微積分

臺北科技大學 114-2 學期課程，課號 355717。

課程大綱

This course aims at developing comprehension of Derivation and Integral、activating capabilities of Logic Inference and Induction、enlightening confidence and independence、strengthening calculating abilities with an emphasis on its application and diagram、furnishing a sound basis for future specialty. The content includes: 1.Limits and Continuity, 2.Derivative and Application, 3.Indefinite and Definite Integral, 4.Transcendental Functions and their Inverses, 5.Techniques of Integration, 6.Indeterminate Forms and Improper Integral, 7.Application of Integration, 8.Basic Vector Analysis, 9. Sequences and series 10.Infinite Series. 11.Partial Derivative, 12.Multiple Integration.

課程進度

week 1: polar coordinates, calculus in polar coordinates. week 2: sequences, series. week 3: integral test, comparison test. week 4: alternating series, ratio and root test. week 5: power series, representations of functions as power series. week 6: Taylor series and its applications. week 7: functions of several variables, limits and continuity. week 8: partial derivatives, tangent planes. week 9: midterm. week 10: chain rules, directional derivatives. week 11: extreme values, Lagrange multipliers. week 12: double integral over rectangles and general regions. week 13: double integrals in polar coordinates and its applications. week 14: triple integrals. week 15: triple integrals in cylindrical coordinates. week 16: triple integrals in spherical coordinates. week 17: change of variables in multiple integrals. week 18: final.

評量方式

(1) Midterm Exam: 30% (2) Final Exam: 30% (3) Homework Assignments: 20% (4) Quiz: 20% To be announced in the class for further details.

教材

【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 Essential Calculus: Early Transcendentals, Metric Version 2e(Custom Solutions), James Stewart, Daniel Clegg, Saleem Watson