Service from Sungkyunkwan University BK21 Math Modeling HRD Division, Copyright http://bkmath.skku.ac.kr/

Week 1

2.1 The Tangent and Velocity Problems

2.2 The Limit of a Function

2.3 Calculating Limits Using the Limit Laws

2.4 Continuity

Week 9

6.1 More About Areas

6.2 Volumes

6.3 Volumes by Cylindrical Shells

Week 2

2.5 Limits Involving Infinity

2.6 Derivatives and Rates of Change

2.7 The Derivative as a Function

2.8 What Dose f' Say about f ?

Week 10

6.4 Arc Length

6.5 Average Value of a Function

Week 3

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

Week 11

7.1 Modeling with Differential Equations

7.2 Direction Fields and Euler's Method

7.3 Separable Equations

Week 4

3.5 Implicit Differentiation

3.6 Inverse Trigonometric Functions and Their Derivatives

3.7 Derivatives of Logarithmic Functions

3.9 Linear Approximations and Differentials

Week 12

7.4 Exponential Growth and Decay

7.5 The Logistic Equation

Week 5

4.1 Related Rates

4.2 Maximum and Minimum Values

4.3 Derivatives and the Shapes of Curves

4.5 Indeterminate Forms and L'Hospital's Rule

Week 13

8.1 Sequences

8.2 Series

8.3 The Integral and Comparison Tests; Estimating Sums

Week 6

4.6 Optimization Problems

4.8 Antiderivatives

5.2 The Definite Integral

5.3 Evaluating Definite Integrals

Week 14

8.4 Other Convergence Tests

8.5 Power Series

8.6 Representations of Functions as Power Series

Week 7

5.4 The Fundamental Theorem of Calculus

5.5 The Subsitution Rule

5.6 Integration by Parts

5.7 Additional Techniques of Integration

Week 15

8.7 Taylor and Maclaurin Series

Week 8

Week 16

+ Final Exam