English

Differential Equations And The Calculus Of Variations

This text is meant for students of higher schools and deals with the most important sections of mathematics-differential equations and the calculus of variations. The book contains a large number of examples and problems with solutions involving applications of mathematics to physics and mechanics. The book was translated from the Russian by George Yankovsky and was first published by Mir Publishers in 1970. There were two reprints one in 1973 and one in 1977. The book here is to the third reprint. Contents Chapter 1. First-Order Differential Equations 19 1. First-Order Differential Equations Solved for the Derivative 19 2. Separable Equations 23 3. Equations That Lead to Separable Equations 29 4. Linear Equations of the First Order 32 5. Exact Differential Equations 37 6. Theorems of the Existence and Uniqueness of Solution of the equation dy/dx = f(x,y) 44 7. Approximate Me~hods of Integrating First-Order Equations 66 8. Elementary Types of Equations Not Solved for the Derivative 73 9. The Existence and Uniqueness Theorem for Differential Equations Not Solved for the Derivative. Singular Solutions 81 Problems 88 Chapter 2. Differential Equations of the Second Order and Higher 91

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