﻿ 微積分統一教學網-模13-16班課程大綱

# 微積分統一教學網

## 模13-16班課程大綱

### 手機版選單

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 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(四) 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(二)微積分1停修截止 4.4 Indeterminate Forms and l’Hospital‘s Rule 4.5 Summary of Curve Sketching 4.7 Optimization Problems 10/28(四) 17:30-18:20  Quiz 2 (範圍：3.1-3.6、3.8、3.10) 第七週 4.9 Antiderivatives Applications: Profit Maximization and Cost Minimization Applications: Demand and Elasticity 第八週 11/11(四) 17:30-18:20  Quiz 3 (範圍：4.1-4.5、4.7) 期考 11/13(六)   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 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(二) 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(四) 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(四) 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(四) 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(日)  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(四) 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(四) 17:30-18:20  Quiz 2 第六週 3/25(五)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(四) 17:30-18:20  Quiz 3 第八週 緩衝時間 期考 4/9(六) 英文命題

 微積分4 -- 在經濟商管的應用 第九週 4/15(五) 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(五) 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(六)  英文命題