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James Drewry Stewart, MSC (March 29, 1941 – December 3, 2014) was a Canadian mathematician, violinist, and professor emeritus of mathematics at McMaster University. Stewart is best known for his series of calculus textbooks used for high school, college, and university-level courses.
In that the existence of uniquely characterises the number ′ (), the fundamental increment lemma can be said to characterise the differentiability of single-variable functions. For this reason, a generalisation of the lemma can be used in the definition of differentiability in multivariable calculus .
James Stewart, Daniel Clegg, Saleem Watson (2016) Single Variable Calculus: Early Transcendentals (Instructor's Edition) 9E, Cengage ISBN 978-0-357-02228-9 E. T. Whittaker & G. N. Watson (1963) A Course in Modern Analysis , 4th edition, §2.3, Cambridge University Press ISBN 0-521-58807-3
By noting that | x − p | represents a distance, the definition of a limit can be extended to functions of more than one variable. In the case of a function f : S × T → R {\displaystyle f:S\times T\to \mathbb {R} } defined on S × T ⊆ R 2 , {\displaystyle S\times T\subseteq \mathbb {R} ^{2},} we defined the limit as follows: the limit of ...
The first part of the theorem, the first fundamental theorem of calculus, states that for a continuous function f, an antiderivative or indefinite integral F can be obtained as the integral of f over an interval with a variable upper bound. [1]
In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form () (,), where < (), < and the integrands are functions dependent on , the derivative of this integral is expressible as (() (,)) = (, ()) (, ()) + () (,) where the partial derivative indicates that inside the integral, only the ...
These men, women and children make up just some of the over one million migrants and refugees who have sought asylum in Europe this past year. Here, we follow the story of a young Eritrean woman who crossed mountains, oceans and deserts to escape the small, secretive East African nation.
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