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微積分統一教學網

模03-12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
第二週 2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
第三週 2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function
第四週 3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
第五週 3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions
第六週
11/2(二)微積分1停修截止
3.9 Related Rates
3.10 Linear Approximations and Differentials
4.1 Maximum and Minimum Values
第七週 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
第八週 4.5 Summary of Curve Sketching
4.7 Optimization Problems
4.9 Antiderivatives
期考 11/13(六)  考試以英文命題

微積分

2

第九週
11/23(二) 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
第十週 5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule
第十一週
12/7(二) 微積分2停修截止
6.1 Areas Between Curves
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.5 Average Value of a Function
第十二週 7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
第十三週 7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.8 Improper Integrals
第十四週 8.1 Arc Length
8.2 Area of a Surface of Revolution (*)
9.1 Modeling with Differential Equations
9.3 Separable Equations
第十五週 9.5 Linear Equations
10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves
第十六週 10.3 Polar Coordinates
10.4 Calculus in Polar Coordinates
期考1/9(日) 考試以英文命題

微積分

3

第一週 12.6 Cylinders and Quadric Surfaces
14.1 Functions of Several Variables
14.2 Limits and Continuity
第二週 14.3 Partial Derivatives
14.4 Tangent Planes and Linear Approximations
第三週 14.5 The Chain Rule
14.6 Directional Derivatives and the Gradient Vector
14.7 Maximum and Minimum Values
第四週 14.8 Lagrange Multipliers
15.1 Double Integrals over Rectangles
15.2 Double Integrals over General Regions
第五週 15.3 Double Integrals in Polar Coordinates
15.4 Applications of Double Integrals   (教到 Moments and Center of Mass)
第六週
3/25(五)微積分3停修截止
15.5 Surface Area
15.6 Triple Integrals
15.7 Triple Integrals in Cylindrical Coordinates
第七週 15.8 Triple Integrals in Spherical Coordinates
15.9 Change of Variables in Multiple Integrals
第八週 緩衝時間
期考 4/9(六) 考試以英文命題

微積分

4

第九週
4/15(五) 微積分4退選截止
16.1 Vector Fields
16.2 Line Integrals
16.3 The Fundamental Theorem for Line Integrals
第十週 16.4 Green's Theorem
16.5 Curl and Divergence
16.6 Parametric Surfaces and Their Areas
第十一週
4/29(五) 微積分4停修截止
16.7 Surface Integrals
16.8 Stokes' Theorem
16.9 The Divergence Theorem
第十二週 16.10 Summary
11.1 Sequences
11.2 Series
第十三週 11.3 The Integral Test and Estimates of Sums
11.4 The Comparison Tests
11.5 Alternating Series and Absolute Convergence
第十四週 11.6 The Ratio and Root Tests
11.7 Strategy for Testing Series
11.8 Power Series
第十五週 11.9 Representations of Functions as Power Series
11.10 Taylor and Maclaurin Series
11.11 Applications of Taylor Polynomials
第十六週 緩衝時間
期考 6/4(六) 考試以英文命題