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Calculus : early transcendentals
'Calculus' covers exponential and logarithmic functions. It looks at their limits, derivatives, polynomials and other elementary functions.
Book
Focus on Calculus
\"This book is devoted to some recent aspects of calculus. The book contains seven chapters. Chapter 1 introduces the conception for conformable delta (Hilger) derivative and some of its properties. Results in this chapter include basic conformable delta derivative, the conformable exponential function, conformable trigonometric and hyperbolic functions, conformable delta integral and integral rules and Taylor's formula. They are considered first order conformable dynamic equations on time scales. Chapter 2 is devoted to some classes second order quadratic difference equations. They are given criteria for existence of a unique equilibrium point that is stable and unstable, existence of prime period-two solutions. Chapter 3 is aimed to develop two calculi over the specific algebraic operations, preserving the preceding relativistic addition formula and having all ordinary properties. Chapter 4 is devoted to principles of hypercomplex rand
eBook
The how and why of one variable calculus
First course calculus texts have traditionally been either \"engineering/science-oriented\" with too little rigor, or have thrown students in the deep end with a rigorous analysis text. The How and Why of One Variable Calculus closes this gap in providing a rigorous treatment that takes an original and valuable approach between calculus and analysis. Logically organized and also very clear and user-friendly, it covers 6 main topics; real numbers, sequences, continuity, differentiation, integration, and series. It is primarily concerned with developing an understanding of the tools of calculus. The author presents numerous examples and exercises that illustrate how the techniques of calculus have universal application.
The How and Why of One Variable Calculus presents an excellent text for a first course in calculus for students in the mathematical sciences, statistics and analytics, as well as a text for a bridge course between single and multi-variable calculus as well as between single variable calculus and upper level theory courses for math majors.
eBook
Calculus simplified
\"Calculus is a beautiful subject that most of us learn from professors, textbooks, or supplementary texts. Each of these resources has strengths but also weaknesses. In Calculus Simplified, Oscar Fernandez combines the strengths and omits the weaknesses, resulting in a \"Goldilocks approach\" to learning calculus: just the right level of detail, the right depth of insights, and the flexibility to customize your calculus adventure. Fernandez begins by offering an intuitive introduction to the three key ideas in calculus -- limits, derivatives, and integrals. The mathematical details of each of these pillars of calculus are then covered in subsequent chapters, which are organized into mini-lessons on topics found in a college-level calculus course. Each mini-lesson focuses first on developing the intuition behind calculus and then on conceptual and computational mastery. Nearly 200 solved examples and more than 300 exercises allow for ample opportunities to practice calculus. And additional resources -- including video tutorials and interactive graphs - are available on the book's website. Calculus Simplified also gives you the option of personalizing your calculus journey. For example, you can learn all of calculus with zero knowledge of exponential, logarithmic, and trigonometric functions -- these are discussed at the end of each mini-lesson. You can also opt for a more in-depth understanding of topics -- chapter appendices provide additional insights and detail. Finally, an additional appendix explores more in-depth real-world applications of calculus. Learning calculus should be an exciting voyage, not a daunting task. Calculus Simplified gives you the freedom to choose your calculus experience, and the right support to help you conquer the subject with confidence. An accessible, intuitive introduction to first-semester calculus. Nearly 200 solved problems and more than 300 exercises (all with answers)-No prior knowledge of exponential, logarithmic, or trigonometric functions required-Additional online resources - video tutorials and supplementary exercises provided\"--Provided by publisher..
Book
Fundamentals of calculus
Features the techniques, methods, and applications of calculus using real-world examples from business and economics as well as the life and social sciences
An introduction to differential and integral calculus, Fundamentals of Calculus presents key topics suited for a variety of readers in fields ranging from entrepreneurship and economics to environmental and social sciences.
Practical examples from a variety of subject areas are featured throughout each chapter and step-by-step explanations for the solutions are presented. Specific techniques are also applied to highlight important information in each section, including symbols interspersed throughout to further reader comprehension.
In addition, the book illustrates the elements of finite calculus with the varied formulas for power, quotient, and product rules that correlate markedly with traditional calculus. Featuring calculus as the \"mathematics of change,\" each chapter concludes with a historical notes section.
Fundamentals of Calculus chapter coverage includes:
* Linear Equations and Functions
* The Derivative
* Using the Derivative
* Exponents and Logarithms
* Differentiation Techniques
* Integral Calculus
* Integrations Techniques
* Functions of Several Variables
* Series and Summations
* Applications to Probability
Supplemented with online instructional support materials, Fundamentals of Calculus is an ideal textbook for undergraduate students majoring in business, economics, biology, chemistry, and environmental science.
eBook
Calculus deconstructed : a second course in first-year calculus
Calculus Deconstructed is a thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous exposure to calculus techniques but not to methods of proof. This book is appropriate for a beginning Honors Calculus course assuming high school calculus or a \"bridge course\" using basic analysis to motivate and illustrate mathematical rigor. It can serve as a combination textbook and reference book for individual self-study. Standard topics and techniques in single-variable calculus are presented in context of a coherent logical structure, building on familiar properties of real numbers and teaching methods of proof by example along the way. Numerous examples reinforce both practical and theoretical understanding, and extensive historical notes explore the arguments of the originators of the subject.No previous experience with mathematical proof is assumed: rhetorical strategies and techniques of proof (reductio ad absurdum, induction, contrapositives, etc.) are introduced by example along the way. Between the text and exercises, proofs are available for all the basic results of calculus for functions of one real variable.
eBook
Introduction to integral Calculus
An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences
I ntegration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coupled with clear, simple explanations, the authors reinforce new concepts to progressively build skills and knowledge, and numerous real-world examples as well as intriguing applications help readers to better understand the connections between the theory of calculus and practical problem solving.
The first six chapters address the prerequisites needed to understand the principles of integral calculus and explore such topics as anti-derivatives, methods of converting integrals into standard form, and the concept of area. Next, the authors review numerous methods and applications of integral calculus, including:
* Mastering and applying the first and second fundamental theorems of calculus to compute definite integrals
* Defining the natural logarithmic function using calculus
* Evaluating definite integrals
* Calculating plane areas bounded by curves
* Applying basic concepts of differential equations to solve ordinary differential equations
With this book as their guide, readers quickly learn to solve a broad range of current problems throughout the physical sciences and engineering that can only be solved with calculus. Examples throughout provide practical guidance, and practice problems and exercises allow for further development and fine-tuning of various calculus skills. Introduction to Integral Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.
eBook
Introduction to differential calculus
\"Through the use of examples and graphs, this book maintains a high level of precision in clarifying prerequisite materials such as algebra, geometry, coordinate geometry, trigonometry, and the concept of limits. The book explores concepts of limits of a function, limits of algebraic functions, applications and limitations for limits, and the algebra of limits. It also discusses methods for computing limits of algebraic functions, and explains the concept of continuity and related concepts in depth. This introductory submersion into differential calculus is an essential guide for engineering and the physical sciences students\"--
eBook