Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
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Yes, you can access Introduction to Partial Differential Equations by Donald Greenspan in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over one million books available in our catalogue for you to explore.
One of the fundamental concepts of modern mathematical thought is that of a set. From the strictly logical point of view, the term set may be left undefined. Intuitively, however, one may think of a set as a collection, or aggregate, of objects called elements or points.
Example 1. The positive integers 1, 2, 3, 4, . . . constitute a set.
Example 2. All polynomials with rational coefficients constitute a set.
Example 3. All real numbers which satisfy the inequality 0 ≤ x ≤ π constitute a set.
Example 4. All points (x,y) of the plane whose coordinates satisfy the inequality x2 + y2 ≤ 1 constitute a set.
The set of no elements is called the empty set and is denoted by θ.
Example. The set of all real numbers x which satisfy x2 < 0 is θ.
Definition 1.1. The union, or sum, of two sets A and B, denoted A ∪ B, is the set of all elements which belong to at least one of A and B.
Example 1. If A is the set whose elements are the integers 1, 2, 3 and B is the set whose elements are the integers 3, 4, 5, then A ∪ B is the set whose elements are the integers 1, 2, 3, 4, 5.
Example 2. If A is the set of rational numbers and B is the set of irrational numbers, then A ∪ B is the set of real numbers.
Definition 1.2. The union, or sum, of an arbitrary collection of sets Aα, denoted
, is the set of all elements which belong to at least one of the Aα.
Definition 1.3. The intersection, or product, of two sets A and B, denoted A ∩ B, is the set of all elements which belong to both A and B.
Example 1. If A is the set whose elements are the integers 1, 2, 3 and B is the set whose elements are the integers 3, 4, 5, then A ∩ B is the set which consists of the single integer 3.
Example 2. If A is the set of rational numbers and B is the set...
