendices and an index, which are:


Appendix A: Review of Algebra and Trigonometry




This appendix reviews some of the basic concepts and skills of algebra and trigonometry that are essential for calculus. It covers topics such as fractions, exponents, radicals, logarithms, complex numbers, polynomials, rational functions, inequalities, absolute values, trigonometric functions, identities, inverses, graphs, angles, and triangles.


Appendix B: Tables of Integrals




This appendix provides tables of integrals that can be used to find antiderivatives or definite integrals of various types of functions. It includes tables of elementary integrals, trigonometric integrals, exponential and logarithmic integrals, hyperbolic integrals, inverse trigonometric and hyperbolic integrals, and miscellaneous integrals.


Appendix C: Answers to Selected Exercises




This appendix provides answers to selected exercises from each chapter of the textbook. It includes answers to odd-numbered exercises from each section and answers to all exercises from each project. The answers are given in simplified form or with appropriate units or explanations.


Index




This index provides an alphabetical list of terms, concepts, formulas, theorems, or examples that appear in the textbook. It includes page numbers or cross-references for each entry. The index can be used to locate information or review topics quickly and easily.


Conclusion




```html Conclusion




Calculus by Strauss, Bradley and Smith is a comprehensive textbook that covers all the topics you need to know for calculus. It offers clear explanations, rigorous proofs, numerous examples, varied exercises, and interesting projects. It also features helpful notes, graphs, figures, cross-references, historica


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