le1Introduction and evaluation using inequalities (1): Error and approximation3Evaluation using inequalities (3): How to write a proof using the (ε,δ)-5Convergence/divergence of series sums, absolute convergence, conditional convergence6Simple method of determining convergence or divergence for series sumsClass Schedu7Power series and its radius of convergence, Riemann's zeta function, Taylor's theorem8Topics from the mean-value theorem to Taylor's theorem, evaluation of ⓾New functions such as inverse trigonometric functions and Euler's formula⓫Basics of integrals (1): Definition of definite integrals⓬Basics of integrals (2): Integrability of continuous functions⓭Improper integral and its convergence and divergence, examples of functions ⓮Calculations of various integrals and corresponding problems leading to them10 Learning at the Faculty of Science and Technology This lecture deals with analytical methods in mathematics such as differential and integral calculus, focusing on the case of a single variable. It starts with the topic of "evaluation using inequalities," which is not often used in the "mathematics of equations" in high school, and then discusses limit, convergence, infinite sums, differentiation, integration, approximate calculation, etc., in relation to the theory of Taylor expansion as the major subject. A more solid foundation will be given to mathematical analysis while knowledge learned in high school is fully utilized. It is important to gain a feel for theoretical problems through exercises and many examples, as well as to become familiar with various practical examples to be encountered in the future.2Evaluation using inequalities (2): Limit and (ε,δ)-definitiondefinition of a limit and introduction to the Taylor expansion4 What is the Taylor expansion: Examples and applicationsremainder terms using Taylor's theorem9Use and application of the Taylor expansion: Calculation of approximate values and error evaluation, term-wise calculus, calculation of limitsdefined with improper integrals (gamma function, beta function)■is section introduces courses common to the three departments in the Faculty of Science and TechnologyMajor Flow of ClassesMathematics B1 FST General Subject Group 1(compulsory course for the ■rst year)FST General Subjects
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