Week 1. 2/18 ~ 2/24

課程進度 :
Review of Differentiation Rules and Fundamental Theorem of Calculus (簡短複習)
Section 8.1 Basic Integration Rules
  • Review of Basic Integration Rules :
  • Procedure for Fitting Integral to Basic Integration Rules
    1. Expand the integrand
    2. Complete a square
    3. Separate numerator and divide improper rational function : EX 1. a、b、c
    4. Use trigonometric identities : EX 6
  • EX 2 ~ EX 5
 
演習課 :
上課練習檔 : 第一周上課練習檔 課後作業檔


Week 2. 2/25 ~ 3/3

課程進度 : 2/28、3/1 -- 228 紀念日 放假
Section 8.2 Integration by Parts
  • Theorem 8.1 : EX1、EX2、EX3、Ex4、EX5
Section 8.3 Trigonometric Integrals
  • Integration involving Powers of Sine and Cosine: EX1、EX3
  • Integration involving Powers of Secant and Tangent: EX4~EX7
  • Integration involving Sine-Cosine Products with Different Angles: EX8


Week 3. 3/4~ 3/10

課程進度 :
Section 8.4 Trigonometric Substitution
  • EX1~EX4
Section 8.5 Partial Fractions
  • Decomposition of Rational Function into Partial Fractions: EX1~EX4


Week 4. 3/11 ~ 3/17

課程進度 :
Section 8.7 Integration by Tables and Other Integration Techniques (Section 8.6 in 10th edition)
  • EX1~EX4
  • Substitution by Rational Functions of Sine and Cosine (選擇性)
Section 5.6 Indeterminate Forms and L’Hopital’s Rule (Section 8.7 in 10th edition)
  • Indeterminate Forms
  • Theorem 5.17: EX1~EX4 (完成後,請接 EX5 ~ EX7。)


Week 5. 3/18 ~ 3/24

課程進度 :
Section 5.6 Indeterminate Forms and L’Hopital’s Rule (Section 8.7 in 10th edition)
  • EX5~EX7 (接上星期)
Section 8.8 Improper Integral
  • Definition of Improper Integrals with Infinite Integration Limits: EX1~EX4
  • Definition of Improper Integrals with Infinite Discontinuities: EX6~EX8
  • EX9 (選擇性)


Week 6. 3/25

課程進度 : 第一次期中考

 
演習課 :
上課練習檔 : 期中考周上課練習檔


Week 7. 4/1 ~ 4/7

課程進度 :
Section 7.1 Area of a Region Between Two Curves
  • EX1,EX2,EX4,EX5
Section 7.2 Volume: The Disk Method
  • The Disk Method: EX2
  • The Washer Method: EX3,EX4


Week 8. 4/8 ~ 4/14

課程進度 :
Section 7.4 Definition of Arc Length (選擇性)
  • Section 8.4 EX5 (選擇性)
  • Section 8.8 EX10 (選擇性)
Section 10.2 Plane Curve and Parametric Equations
  • Definition of Parametric Equations
  • Definition of a Plane Curve: EX1
  • Finding Parametric Equation: EX4
Section 10.3 Parametric Equations and Calculus
  • Theorem 10.7: EX1, EX2
  • Theorem 10.8 Arc Length in Parametric Form EX4 (選擇性)


Week 9. 4/15 ~ 4/21

課程進度 :
Section 10.4 Polar Coordinates
  • Definition of Polar Coordinates
  • Theorem 10.10: EX1, EX2
  • Theorem 10.11: EX5
Section 11.1 Vectors in the Plane
  • Component Form of a Vector: EX1
  • Definition of Component Form of a Vector in the Plane: EX2
  • Vector Operations: EX3
  • Theorem 11.1, 11.2, 11.3: EX4
  • Unit Vector: EX5


Week 10. 4/22 ~ 4/28

課程進度 :
Section 11.2 Space Coordinates and Vectors in Space
  • Coordinates in Space: EX1, EX2
  • Vectors in Space: EX3
  • Definition of Parallel Vectors: EX4~EX6
Sec 11.3 The Dot Product of Two Vectors (選擇性)
  • Definition of Dot Product
  • Theorem 11.4, 11.5
  • Definition of Orthogonal Vectors EX2
Section 13.1 Introduction to Functions of Several Variables
  • Definition of Function of two Variables: EX1
  • The Graph of a Function of two Variables: EX2
  • Definition of Level Curve: EX3


Week 11. 4/29 ~ 5/05

課程進度 :
Section 13.2 Limit and Continuity
  • Definition of Limit of a Function of two Variables
  • Properties of Limits, Uniqueness of Limit: EX2, EX4
  • Definition of Continuity of a Function of two Variables
  • Theorem 13.1, 13.2: EX5(a)
Section 13.3 Partial Derivatives
  • Definition of Partial Derivatives of a Function of two Variables : EX1
  • Notation for the First Partial Derivatives : EX2, EX3
  • Partial Derivatives of a Function of three or more Variables : EX6
  • Higher-Order Partial Derivatives: EX7
  • Theorem 13.3


Week 12. 5/06

課程進度 : 第二次期中考
 
演習課 :
上課練習檔 : 期中考周上課練習檔

 



Week 13. 5/13 ~ 5/19

課程進度 :
Section 13.5 Chain Rules for Functions of Several Variables
  • Theorem 13.6, EX1
  • EX3 (選擇性)
  • Theorem 13.7, EX4
  • EX5 (選擇性)
  • Implicit Partial Differentiation, Theorem 13.8, EX6, EX7
Section 13.6 Directional Derivatives and Gradients
  • Definition of Directional Derivatives, Theorem 13.9, EX1, EX2
  • Definition of Gradient of a Function of two Variables, Theorem 13.10, EX4
  • Theorem 13.11, EX5,
  • EX6 (選擇性)
  • Theorem 13.12 Gradient is Normal to Level Curves (選擇性)


Week 14. 5/20 ~ 5/26

課程進度 :
Section 13.8 Extrema of Functions of Two Variables
  • Theorem 13.15, 13.16 and Definition of Critical Point
  • Theorem 13.16, EX1, EX2
  • The Second Partial Test, Theorem 13.17, EX3, EX4, EX5
Section 13.10 Lagrange Multipliers
  • Definition of Lagrange Multiplier, Theorem 13.19
  • Method of Lagrange Multipliers: EX1, EX3
 
演習課 :
上課練習檔 : 第十四周上課練習檔 課後作業檔


Week 15. 5/27 ~ 6/02

課程進度 :
Section 14.1 Iterated Integrals and Area in the Plane
  • Definition of Iterated Integral: EX1, EX2
  • Area of a Plane Region: EX3 ~ EX6
Section 14.2 Double Integrals and Volume
  • Definition of Double Integral and Volume of a Solid Region
  • Theorem 14.1, Theorem 14.2
  • EX2~EX5 (例題 3、5省略非必要的計算)
  • Definition of the Average Value a Function over Region: EX6
 
演習課 :
上課練習檔 : 第十五周上課練習檔 課後作業檔


Week 16. 6/03 ~ 6/09

課程進度 :
Section 14.3 Change of Variables: Polar Coordinates
  • Double Integral in Polar Coordinates: EX1
  • Theorem 14.3, EX2, EX3, EX4
 
演習課 :
上課練習檔 : 第十六周上課練習檔 課後作業檔


Week 17. 6/10 ~ 6/16

課程進度 :
Section 14.6 Triple Integrals and Applications (選擇性)
  • Definition of Triple Integrals
  • Theorem 14.4, EX1
Section 14.8 Change of Variables (選擇性)
  • Definition of Jacobian, EX1
  • Theorem 14.5: 利用 Sec 14.3 的 Theorem14.3 當例子
 
演習課 :
上課練習檔 : 第十七周上課練習檔


Week 18. 6/17

課程進度 : 期末考

Good Luck!

 
演習課 :
上課練習檔 : 第十八周上課練習檔