Applied Calculus

Author: Zhao Zhaoji
Publisher:
Publish Date: 2005-09-01
Features: During the writing process of this book, we believe that traditional college mathematics textbooks have been formed through long-term teaching practice and are recognized by teachers and students. They should be inherited. At the same time, we have made some new attempts, mainly including the following four points:
1. Added some relatively novel applied problems and several mathematical modeling contents related to calculus, aiming to give the traditional textbook a touch of modernity.
2. Considering that students of engineering should have some knowledge of economics and management, some simple marginal analysis and other economic application problems have been included in the book.
3. Calculus primarily discusses continuous variables. Given that the treatment of discrete variables is becoming increasingly important, we have inserted a second-order linear differential equation that is very similar in form and solution to a second-order difference equation after discussing second-order linear differential equations.
4. The "Basic Requirements" specify the need to "increase the experimental course" component. Initially, this mainly referred to physics, chemistry, and other courses. However, with the growing popularity of computers and the increasing perfection of mathematical software, mathematics has also begun to introduce experimental methods. Therefore, we have arranged four mathematical experiments in both the upper and lower volumes of this book, introducing how to use the mathematical software Mathematica for symbolic calculations in calculus (such as finding limits, derivatives, integrals, and solving differential equations), approximate calculations, and drawing graphs of curves and surfaces. The powerful functions and rich, interesting content of this software have greatly enhanced calculus, expanding its application scope and undoubtedly being highly beneficial for cultivating students' hands-on skills and problem-solving abilities. Of course, considering the differences in hardware and software across regions and schools, we have placed them at the end of the book. Schools that currently lack the necessary conditions can skip them.