課程資訊

CALCULUS (GENERAL MATHEMATICS) (B)(2)

97-2

MATH1204

201 101B2

07

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/972med

1. The continuity of chapter 7 from the first semester: exponential growth and decay, inverse of trigonometric functions, Hyperbolic functions, indeterminate forms and L’Hospital’s Rule
2. Techniques of Integration: integration by parts, trigonometric integrals, trigonometric substitution, integration of rational functions by partial fractions, approximate integration. improper integrals,
3. Further applications of integration: arc length, area of surface of revolution, application to Physics, Engineering, application to Economics and Biology, Probability.
4. Differential Equation: Modeling with differential equations, direction fields and Euler’s Method, separable equations, linear equations, Predator-Prey Systems.
5. Parametric equations and polar coordinates: curves defined by parametric equations, polar coordinates, areas and lengths in polar coordinates, conic sections, conic sections in polar coordinates.
6. Infinite sequences and series: sequences, series, the integral test and estimate of sums, comparison tests, alternating series, absolute convergence, the ratio and root test, power series, representations of functions as power series, Taylor and Maclaurin series, application of Taylor polynomials
7. Vectors and the geometry of space: dot product, cross product, equations of lines and planes, cylinders and quadric surfaces
8. Vector functions: vector functions and space curves, arc length and curvature, derivatives and integral of vector functions
9. Partial derivatives: Functions of several variables, limits and continuity, partial derivatives, tangent planes and linear approximations, the chain rule, directional derivatives and the gradient vector, maximum and minimum values, Lagrange Multipliers

We will complete the techniques of integration with one variable. In order to understand a function with one variable, we will learn the Taylor series of a function. We will introduce the context of functions with several variables. We will also learn polar coordinates for two variable and other coordinates systems for better expression. We will learn the calculus with several variables functions and vector functions

Office Hours

Calculus by James Steward-metric international version

(僅供參考)

 No. 項目 百分比 說明 1. 期中考 40% 2. 期末考 40% 3. 隨堂測驗 20% 4. 作業 0% 5. 報告 0%

 課程進度
 週次 日期 單元主題 第1週 2/17,2/19 7-5,7-6 第11週 4/28,4/30 10-3, 10-4 第12週 5/05,5/07 10-4, 10-5, 第四次小考