| Description |
1 online resource (xi, 299 pages) |
| Series |
Intelligent systems reference library ; v. 9 |
|
Intelligent systems reference library ; v. 9.
|
| Contents |
Machine generated contents note: 1. Historical Background -- 1.1. Prelude to Calculus or the Terror of the ̀Infinite' -- 1.2. Calculus -- Where Do We Start? -- 1.3. Countdown -- 1.4. Birth of Calculus -- 1.5. Priority Dispute -- 2. Number System -- 2.1. Basic Concepts about Sets -- 2.2. Natural Numbers -- 2.3. Integers and Rational Numbers -- 2.3.1. Integers -- 2.3.2. Rational Numbers -- 2.4. Real Numbers -- 2.5. Additional Properties of the Real Numbers -- 3. Functions, Sequences and Limits -- 3.1. Introduction -- 3.2. Functions -- 3.3. Algebraic Functions -- 3.4. Sequences -- 3.5. Basic Limit Theorems -- 3.6. Limit Points -- 3.7. Special Sequences -- 3.7.1. Monotone Sequences -- 3.7.2. Convergence to Infinity -- 3.7.3. Cauchy Sequences -- 4. Continuous Functions -- 4.1. Limits of Functions -- 4.2. Continuity -- 4.3. Properties of Continuous Functions -- 4.4. Continuity of Special Functions -- 4.5. Uniform Continuity -- 5. Differentiable Functions -- 5.1. Derivative of a Function -- 5.2. Basic Properties of Differentiable Functions -- 5.3. Derivatives of Special Functions -- 5.4. Higher Order Derivatives; Taylor's Theorem -- 5.5. L'Hospital's Rules -- 6. Integration -- 6.1. Riemann Integral -- 6.2. Integrable Functions -- 6.3. Basic Properties of the Riemann Integral -- 6.4. Fundamental Theorem of Calculus -- 6.5. Mean-Value Theorems -- 6.6. Methods of Integration -- 6.7. Improper Integrals -- 7. Infinite Series -- 7.1. Convergence -- 7.2. Tests for Convergence -- 7.3. Conditional and Absolute Convergence -- 7.4. Multiplication of Series and Infinite Products -- 7.5. Power Series and Taylor Series -- 8. Fourier Series -- 8.1. Trigonometric Series -- 8.2. Convergence -- ̂ |
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Note continued: 9.1. Introduction -- 9.2. Iteration -- 9.3. Newton -- Raphson Method -- 9.4. Interpolation Methods -- 9.4.1. Lagrange Polynomial -- 9.4.2. Cubic Splines -- 9.5. Least -- Squares Approximations -- 9.5.1. Linear Least -- Squares Method -- 9.5.2. Quadratic Least -- Squares Method -- 9.6. Numerical Integration -- 9.6.1. Trapezoidal Rule -- 9.6.2. Simpson Rule -- 9.6.3. Gaussian Integration -- 10. Special Topics -- 10.1. Irrationality of e -- 10.2. Euler's Summation Formula -- 10.3. Lagrange Multipliers -- 10.3.1. Introduction: Multi-variable Functions -- 10.3.2. Lagrange Multipliers |
| Summary |
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 |
| Notes |
Print version record |
| In |
Springer eBooks |
| Subject |
Calculus.
|
|
Engineering.
|
|
Mathematics.
|
|
Engineering
|
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Mathematics
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calculus.
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engineering.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Ingénierie.
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Calculus
|
| Form |
Electronic book
|
| Author |
Kandel, Abraham.
|
| ISBN |
9783642178481 |
|
3642178480 |
|
3642178472 |
|
9783642178474 |
|
