Edouard Goursat's three-volume A Course in Mathematical Analysis remains a classic study and a thorough treatment of the fundamentals of calculus. As an advanced text for students with one year of calculus, it offers an exceptionally lucid exposition. The first volume in this series addresses ... read more
A Course in Advanced Calculus by Robert S. Borden An excellent undergraduate text examines sets and structures, limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, more. Problems with tips and solutions for some.
Advanced Calculus: Second Edition by David V. Widder Classic text offers exceptionally precise coverage of partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Includes exercises and selected answers.
Advanced Calculus of Several Variables by C. H. Edwards, Jr. Modern conceptual treatment of multivariable calculus, emphasizing interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. Over 400 well-chosen problems. 1973 edition.
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Edouard Goursat's three-volume A Course in Mathematical Analysis remains a classic study and a thorough treatment of the fundamentals of calculus. As an advanced text for students with one year of calculus, it offers an exceptionally lucid exposition. The first volume in this series addresses derivatives and differentials, definite integrals, expansion in series, and applications to geometry; the succeeding volume explores functions of a complex variable and differential equations. This, the third and final volume, examines variation of solutions and partial differential equations of the second order in its first part. The second part investigates integral equations and calculus of variations. Topics related to variations of solutions and partial differential equations of the second order include equations of Monge-Ampère; linear equations in n variables; linear equations of the hyperbolic and elliptic types; and harmonic functions in three variables. Subjects relevant to integral equations and calculus of variations include the solution of integral equations by successive approximations; Fredholm's equation; the fundamental functions; applications of integral equations; and the calculus of variations. The text concludes with a note on conformal representation by Paul Montel.
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