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微積分統一教學網

模05-09班課程大綱

  1131 M05-09      
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 2.5 Continuity Worksheet 2 (The Precise Definition of a Limit)
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  
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions
3.10 Linear Approximations and Differentials
Week 5 4.1 Maximum and Minimum Values Worksheet 3 (Related Rates)
4.2 The Mean Value Theorem
4.3 What Derivatives Tell Us about the Shape of a Graph
Week 6
10/11(Fri) Calculus 1 Drop Deadline
4.4 Indeterminate Forms and l'Hospital's Rule  
4.5 Summary of Curve Sketching
Week 7 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
7.1 Integration by Parts
Week 11 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 Worksheet 2 (Other Applications)
7.5 Strategy for Integration
Week 13 7.8 Improper Integrals  
8.5 Probability
Week 14 9.1 Modeling with Differential Equations Worksheet 3 (More on Probability)
9.3 Separable Equations
9.5  Linear Equations
Week 15 Buffer  
12/14(Sat)  Exam
Week 16      
  1132 M05-09      
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
14.3 Partial Derivatives
Week 2 14.4 Tangent Planes and Linear Approximations  
14.5 The Chain Rule
Week 3 14.6 Directional Derivatives and the Gradient Vector Worksheet 2 (Polar Coordinates)
14.7 Maximum and Minimum Values
Week 4 14.8 Lagrange Multipliers  
15.1 Double Integrals over Rectangles
Week 5 15.2 Double Integrals over General Regions  
15.3 Double Integrals in Polar Coordinates
Week 6
3/28(Fri) Calculus 3 Drop Deadline
15.6 Triple Integrals Worksheet 3 (Applications of Double Integrals)
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
Week 10 16.4 Green's Theorem  
16.5 Curl and Divergence
Week 11 16.6 Parametric Surfaces and Their Areas Worksheet 2 (More on Conservative Fields)
16.7 Surface Integrals
Week 12
5/9(Fri) Calculus 4 Drop Deadline
16.8 Stokes' Theorem  
16.9 The Divergence Theorem
11.1 Sequences (*)
Week 13 11.2 Series Worksheet 3 (Convergence Tests)
11.3 The Integral Test and Estimates of Sums
11.4 The Comparison Tests (Skip the Limit Comparison Test)
11.5 Alternating Series and Absolute Convergence
Week 14 11.6 The Ratio and Root Tests  
11.8 Power Series
11.9 Representations of Functions as Power Series
Week 15 11.10 Taylor and Maclaurin Series  
Bonus Introduction to Multivariable Taylor Series (*)
Week 16 Buffer  
6/7(Sat)  Exam