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微積分統一教學網

模01-04班課程大綱

  1131 M01-04      
Calculus 1 Week 1 2.1 The Tangent and Velocity Problems Worksheet 1 (Inverse Trigonometric Functions)
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
Week 2 2.4 The Precise Definition of a Limit (WS) Worksheet 2 (The Precise Definition of a Limit)
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
Week 3 2.8 The Derivative as a Function  
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
Week 4 3.4 The Chain Rule 9/23 (Mon) 17:30-18:20 Quiz 1 (2.1 - 3.2、WS1、WS2)
3.5 Implicit Differentiation
Week 5 3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions Worksheet 3 (Related Rates)
3.10 Linear Approximations and Differentials
4.1 Maximum and Minimum Values
Week 6
10/11(Fri) Calculus 1 Drop Deadline
4.2 The Mean Value Theorem  
4.3 What Derivatives Tell Us about the Shape of a Graph
4.4 Indeterminate Forms and l'Hospital's Rule
Week 7 4.5 Summary of Curve Sketching 10/14(Mon) 17:30-18:20 Quiiz 2 (3.3 - 4.2、WS3)
4.7 Optimization Problems
4.9 Antiderivatives (*)
Week 8 Buffer  
10/26(Sat)  Exam
Calculus 2 Week 9
11/1(Fri) Calculus 2 Withdrawal Deadline
5.1 The Area and Distance Problems  
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
Week 10 5.5 The Substitution Rule Worksheet 1 (Volumes)
6.1 Areas Between Curves
6.2 Volume (WS)
6.3 Volumes by Cylindrical Shells (WS)
Week 11 7.1 Integration by Parts Worksheet 2 (Other Applications of Integrations)
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
Week 12
11/22(Fri) Calculus 2 Drop Deadline
7.4 Integration of Rational Functions by Partial Fractions 11/18(Mon) 17:30-18:20 Quiz 1 (5.1 - 7.1、WS1)
7.5 Strategy for Integration
7.8 Improper Integrals
  Laplace Transforms of Special Functions (*)
Week 13 9.1 Modeling with Differential Equations  
9.3 Separable Equations
9.5  Linear Equations
Week 14 17.1 Second-Order Linear Equations  12/2(Mon) 17:30-18:20 Quiz 2 (7.2 - 9.1、WS2)
17.2 Nonhomogeneous Linear Equations
  Solving Differential Equations by Laplace Transform (WS)
Week 15 Buffer Worksheet 3 (Solving Differential Equztions by Laplace Transform)(*)
12/14(Sat)  Exam
Week 16      
  1132 M01-04      
Calculus 3 Week 1 12.6 Cylinders and Quadric Surfaces Worksheet 1 (Space Curves and Their Tangents)
14.1 Functions of Several Variables
14.2 Limits and Continuity
Week 2 14.3 Partial Derivatives  
14.4 Tangent Planes and Linear Approximations
Week 3 14.5 The Chain Rule Worksheet 2 (Polar Coordinates)
14.6 Directional Derivatives and the Gradient Vector
14.7 Maximum and Minimum Values
Week 4 14.8 Lagrange Multipliers 3/10 (Mon) 17:30-18:20 Quiz 1 (12.6、14.1 - 14.5、WS1)
15.1 Double Integrals over Rectangles
Week 5 15.2 Double Integrals over General Regions Worksheet 3 (Applications of Double Integrals)
15.3 Double Integrals in Polar Coordinates
Week 6
3/28(Fri) Calculus 3 Drop Deadline
15.6 Triple Integrals 3/24 (Mon) 17:30-18:20 Quiz 2 (14.6 - 15.3、WS2)
15.7 Triple Integrals in Cylindrical Coordinates
15.8 Triple Integrals in Spherical Coordinates
Week 7 15.9 Change of Variables in Multiple Integrals  
Week 8 Buffer  
4/12(Sat)  Exam
Calculus 4 Week 9
4/18(Fri) Calculus 4 Withdrawal Deadline
16.1 Vector Fields Worksheet 1 (Parametric Surfaces)
16.2 Line Integrals
16.3 The Fundamental Theorem for Line Integrals (WS)
Week 10 16.4 Green's Theorem Worksheet 2 (Conservative Vector Fields)
16.5 Curl and Divergence
16.6 Parametric Surfaces and Their Areas (WS)
Week 11 16.7 Surface Integrals 4/28 (Mon) 17:30-18:20 Quiz 1 (16.1 - 16.4)
16.8 Stokes' Theorem
16.9 The Divergence Theorem
Week 12
5/9(Fri) Calculus 4 Drop Deadline
11.1 Sequences (*)  
11.2 Series
11.3 The Integral Test and Estimates of Sums (WS)
Week 13 11.4 The Comparison Tests ( Skip the Limit Comparison Test) Worksheet 3 (Tests for Convergence of Series)
11.5 Alternating Series and Absolute Convergence (WS)
11.6 The Ratio and Root Tests
Week 14 11.7 Strategy for Testing Series (*) 5/19 (Mon) 17:30-18:20 Quiz 2 (16.5 - 16.9、11.2 - 11.4、WS1)
11.8 Power Series
11.9 Representations of Functions as Power Series
Week 15 11.10 Taylor and Maclaurin Series  
11.11 Applications of Taylor Polynomials (WS)  
Week 16 Buffer  
6/7(Sat)  Exam