Mathematics I serves as an introductory course for all Renaissance students in Year 1. This course covers topics in basic mathematics with emphasis on real valued functions of a real variable. Limits of such functions, continuity and the Intermediate Value Theorem. Differentiability, chain rule, critical points, the Mean Value Theorem. Inverse functions and derivatives of inverse functions. Integrability and integrals. Fundamental Theorems of Calculus. Trigonometric, logarithm and exponential functions. Techniques of integration. Taylor?s formula. Infinite sequences. Infinite series. Power series and radius of convergence. Ordinary Differential Equations and techniques for solving such. Through the sample questions/exercises provided in the course material, the students will have chances to pick up the fundamental principles related concepts into engineering science applications.
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