The content of advanced mathematics is unary function calculus and multivariate function calculus. This requires self-learners to learn the knowledge of "function", "trigonometric function" and "anti-trigonometric function" in senior high school mathematics curriculum. If these preparatory knowledge is not learned well, it will inevitably affect the calculation of derivatives and integrals. In addition to these necessary knowledge, candidates should also be familiar with some formulas and methods learned in middle school, such as factorization formula, general division and simplification of fractions, solution of quadratic equation in one variable, trigonometric function formula, double angle formula and so on. Before studying this course, candidates are advised to make up this part before continuing their advanced mathematics study, if these preparatory knowledge is not enough. As the most important formulas in higher mathematics, derivative formula and basic integral formula must be memorized and used flexibly. It is suggested that self-learners do more problems when studying the integral part of this course, because many integral formulas are not easy to "product" and must be transformed, and various calculation methods and skills must be fully used to continue. In addition, candidates must be careful in the learning process. For example, when solving indefinite integrals, points are deducted because the constant c is not enough. Unfortunately, the study of advanced mathematics should focus on several points.