Post-Reading Activity

Ex. 11. Answer the following questions.

1. When was the term “differential equation” first used? 2. What did this term denote at that time? 3. What does this term denote now? 4. In what ways are differential equations classified? 5. What kinds of differential equations do you know? 6. What does an ordinary differential equation express? 7. What does a partial differential equation involve? 8. What does a total differential equation contain? 9. What is the order of a differential equation? 10. What is the degree of a differential equation? 11. When is an ordinary or a partial differential equation linear? 12. What does the most general solution of an ordinary equation of order n involve?

Ex. 12. Match the English words and word combinations with the Russian equivalents.

an ordinary differential equation, a partial differential equation, a total differential equation, an auxiliary variable, a primitive, differentiability and continuity, point of view, an existence theorem, arbitrary constants, simultaneously, the first integral of the equation, a step-by-step process, differential coefficients, apart from.

дифференцируемость и непрерывность; произвольные константы; обыкновенное дифференциальное уравнение; точка зрения; одновременно; дифференциальное уравнение в частных производных; первый интеграл уравнения; теорема существования; уравнение в полных дифференциалах; кроме, не говоря о, не считая; поэтапный процесс; вспомогательная переменная; дифференциальные коэффициенты; первообразная.

Ex. 13. Translate the following sentences into Russian.

1. Differential equations are now understood to include any algebraical or transcendental equalities which involve either differentials or differential coefficients. 2. When an equation is polynomial in all the differential coefficients involved, the power to which the highest differential coefficient is raised is known as the degree of the equation. 3. The coefficients of the linear equation are either constants or functions of the independent variable or variables. 4. In the formation of a differential equation from a given primitive it is necessary to assume certain conditions of differentiability and continuity of derivatives. 5. From this theorem, it follows that the most general solution of an ordinary equation of order n involves n, and only n, arbitrary constants. 6. Let the primitive be solved for c and this value of c be substituted into the derived equation. 7. When the given equation is of order n, and by a process of integration an equation of order involving an arbitrary constant is obtained, the latter is known as the first integral of the given equation. 8. To make this point clear, let us consider, for instance, the differential equation of the following formc² + 2cy + a² - x² = 0.

Ex. 14. Find out whether the statements are true or false. Use introductory phrases.

Exactly. Quite so. Quite the contrary.