Textbook: Calculus 8th Edition Metric Version by James Stewart References:
1. Calculus One and Several Variables 10th Edition by Satunino L. Salas 2. The Elements of real Analysis 2nd Edition by Robert G. Bartle
Chapter 1 Functions and Limits
第一週 9/10, 9/12
1.4 The Tangent and Velocity Problems 1.5 The Limit of a Function
1.7 The Precise Definition of a Limit
1.6 Calculating Limits Using the Limit Laws
第二週 9/17, 9/20
1.8 Continuity
3.4 Limits at Infinity; Horizontal Asymptotes
Chapter 2 Derivatives
2.1 Derivatives and Rates of Change 2.2 The Derivative as a Function
第三週 9/24, 9/26
9/24 中秋節放假
2.3 Differentiation Formulas
2.4 Derivatives of Trigonometric Functions 2.5 The Chain Rule
6.1 Inverse Functions 2.6 Implicit Differentiation 2.8 Related Rates
第五週 10/8, 10/10
10/10 放假
2.9 Linear Approximations and Differentials
Chapter 3 Applications of Differentiation
3.1 Maximum and Minimum Values
第六週 10/15, 10/17
3.2 The Mean Value Theorem
6.8 Indeterminate Forms and l’Hopital’s Rule 3.3 How Derivatives Affect the Shape of a Graph 3.5 Summary of Curve Sketching
第七週 10/22, 10/24
3.7 Optimization Problems 3.9 Antiderivatives
Chapter 4 Integrals
4.1 Areas and Distances 4.2 The Definite Integral
第八週 10/29, 10/31
4.3 The Fundamental Theorem of Calculus Review
Midterm Exam 10/31 (Wednesday) 18:00-20:30, 考試範圍 Sec 1.4-3.7
第九週 11/5, 11/7
4.4 Indefinite Integrals and the Net Change Theorem 4.5 The Substitution Rule
Chapter 5 Applications of
5.1 Areas Between Curves 5.2 Volume
Integration
第十週 11/12, 11/14
5.3 Volumes by Cylindrical Shells 5.5 Average Value of a Function
Chapter 6 Inverse Functions
6.2* The Natural Logarithmic Function 6.3* The Natural Exponential Function
第十一週 11/19, 11/21
6.4* General Logarithmic and Exponential Functions 6.5 Exponential Growth and Decay
6.6 Inverse Trigonometric Functions 6.7 Hyperbolic Functions
Chapter 7 Techniques of Integration
第十二週 11/26, 11/28
7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
第十三週 12/3, 12/5
7.5 Strategy for Integration 7.8 Improper Integrals L1 Laplace Transform
Laplace Transform Chapter 8
Further
Applications of
Integration 第十四週
12/10, 12/12
8.1 Arc Length
Chapter 10 Parametric Equations and Polar
Coordinates
10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves
10.3 Polar Coordinates
第十五週 12/17, 12/19
10.4 Areas and Lengths in Polar Coordinates
Chapter 9 Differential Equations
9.1 Modeling with Differential Equations 9.3 Separable Equations
9.4 Models for Population Growth
第十六週 12/24, 12/26
9.5 Linear Equations Chapter 17
Second-Order Differential Equations
17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations
第十七週 12/31, 1/2
12/31 放假 Review 第十八週
1/7, 1/9
Final Exam 1/7 (Monday) 8:30-11:00, 考試範圍 Sec 3.9-17.2
