跳到主要內容區塊

微積分統一教學網

模14-17班課程大綱

  1131 M14-17  
Calculus 1 Week 1 1.4 Exponential Functions (Brief)  
1.5 Inverse Functions and Logarithms
2.1 The Tangent Problem
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
Week 2 2.5 Continuity 9/12(Thu) 17:50-18:20 Quiz 1 (Coverage : 1.4-2.3)
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function
3.1 Derivatives of Polynomials and Exponential Functions
Week 3 3.2 The Product and Quotient Rules 9/19(Thu) Worksheet 1 (Derivatives in Economics)
3.3 Derivatives of Trigonometric Functions
3.10 Linear Approximations and Differentials
Week 4 3.4 The Chain Rule 9/26(Thu) 17:30-18:20 Exam 1 (Coverage : 1.4-3.3)
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions
Week 5 3.7 Rates of Change in Natural and Social Science (Biology and Economics)  
4.2 The Mean Value Theorem
4.4 Indeterminate Forms and L’Hospital Rule
Week 6
10/11(Fri) Calculus 1 Drop Deadline
4.1 Maximum and Minimum Values 10/8(Tue) Quiz 2 (Coverage 3.4-3.6、3.10、WS1)
Class 14-16:8:30-9:00 ; Class 17:9:10-9:40
4.3 What Derivatives Tell Us about the Shape of a Graph
Week 7 4.5 Summary of Curve Sketching 10/17(Thu) Worksheet 2 (Higher order approximations)
4.7 Optimization Problems
Week 8 4.9 Antiderivatives(*) 10/24(Thu) 17:30-18:20 Exam 2 (Coverage : Week 4-7, WS2)
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 11/7(Thu) 17:50-18:20 Quiz 1 (Coverage : 5.1-5.4)
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
Week 11 7.1 Integration by Parts 11/14(Thu)  Worksheet 1 (Medical Imaging)
7.4 Integration of Rational Functions by Partial Fractions
7.8 Improper Integrals
Week 12
11/22(Fri) Calculus 2 Drop Deadline
6.1 Areas Between Curves 11/21(Thu) 17:30-18:20 Exam 1 (Coverage : Week 9-11)
6.5 Average Value of a Function 
8.5 Probability
Week 13 9.1 Modeling with Differential Equations  
9.3 Separable Equations
9.4 Models for Population Growths
9.5 Linear Equations
Week 14 11.8 Power series (No convergence issues) 12/5(Thu) 17:50-18:20 Quiz 2 (Coverage : Week 12-13)
11.9 Representations of Functions as Power Series
Week 15 11.10 Taylor and Maclaurin Series 12/12(Thu) Worksheet 2 (Introduction to Bifurcation)
Week 16 12/19(Thu) 17:30-18:20 Exam 2 (Coverage : Week 12-15)
  1132 M14-17  
Calculus 3 Week 1 10.1 Curves Defined by Parametric Equations  
10.2 Calculus with Parametric Curves (No lengths, volumes and surface areas)
12.6 Cylinders and Quadric Surfaces
14.1 Functions of Several Variables
Week 2 14.3 Partial Derivatives 2/27(Thu) 17:50-18:20 Quiz 1 (Coverage : 10.1-10.2, 12.6, 14.1) 
14.4 Tangent Planes and Linear Approximations
Week 3 14.5 The Chain Rules 3/6(Thu) Worksheet 1 (Partial Derivatives in Economics)
14.6 Directional Derivatives and the Gradient Vector
Week 4 14.7 Maximum and Minimum Values 3/13(Thu) 17:30-18:20 Exam 1 (Coverage : Week 1-3)
14.8 Lagrange Multipliers
Week 5 15.1 Double Integrals over Rectangles 3/20(Thu) Worksheet 2 (The Least Square Method and Shadow Price)
15.2 Double Integrals over General Regions
10.3 Polar Coordinates 
Week 6
3/28(Fri) Calculus 3 Drop Deadline
15.3 Double Integrals in Polar Coordinates 3/27(Thu) 17:50-18:20 Quiz 2 (Coverage : 14.7-14.8)
15.9 Change of Variables in Multiple Integrals
Week 7 15.4 Applications of Double Integrals (Probability) (*)  
15.6 Triple Integrals (*)
Week 8 4/10(Thu) 17:30-18:20 Exam 2 (Coverage : Week 4-6)