Home for Calculus II (Spring, 2010)
新春開工嘍！你不可不點 課程簡介及教學計畫。
去年習題參考解答請由此進 。
上課內容摘要
Week 1
1. Power series, radius of convergence, interval of convergence.
2. Differentiation and integration term by term, product of two power series.
3. Taylor and Maclaurin series.
4. Taylor's theorem and analytic functions.
Week 2
1.Homework #1(due 3/9):§11.7,16,26,32,35,39,40,44,46;§11.8,17,28,29,32;§11.9,6,14,23,24,30(a).
2. Fourier series.
3. Calculus of vector-valued functions.
4. Tangent vectors, normal vectors, binormal vectors.
5. Curvature, torsion.
Week 3
1. Quiz #1, 3/16.
2. Functions of several variables.
3. Graph of a function, level set.
4. Limits of a function, continuity.
5. Partial derivatives, differentiability.
Week 4
1. Differentiability, the chain rule.
2. Directional derivatives, gradient.
3. Normal direction, tangent plane, linear approximation.
4. Necessary condition for an extremum, saddle points.
5. Homework #2(due 3/25):§14.2,35,38,41,46,47,55,58;§14.3,58,65,74,76,77;§14.4,42,48;§14.5,16,18,21;§14.6,5,21,29,42,60,62,63.
Week 5
1. Finding extreme values, second order derivative test.
2. Optimization under constraints.
3. Method of Lagrange multipliers.
4. Quiz #2, 3/30.
Week 6
1. Taylor's formula for a function of multivariable.
2. Definition of double integrals.
3. Iterated integrals, Fubini's theorem for computing double integrals.
4. Area, moments, centers of mass.
5. Double integral in polar coordinates.
6, Homework #3 (due 4/8): §14.7,27,28,39,41,46,52,53;§14.8,16,29,38,42,43;§14.10,6,11
Week 7
1. No class on 4/6. The midterm is on 4/27.
2. Double integral in polar coordinates.
3. Triple integrals, Fubini's theorem.
4. Quiz #3, 4/13.
Week 8
1. Homework #4 (due 4/20): §15.1,36,38,52,59,61,66;§15.2,33,43;§15.3,13,14,42;§15.4,28,29,32,42,44.
2. Applications of triple integrals.
3. Triple integrals in the cylindrical and spherical coordinates.
4. Integrals in terms of a general change of coordinates, Jacobian.
Week 9
1. Some examples of calculating integrals using suitable change of coordinates.
2. Line integrals.
3. Mathematical foundation of the CT scan.
4. Line integrals involving vector fields.
5. Midterm on 4/27 ( §11.7 ― end of Chapter 15).
6. 準備考試，放鬆心情，聽個歌吧。