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微積分統一教學網

模13-16班課程大綱

微積分1

第一週

2.1

The Tangent and Velocity Problems

2.2

The Limit of a Function

2.3

Calculating Limits Using the Limit Laws

2.4

The Precise Definition of a Limit ()

第二週

2.5

Continuity

2.6

Limits at Infinity; Horizontal Asymptotes

2.7

Derivatives and Rates of Change

2.8

The Derivative as a Function

第三週

3.1

Derivatives of Polynomials and Exponential Functions

3.2

The Product and Quotient Rules

3.3

Derivatives of Trigonometric Functions

3.4

The Chain Rule

第四週

3.5

Implicit Differentiation

3.6

Derivatives of Logarithmic and Inverse Trigonometric Functions

3.8

Exponential Growth and Decay (Compounded Interest, and Present Value)

3.10

Linear Approximations and Differentials (不教 differentials)

10/14() 17:30-18:20  Quiz 1 (範圍:2.1-2.8)

第五週

4.1

Maximum and Minimum Values

4.2

The Mean Value Theorem

4.3

What Derivatives Tell Us about the Shape of a Graph

第六週
11/2()微積分1停修截止

4.4

Indeterminate Forms and lHospitals Rule

4.5

Summary of Curve Sketching

4.7

Optimization Problems

10/28() 17:30-18:20  Quiz 2 (範圍:3.1-3.63.83.10)

第七週

4.9

Antiderivatives

 

Applications: Profit Maximization and Cost Minimization

 

Applications: Demand and Elasticity

第八週

11/11() 17:30-18:20  Quiz 3 (範圍:4.1-4.54.7)

期考 11/13()   英文命題

 

微積分2

第九週
11/23() 微積分2退選截止

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

第十週

5.5

The Substitution Rule

6.1

Areas Between Curves

6.2

Volume

6.3

Volumes by Cylindrical Shells

第十一週
12/7() 微積分2停修截止

6.5

Average Value of a Function ()

7.1

Integration by Parts

7.2

Trigonometric Integrals

7.3

Trigonometric Substitution

12/2() 17:30-18:20  Quiz 1 (範圍:5.1-5.5)

第十二週

7.4

Integration of Rational Functions by Partial Fractions

7.5

Strategy for Integration

7.8

Improper Integrals

第十三週

8.4

Applications to Economics (Consumer and Producer Surplus)

8.5

Probability

9.1

Modeling with Differential Equations

12/16() 17:30-18:20  Quiz 2 (範圍:6.1-6.3、7.1-7.3)

第十四週

9.3

Separable Equations

9.4

Models for Population Growth

9.5

Linear Equations

第十五週

10.1

Curves Defined by Parametric Equations

10.2

Calculus with Parametric Curves

10.3

Polar Coordinates

12/30() 17:30-18:20  Quiz 3 (範圍:7.4-7.5、7.8、8.4-8.5、9.1、9.3)

第十六週

緩衝時間

期考1/9(英文命題

 

微積分3

第一週

12.6

Cylinders and Quadric Surfaces

14.1

Functions of Several Variables

14.2

Limit and Continuity ()

14.3

Partial Derivatives

第二週

14.4

Tangent Planes and Linear Approximation

14.5

The Chain Rules

14.6

Directional Derivatives and the Gradient Vector

第三週

14.7

Maximum and Minimum Values

14.8

Lagrange Multipliers

3/3() 17:30-18:20  Quiz 1 

第四週

15.1

Double Integrals over Rectangles

15.2

Double integrals over General Regions

15.3

Double Integrals in Polar Coordinates

第五週

15.6

Triple Integrals

15.9

Change of Variables in Multiple Integrals

3/17() 17:30-18:20  Quiz 2 

第六週
3/25()微積分3停修截止

15.4

Probability

第七週

11.9

Representation of Functions as Power Series

11.1

Taylor and Maclaurin Series

3/31() 17:30-18:20  Quiz 3 

第八週

緩衝時間

期考 4/9() 英文命題

 

 

微積分4-在經濟商管的應用

參考用書:Carl P. Simon and Lawrence Blume, Mathematics for Economics

微積分4 -- 在經濟商管的應用

第九週
4/15() 微積分4退選截止

 

Vector Spaces (Linear Independence, Basis, Dimension)

 

Matrix (Row/Column Space, Rank, Determinant)

第十週

 

Eigenvalues and Eigenvectors

 

Symmetric Matrices

第十一週
4/29() 微積分4停修截止

 

Definiteness of Quadratic Forms

 

Application: Markov Processes

第十二週

18.1

Constrained Optimization: Examples

18.2

Constrained Optimization: Equality Constraints

18.3

Constrained Optimization: Inequality Constraints

第十三週

18.4

Constrained Optimization: Mixed Constraints

18.5

Constrained Minimization Problems

18.6

Kuhn-Tucker Formulation

第十四週

19.1

The Meaning of the Multiplier

19.2

Envelope Theorems

第十五週

19.3

Constrained Optimization: Second Order Conditions

19.5

Constraint Qualifications (*)

第十六週

19.6

Proofs of First order conditions (*)

期考  6/4(英文命題