Integration For Calculus, Analysis, And Differential Equations
Subtitle: Techniques, Examples, And Exercises
Edition: First edition
Publisher: World Scientific Publishing Company Pvt. Ltd.
Published: July 13, 2018
Place of publication: New Jersey, USA
Language: eng
Format: Paperback
Number of pages: 180
ISBN-13: 9789813275157
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.