微積分的危機，總讓大家愁眉苦臉，講台上的老師，也憂心忡忡的回望。遇到這種摸不著頭緒的學習情形，歡迎收看【化危機為轉機的: 高淑蓉老師微積分課程】 老師將憂心轉化成嚴格的教學，帶領大家度過數學危機！讓您的愁眉只在一瞬間！ 《keywords：微積分Calculus, ☑️極限Limit, ☑️連續Continuity, ☑️微分Differentiation, ☑️中間值定理The Intermediate Value Theorem, ☑️均值定理The Mean Value Theorem, ☑️積分Integrals, ☑️微積分第一第二基本定理The First and Second , ☑️Fundamental Theorem of Calculus), ☑️變數變換Variable Substitution, ☑️分部積分Integration by Parts》

微積分的危機，總讓大家愁眉苦臉，講台上的老師，也憂心忡忡的回望。遇到這種摸不著頭緒的學習情形，歡迎收看【化危機為轉機的: 高淑蓉老師微積分課程】 老師將憂心轉化成嚴格的教學，帶領大家度過數學危機！讓您的愁眉只在一瞬間！《keywords：微積分Calculus, ☑️極限Limit, ☑️向量函數Vector Functions, ☑️單變數函數One-variable Functions, ☑️多變數函數Several variables Functions, ☑️梯度Gradient, ☑️方向微分Directional derivatives, ☑️隱函數微分Implicit derivatives, ☑️二變數函數積分Double integrals》

Basically we shall cover the following topics. (1) Cauchy-Riemann equation，Cauchy theorem for holomorphic functions, (2) Cauchy integral formula, (3) Maximum modulus Principle, (4) Laurent series,meromorphic functions, (5) Calculus of residues, (6) Harmonic functions of two real variables, (7) Conformal mappings, Riemann mapping theorem.《keywords：複變數函數論Complex Analysis, ☑️解析函數holomorphic function, ☑️柯西積分公式Cauchy integral formula, ☑️最大模數原則maximum modulus principle, ☑️調和函數harmonic function, ☑️保角映射conformal mapping》

Applied Mathematics is a two-semester course, emphasizing the basic mathematical training encountered in science and engineering. Facing the modern frontiers with brand-new challenges, the course contains the following key modules: (1) Complex Analysis, (2) Partial Derivative, (3) Linear Algebra, (4) Quantum Operators, (5) Fourier Transform. (6) Vector calculus. It is important to maintain the balance between mathematical rigor and hands-on applications. Meanwhile, the last module (numerical methods) will be integrated into other modules to facilitate complementary usage of analytic and numeric techniques. 《keywords：applied mathematics, ☑️ partial differentiation, ☑️ matrices, ☑️ vector calculus, ☑️ ordinary differential equations, ☑️ numerical methods》