Fast start integral calculus /
By: Ashlock, Daniel [author.].
Material type:
BookSeries: Synthesis lectures on mathematics and statistics: #29.; Synthesis digital library of engineering and computer science: Publisher: [San Rafael, California] : Morgan & Claypool, [2019]Description: 1 PDF (xiii, 191 pages) : illustrations.Content type: text Media type: electronic Carrier type: online resourceISBN: 9781681736518.Subject(s): Calculus, Integral -- Textbooks | integral calculus | polynomials | parametric functions | polar functions | vector functions | methods of integrationDDC classification: 515/.43 Online resources: Abstract with links to resource | Abstract with links to full text Also available in print.| Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
E books
|
PK Kelkar Library, IIT Kanpur | Available | EBKE940 |
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Part of: Synthesis digital library of engineering and computer science.
Includes index.
1. Integration, area, and initial value problems -- 1.1. Anti-derivatives -- 1.2. The fundamental theorem -- 1.3. Initial value problems -- 1.4. Induction and sums of rectangles
2. Parametric, polar, and vector functions -- 2.1. Parametric functions -- 2.2. Polar coordinates -- 2.3. Vector functions
3. The arithmetic, geometry, and calculus of polynomials -- 3.1. Polynomial arithmetic -- 3.2. Qualitative properties of polynomials -- 3.3. L'Hôpital's rule; strange polynomials
4. Methods of integration i -- 4.1. U-substitution -- 4.2. Integration by parts -- 4.3. Integrating trig functions
5. Methods of integration ii -- 5.1. Trigonometric substitution -- 5.2. Partial fractions -- 5.3. Practicing integration
A. Useful formulas -- A.1. Powers, logs, and exponentials -- A.2. Trigonometric identities -- A.3. Speed of function growth -- A.4. Derivative rules -- A.5. Vector arithmetic -- A.6. Polar and rectangular conversion -- A.7. Integral rules.
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
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This book introduces integrals, the fundamental theorem of calculus, initial value problems, and Riemann sums. It introduces properties of polynomials, including roots and multiplicity, and uses them as a framework for introducing additional calculus concepts including Newton's method, L'Hôpital's Rule, and Rolle's theorem. Both the differential and integral calculus of parametric, polar, and vector functions are introduced. The book concludes with a survey of methods of integration, including u-substitution, integration by parts, special trigonometric integrals, trigonometric substitution, and partial fractions.
Also available in print.
Title from PDF title page (viewed on September 27, 2019).
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