大氣科學是一門理論與實際兼備的科學，這些實際的問題仍然是有其理論基礎的，因此數理的基礎相當重要，數學相關的課程很重，其中應用數學是指要的數學核心課程。應用數學乃一學年的課程，培養大氣科學及相關科系學生所需之基本數學原理及計算能力，此基礎課程將用於往後與大氣相關之基礎課程及應用課程如流體力學、大氣熱力、大氣動力、天氣學、數值方法及數值預報等等。乃大氣科學系之必修科程。本課程由淺入深，首先介紹什麼是微分方程式及一階微分方程式，及一階方程式所伴隨的物理問題，進而介紹二階及高階微分方程式。由於某些重要的微分方程式無基本函數解，因此需利用級數方式解及拉式轉換求解。此外富利業級數更是重要的一環，舉凡大氣的任何現象均可視為是波動，富利業級數就是處理波動問題不可或缺的數學方法。再者，許多資料處理皆需要透過矩陣進行運算，因此本課程也將介紹線性代數。
The atmospheric science is a kind of science that covers theories and real phenomena. However, all the phenomena have their theoretic background. Therefore, the mathematical background is extremely important. The purpose of this course is to establish the solid background for students to advance their ability for other basic and application courses, such as fluid dynamic, atmospheric thermodynamic, synoptic dynamics, numerical weather prediction, and so on. This course covers many aspects that students have to study, such as ordinary differential equations, power series method, Laplace transform and Fourier transform. Also, in data analysis, matrices are often used, so in this course we will introduce linear algebra.