Integration For Calculus, Analysis, And Differential Equations
Techniques, Examples, And Exercises
by Marat V. Markin
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The book assists Calculus students to gain a better understanding and command of integration and its applications. It reaches to students in more advanced courses such as Multivariable Calculus, Differential Equations, and Analysis, where the ability to effectively integrate is essential for their success. Keeping the reader constantly focused on the three principal epistemological questions: "What for?", "Why?", and "How?", the book is designated as a supplementary instructional tool and consists of •9 Chapters treating the three kinds of integral: indefinite, definite, and improper. Also covering various aspects of integral calculus from abstract definitions and theorems (with complete proof whenever appropriate) through various integration techniques to applications, •3 Appendices containing a table of basic integrals, reduction formulas, and basic identities of algebra and trigonometry. It also contains •143 Examples, including 112 thoughtfully selected Problems with complete step-by-step solutions, the same problem occasionally solved in more than one way while encouraging the reader to find the most efficient integration path, and •6 Exercises, 162 Practice Problems offered at the end of each chapter starting with Chapter 2 as well as 30 Mixed Integration Problems "for dessert", where the reader is expected to independently choose and implement the best possible integration approach. The Answers to all the 192 Problems are provided in the Answer Key. The book will benefit undergraduates, advanced undergraduates, and members of the public with an interest in science and technology, helping them to master techniques of integration at the level expected in a calculus course.
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Integration For Calculus, Analysis, And Differential Equations: Techniques, Examples, And Exercises
July 13, 2018, World Scientific Publishing Company Pvt. Ltd.
Paperback
in English
- First edition
9813275154 9789813275157
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Integration for Calculus, Analysis, and Differential Equations: Techniques, Examples, and Exercises
2018, World Scientific Publishing Co Pte Ltd
in English
9813272031 9789813272033
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Book Details
Edition Notes
Machine generated contents note: 1.Indefinite and Definite Integrals --
1.1.Antiderivatives and Indefinite Integral --
1.1.1.Definitions and Examples --
1.1.2.Validation of Indefinite Integrals --
1.1.3.Which Functions Are Integrable? --
1.1.4.Properties of Indefinite Integral (Integration Rules) --
1.2.Definite Integral --
1.2.1.Definitions --
1.2.2.Which Functions Are Integrable? --
1.2.3.Properties of Definite Integral (Integration Rules) --
1.2.4.Integration by Definition --
1.2.5.Integral Mean Value Theorem --
1.2.6.Fundamental Theorem of Calculus --
1.2.7.Total Change Theorem --
1.2.8.Integrals of Even and Odd Functions --
2.Direct Integration --
2.1.Table Integrals and Useful Integration Formula --
2.2.What Is Direct Integration and How Does It Work? --
2.2.1.By Integration Rules Only --
2.2.2.Multiplication/Division Before Integration --
2.2.3.Applying Minor Adjustments --
2.2.4.Using Identities --
2.2.5.Transforming Products into Sums --
Note continued: 2.2.6.Using Conjugate Radical Expressions --
2.2.7.Square Completion --
2.3.Direct Integration for Definite Integral --
2.4.Applications --
2.5.Practice Problems --
3.Method of Substitution --
3.1.Substitution for Indefinite Integral --
3.1.1.What for? Why? How? --
3.1.2.Perfect Substitution --
3.1.3.Introducing a Missing Constant --
3.1.4.Trivial Substitution --
3.1.5.More Than a Missing Constant --
3.1.6.More Than One Way --
3.1.7.More Than One Substitution --
3.2.Substitution for Definite Integral --
3.2.1.What for? Why? How? --
3.3.Applications --
3.4.Practice Problems --
4.Method of Integration by Parts --
4.1.Partial Integration for Indefinite Integral --
4.1.1.What for? Why? How? --
4.1.2.Three Special Types of Integrals --
4.1.3.Beyond Three Special Types --
4.1.4.Reduction Formulas --
4.2.Partial Integration for Definite Integral --
4.2.1.What for? Why? How? --
4.3.Combining Substitution and Partial Integration --
4.4.Applications --
Note continued: 4.5.Practice Problems --
5.Trigonometric Integrals --
5.1.Direct Integration --
5.2.Using Integration Methods --
5.2.1.Integration via Reduction Formulas --
5.2.2.Integrals of the Form [∫] sinm x cosn x dx --
5.2.3.Integrals of the Form [∫] tanm x secn x dx --
5.3.Applications --
5.4.Practice Problems --
6.Trigonometric Substitutions --
6.1.Reverse Substitutions --
6.2.Integrals Containing a2 --
x2 --
6.3.Integrals Containing x2 + a2 --
6.4.Integrals Containing x2 --
a2 --
6.5.Applications --
6.6.Practice Problems --
7.Integration of Rational Functions --
7.1.Rational Functions --
7.2.Partial Fractions --
7.2.1.Integration of Type 1/Type 2 Partial Fractions --
7.2.2.Integration of Type 3 Partial Fractions --
7.2.3.Integration of Type 4 Partial Fractions --
7.3.Partial Fraction Decomposition --
7.4.Partial Fraction Method --
7.5.Applications --
7.6.Practice Problems --
8.Rationalizing Substitutions --
8.1.Integrals with Radicals --
Note continued: 8.1.1.Integrals of the Form [∫] R(x, n ax + b/cx + d) dx --
8.1.2.Integrals of the Form [∫] R(x, xm1/n1,..., xmk/nk) dx --
8.2.Integrals with Exponentials --
8.3.Trigonometric Integrals --
8.3.1.Integrals of the Form [∫] R(tan x) dx --
8.3.2.Integrals of the Form [∫] R(sin x, cos x) dx --
8.4.Applications --
8.5.Practice Problems --
Can We Integrate Them All Now? --
9.Improper Integrals --
9.1.Type 1 Improper Integrals (Unbounded Interval) --
9.1.1.Right-Sided Unboundedness --
9.1.2.Left-Sided Unboundedness --
9.1.3.Two-Sided Unboundedness --
9.2.Type 2 Improper Integrals (Unbounded Integrand) --
9.2.1.Unboundedness at the Left Endpoint --
9.2.2.Unboundedness at the Right Endpoint --
9.2.3.Unboundedness Inside the Interval --
9.3.Applications --
9.4.Practice Problems --
Mixed Integration Problems --
Answer Key.
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| August 13, 2020 | Edited by ImportBot | import existing book |
| July 25, 2020 | Edited by Kaustubh Chakraborty | Added new book |
| July 25, 2020 | Created by Kaustubh Chakraborty | Added new book. |