Calculus Light [electronic resource] /
Friedman, Menahem.author.
Kandel, Abraham.author.
Another Calculus book? As long as students find calculus scary, the failure rate in mathematics is higher than in all other subjects, and as long as most people mistakenly believe that only geniuses can learn and understand mathematics, there will always be room for a new book of Calculus. We call it Calculus Light. This book is designed for a one semester course in "light" calculus – mostly single variable, meant to be used by undergraduate students without a wide mathematical background and who do not major in mathematics but study subjects such as engineering, biology or management information systems. The first chapter contains a historical background of calculus. Every scientific achievement involves people and therefore characterized by victories and disappointments, intrigues and hope. All of these elements exist in the story behind calculus and when you add the time dimension, starting 2400 years ago, it is a saga. We hope the reader enjoys reading this chapter as much as we enjoyed the writing. In addition to classic calculus the book provides tools for practical applications such as Fourier series, Lagrange multipliers and elementary numerical methods.
""Title""; ""Preface""; ""Contents""; ""Historical Background""; ""Prelude to Calculus or the Terror of the â€?Infiniteâ€?""; ""Calculus â€? Where Do We Start?""; ""The Countdown""; ""The Birth of Calculus""; ""The Priority Dispute""; ""The Number System""; ""Basic Concepts about Sets""; ""The Natural Numbers""; ""Integers and Rational Numbers""; ""Integers""; ""Rational Numbers""; ""Real Numbers""; ""Additional Properties of the Real Numbers\""; ""Functions, Sequences and Limits""; ""Introduction""; ""Functions""; ""Algebraic Functions""; ""Sequences""; ""Basic Limit Theorems""
""Limit Points""""Special Sequences""; ""Monotone Sequences""; ""Convergence to Infinity""; ""Cauchy Sequences""; ""Continuous Functions""; ""Limits of Functions""; ""Continuity""; ""Properties of Continuous Functions""; ""Continuity of Special Functions""; ""Uniform Continuity""; ""Differentiable Functions""; ""A Derivative of a Function""; ""Basic Properties of Differentiable Functions""; ""Derivatives of Special Functions""; ""Higher Order Derivatives;  Taylor's Theorem""; ""L'Hospital's Rules""; ""Integration""; ""The Riemann Integral""; ""Integrable Functions""
""Basic Properties of the Riemann Integral""""The Fundamental Theorem of Calculus""; ""The Mean-Value Theorems""; ""Methods of Integration""; ""Improper Integrals""; ""Infinite Series""; ""Convergence""; ""Tests for Convergence""; ""Conditional and Absolute Convergence""; ""Multiplication of Series and Infinite Products""; ""Power Series and Taylor Series""; ""Fourier Series""; ""Trigonometric Series""; ""Convergence""; ""Even and Odd Functions""; ""Even Functions""; ""Odd Functions""; ""Elementary Numerical Methods""; ""Introduction""; ""Iteration""; ""The Newton - Raphson Method""
""Interpolation Methods""""Cubic Splines""; ""Least â€? Squares Approximations""; ""Linear Least â€? Squares Method""; ""Quadratic Least â€? Squares Method""; ""Numerical Integration""; ""The Trapezoidal Rule""; ""Simpson Rule""; ""Gaussian Integration""; ""Special Topics""; ""The Irrationality of e""; ""Euler's Summation Formula""; ""Lagrange Multipliers""; ""Introduction: Multi-variable Functions""; ""Lagrange Multipliers""; ""Solutions to Selected Problem""; ""Index""
Includes index.
Another Calculus book? As long as students find calculus scary, the failure rate in mathematics is higher than in all other subjects, and as long as most people mistakenly believe that only geniuses can learn and understand mathematics, there will always be room for a new book of Calculus. We call it Calculus Light. This book is designed for a one semester course in "light" calculus – mostly single variable, meant to be used by undergraduate students without a wide mathematical background and who do not major in mathematics but study subjects such as engineering, biology or management information systems. The first chapter contains a historical background of calculus. Every scientific achievement involves people and therefore characterized by victories and disappointments, intrigues and hope. All of these elements exist in the story behind calculus and when you add the time dimension, starting 2400 years ago, it is a saga. We hope the reader enjoys reading this chapter as much as we enjoyed the writing. In addition to classic calculus the book provides tools for practical applications such as Fourier series, Lagrange multipliers and elementary numerical methods.
Computational intelligence.
Information theory.
Applied mathematics.
Engineering mathematics.
Computational Intelligence.
Information and Communication, Circuits.
Mathematical and Computational Engineering.
Intelligent Systems Reference Library