101 學年度 微甲 01-04 班 下學期課程進度
章次 週次 課程進度
12. Infinite Series
民國 102 年 第 1 週 2/18~2/22
[12.1] Sigma Notation.
[12.2] Infinite Series.
[12.3] The Integral Test; Basic Comparison, Limit Comparison.
[12.4] The Root Test; The Ratio Test.
第 2 週 2/25~3/1
[12.5] Absolute and Conditional Convergence; Alternating Series.
[12.6] Taylor Polynomials in x; Taylor Series in x.
[12.7] Taylor Polynomials and Taylor Series in x–a.
[12.8] Power Series.
第 3 週 3/4~3/8
[12.9] Differentiation and Integration of Power Series.
13. Vectors
[13.3] The Dot Product.
[13.4] The Cross Product.
第 4 週 3/11~3/15
[13.5] Lines.
[13.6] Planes.
[13.7] Higher Dimensions.
14. Vector Calculus
[14.1] Limit, Continuity, Vector Derivative.
[14.2] The Rules of Differentiation.
第 5 週 3/18~3/22
[14.3] Curves.
[14.4] Arc Length.
[14.5] Curvilinear Motion; Curvature.
＊[14.6] Vector Calculus in Mechanics. (Optional)
15. Functions of Several Variables
第 6 週 3/25~3/29
[15.1] Elementary Examples.
[15.3] Graphs; Level Curves and Level Surfaces.
[15.4] Partial Derivatives.
[15.5] Open Sets and Closed Sets.
[15.6] Limits and Continuity; Equality of Mixed Partials.
第 7 週 4/1~4/5
Holiday Holiday
16. Gradients;
Extreme Values;
Differentials
第 8 週 4/8~4/12
[16.1] Differentiability and Gradient.
[16.2] Gradients and Directional Derivatives.
[16.3] The Mean-Value Theorem; the Chain Rule.
第 9 週 4/15~4/19
[16.4] The Gradient as a Normal; Tangent Lines and Tangent Planes.
[16.5] Local Extreme Values.
[16.6] Absolute Extreme Values.
[16.7] Maxima and Minima with Side Conditions.
第 10 週 4/22~4/26
[16.8] Differentials.
[16.9] Reconstructing a Function from Its Gradient.
Buffer time
暫定 4/27(六) 09:00~11:30 期中考 考試範圍 12.1~16.9 not including 14.6 (英文命題).
17. Multiple Integrals
第 11 週 4/29~5/3
[17.1] Multiple-Sigma Notation.
[17.2] Double Integrals.
[17.3] The Evaluation of Double Integrals by Repeated Integrals.
第 12 週 5/6~5/10
[17.4] The Double Integral as the Limit of Riemann Sums; Polar Coordinates.
[17.5] Further Applications of Double Integration.
[17.6] Triple Integrals.
[17.7] Reduction to Repeated Integrals.
第 13 週 5/13~5/17
[17.8] Cylindrical Coordinates.
[17.9] The Triple Integral as the Limit of Riemann Sums; Spherical Coordinates.
[17.10] Jacobians; Changing Variables in Multiple Integration.
18. Line Integrals and Surface
Integrals
第 14 週 5/20~5/24
[18.1] Line Integrals.
[18.2] The Fundamental Theorem for Line Integrals.
＊[18.3] Work-Energy Formula; Conservation of Mechanical Energy. (Optional)
第 15 週 5/27~5/31
[18.4] Another Notation for Line Integrals; Line Integrals with Respect to Arc Length.
[18.5] Green’s Theorem.
[18.6] Parametrized Surfaces; Surface Area.
第 16 週 6/3~6/7
[18.7] Surface Integrals.
[18.8] The Vector Differential Operator . [18.9] The Divergence Theorem.
[18.10] Stokes’s Theorem.
第 17 週 6/10~6/14
Holiday Buffer time
6/16(日)13:30~16:00 期末考 考試範圍 17.1~18.10 not including 18.3 (英文命題).
