Introductory calculus : understanding the derivative /
Geveci, Tunc.,
Introductory calculus : understanding the derivative / Tunc Geveci. - 1 online resource (136 pages) : illustrations
Co-published with Cognella Academic Publishing. Includes index. Title from PDF title page (viewed on December 9, 2015).
1. The foundation of the derivative -- The derivative of a function at a point -- The derivative as a function -- The Leibniz notation 2. Using the derivative for powers and linear combinations -- The derivatives of rational powers of x -- The derivatives of linear combinations -- Higher-order derivatives -- The proof of the power rule for arbitrary rational powers 3. Using the derivatives of sine and cosine -- The derivatives of sine and cosine at 0 -- The derivative functions corresponding to sine and cosine 4. Using the derivative in velocity and acceleration 5. Local linear approximations -- The differential -- The traditional notation for the differential -- The accuracy of local linear approximations 6. Understanding the product and quotient rules -- The quotient rule 7. Applying the chain rule -- A plausibility argument for the chain rule -- The chain rule in the Leibniz notation -- The chain rule for more than two functions -- The proof of the chain rule 8. The problems of related rates 9. The intermediate value theorem -- Newton's method 10. Using implicit differentiation
Annotation With a "less is more" approach to introducing the reader to the fundamental concepts and uses of Calculus, this sequence of four books covers the usual topics of the first semester of calculus, including limits, continuity, the derivative, the integral and important special functions such exponential functions, logarithms, and inverse trigonometric functions.
9781606508558 (electronic) 1606508555
832650 MIL
Calculus.
Derivatives (Mathematics)
Calcul infinitésimal.
Dérivées (Mathématiques)
calculus.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Calculus.
Derivatives (Mathematics)
Electronic books.
Electronic books.
QA300 / .G485 2015
515
Introductory calculus : understanding the derivative / Tunc Geveci. - 1 online resource (136 pages) : illustrations
Co-published with Cognella Academic Publishing. Includes index. Title from PDF title page (viewed on December 9, 2015).
1. The foundation of the derivative -- The derivative of a function at a point -- The derivative as a function -- The Leibniz notation 2. Using the derivative for powers and linear combinations -- The derivatives of rational powers of x -- The derivatives of linear combinations -- Higher-order derivatives -- The proof of the power rule for arbitrary rational powers 3. Using the derivatives of sine and cosine -- The derivatives of sine and cosine at 0 -- The derivative functions corresponding to sine and cosine 4. Using the derivative in velocity and acceleration 5. Local linear approximations -- The differential -- The traditional notation for the differential -- The accuracy of local linear approximations 6. Understanding the product and quotient rules -- The quotient rule 7. Applying the chain rule -- A plausibility argument for the chain rule -- The chain rule in the Leibniz notation -- The chain rule for more than two functions -- The proof of the chain rule 8. The problems of related rates 9. The intermediate value theorem -- Newton's method 10. Using implicit differentiation
Annotation With a "less is more" approach to introducing the reader to the fundamental concepts and uses of Calculus, this sequence of four books covers the usual topics of the first semester of calculus, including limits, continuity, the derivative, the integral and important special functions such exponential functions, logarithms, and inverse trigonometric functions.
9781606508558 (electronic) 1606508555
832650 MIL
Calculus.
Derivatives (Mathematics)
Calcul infinitésimal.
Dérivées (Mathématiques)
calculus.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Calculus.
Derivatives (Mathematics)
Electronic books.
Electronic books.
QA300 / .G485 2015
515