Fast start advanced calculus /
By: Ashlock, Daniel [author.].
Material type:
BookSeries: Synthesis lectures on mathematics and statistics: #30.; Synthesis digital library of engineering and computer science: Publisher: [San Rafael, California] : Morgan & Claypool, [2019]Description: 1 PDF (xiii, 179 pages) : illustrations (some color).Content type: text Media type: electronic Carrier type: online resourceISBN: 9781681736570.Subject(s): Calculus -- Textbooks | partial derivatives | multivariate optimization | constrained optimization | volume | arc-length | surface integrals | multiple integrams | series | power seriesDDC classification: 515 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 | EBKE941 |
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Part of: Synthesis digital library of engineering and computer science.
Includes index.
1. Advanced derivatives -- 1.1. Partial derivatives -- 1.2. The gradient and directional derivatives -- 1.3. Tangent planes
2. Multivariate and constrained optimization -- 2.1. Optimization with partial derivatives -- 2.2. The extreme value theorem redux -- 2.3. Lagrange multipliers
3. Advanced integration -- 3.1. Volumes of rotation -- 3.2. Arc length and surface area -- 3.3. Multiple integrals
4. Sequences, series, and function approximation -- 4.1. Sequences and the geometric series -- 4.2. Series convergence tests -- 4.3. Power series -- 4.4. Taylor series
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. Sums and factorization rules -- A.6. Vector arithmetic -- A.7. Polar and rectangular conversion -- A.8. Integral rules -- A.9. Series convergence tests -- A.10. Taylor series.
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
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This book continues the material in two early Fast Start calculus volumes to include multivariate calculus, sequences and series, and a variety of additional applications. These include partial derivatives and the optimization techniques that arise from them, including Lagrange multipliers. Volumes of rotation, arc length, and surface area are included in the additional applications of integration. Using multiple integrals, including computing volume and center of mass, is covered. The book concludes with an initial treatment of sequences, series, power series, and Taylor's series, including techniques of function approximation.
Also available in print.
Title from PDF title page (viewed on September 27, 2019).
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