| 課程簡述 |
This course provides a comprehensive study of advanced topics in calculus, emphasizing both theoretical understanding and practical problem-solving skills. Beginning with inverse functions, exponential and logarithmic functions, the course develops techniques for differentiation and integration, including methods such as integration by parts, trigonometric substitution, partial fractions, and improper integrals. Students are then introduced to sequences and series, with a focus on convergence tests, power series, and Taylor and Maclaurin expansions and their applications. The latter part of the course extends calculus concepts to functions of several variables, covering partial derivatives, optimization, multiple integrals, and coordinate transformations. Through systematic progression and rigorous applications, the course equips students with essential analytical tools for further study in mathematics, science, engineering, and related fields. |