Course Description:
This subject is to provide students with basic skills of mathematical analysis, which is the core of many quantitative disciplines such as Optimization, Financial Mathematics, Statistics, and Econometrics. The syllabus emphasizes an approach to mathematics of a more abstract and conceptual kind. This emphasis is designed to help students cope with more advanced mathematics that they will meet in their senior years. Topics include: further techniques of differentiation and integration, improper integrals, Riemann integral, numerical integration, infinite sequences and series, and introduction to Ordinary Differential Equations.
Course Intended Learning Outcomes:
1. CILO-1: Master the concepts of indefinite integrals as anti-derivatives and definite integrals as limit of sums, and recognize the fundamental theorem of calculus and other integration theorem.
2. CILO-2: Evaluate indefinite and definite integrals using techniques such as change of variables, integration by parts, and partial fraction decomposition.
3. CILO-3: Test the convergence or divergence of a given series, and obtain Taylor's expansion of a given function.
4. CILO-4: Acquire some rudimentary knowledge on numerical integration.
5. CILO-5: Acquire some rudimentary knowledge on solving simple differential equations.
6. CILO-6: Compute probabilities from continuous probability distributions.
7. CILO-7: Apply the calculus techniques learned in this course to problems in finance.
- Teacher: yunhuilin, Lin Yunhui