Integration for calculus, analysis, and differential equations: techniques, examples, and exercises
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
New Jersey
World Scientific
2019
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Diagramme |
| Physical Description: | xii, 164 Seiten |
| ISBN: | 9789813275157 9789813272033 |
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MARC
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Record in the Search Index
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| adam_text | Contents Preface 1. Indefinite and Definite Integrals 1.1 1.2 2. vii 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) 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.................. 1 1 4 5 5 6 6 9 9 10 11 12 15 16 Direct Integration 17 2.1 2.2 17 20 21 21 22 23 26 Table Integrals and UsefulIntegration Formula................. 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........................ ІХ
Integration for Calculus, Analysis, and Differential Equations x 2.3 2.4 2.5 3. 35 3.1 35 35 36 37 39 40 42 43 45 45 48 49 3.3 3.4 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................................. Substitution for Definite Integral....................................... 3.2.1 What for? Why? How?.......................................... Applications........................................................................... Practice Problems ............................................................... Method of Integration by Parts 51 4.1 51 51 52 55 57 59 59 62 63 64 4.2 4.3 4.4 4.5 5. 27 28 29 31 33 Method of Substitution 3.2 4. 2.2.6 Using Conjugate Radical Expressions.................. 2.2.7 Square Completion ................................................ Direct Integration for Definite Integral.............................. Applications.......................................................................... Practice Problems ............................................................... 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................................................ Partial Integration for Definite Integral.............................. 4.2.1 What for? Why? How?.......................................... Combining Substitution and Partial Integration............... Applications.......................................................................... Practice Problems ............................................................... Trigonometric Integrals 65 5.1 5.2 65 66 66 70 Direct Integration.................................................................. Using Integration Methods................................................... 5.2.1 Integration via ReductionFormulas...................... 5.2.2 Integrals of the Form / sinm x cosn x dx...............
Contents 5.2.3 5.3 5.4 6. 7. J tanm x sec x dx ............ 76 Applications.......................................................................... Practice Problems ............................................................... 79 81 Trigonometric Substitutions 83 6.1 6.2 6.3 6.4 6.5 6.6 83 84 88 92 96 98 Reverse Substitutions............................................................ Integrals Containing a2 — x2................................................ Integrals Containing x2 + a2................................................ Integrals Containing x2 — a2................................................ Applications........................................................................... Practice Problems ............................................................... Integration of Rational Functions 7.1 7.2 7.3 7.4 7.5 7.6 8. Integrals of the Form xi 99 Rational Functions............................................................... 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............... Partial Fraction Decomposition.......................................... Partial Fraction Method...................................................... Applications.......................................................................... Practice Problems ............................................................... Rationalizing Substitutions 8.1 8.2 8.3 8.4 8.5
115 Integrals with Radicals 8.1.1 Integrals of the Form 8.1.2 Integrals of the Form ............ 115 dx . . . 115 ƒ R.(x,xmi/ni,...,x™*/»*) dx Integrals with Exponentials Trigonometric Integrals . . . 99 100 101 101 103 104 107 112 114 ............ 116 ............ ............ 117 118 8.3.1 Integrals of the Form ƒ R (tan x) dx . . . ............ 8.3.2 Integrals of the Form R(sin æ, cos æ) dx ............ 119 ............ 121 ............ 124 Applications........................ Practice Problems ............ J 118
Integration for Calculus, Analysis, and Differential Equations xii Can We Integrate Them All Now? 125 9. Improper Integrals 127 9.1 127 127 130 132 134 135 137 138 141 142 9.2 9.3 9.4 Type 1 Improper Integrals (Unbounded Interval)............ 9.1.1 Right-Sided Unboundedness .................................. 9.1.2 Left-Sided Unboundedness..................................... 9.1.3 Two-Sided Unboundedness..................................... 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......................... Applications.............................................................................. Practice Problems ................................................................. Mixed Integration Problems 145 Answer Key 147 Appendix A Table of Basic Integrals 153 Appendix В Reduction Formulas 155 Appendix C Basic Identities of Algebra and Trigonometry 157 Bibliography 161 Index 163
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| spelling | Markin, Marat V. (DE-588)1169968635 aut Integration for calculus, analysis, and differential equations techniques, examples, and exercises by Marat V. Markin (California State University, Fresno, USA) New Jersey World Scientific 2019 xii, 164 Seiten txt rdacontent n rdamedia nc rdacarrier Diagramme Calculus Textbooks Mathematical analysis Textbooks Differential equations Textbooks Integralrechnung (DE-588)4027232-1 gnd rswk-swf Integralrechnung (DE-588)4027232-1 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030639103&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Markin, Marat V. Integration for calculus, analysis, and differential equations techniques, examples, and exercises Calculus Textbooks Mathematical analysis Textbooks Differential equations Textbooks Integralrechnung (DE-588)4027232-1 gnd |
| subject_GND | (DE-588)4027232-1 |
| title | Integration for calculus, analysis, and differential equations techniques, examples, and exercises |
| title_auth | Integration for calculus, analysis, and differential equations techniques, examples, and exercises |
| title_exact_search | Integration for calculus, analysis, and differential equations techniques, examples, and exercises |
| title_full | Integration for calculus, analysis, and differential equations techniques, examples, and exercises by Marat V. Markin (California State University, Fresno, USA) |
| title_fullStr | Integration for calculus, analysis, and differential equations techniques, examples, and exercises by Marat V. Markin (California State University, Fresno, USA) |
| title_full_unstemmed | Integration for calculus, analysis, and differential equations techniques, examples, and exercises by Marat V. Markin (California State University, Fresno, USA) |
| title_short | Integration for calculus, analysis, and differential equations |
| title_sort | integration for calculus analysis and differential equations techniques examples and exercises |
| title_sub | techniques, examples, and exercises |
| topic | Calculus Textbooks Mathematical analysis Textbooks Differential equations Textbooks Integralrechnung (DE-588)4027232-1 gnd |
| topic_facet | Calculus Textbooks Mathematical analysis Textbooks Differential equations Textbooks Integralrechnung |
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