1. Rate of change
2. Functions and graphs
3. Inverse functions
4. Exponential and logarithmic functions
5. Evaluating limits
6. Continuity and one sided limits
7. Infinite limits

Differentiation

1. Derivatives and tangent line
2. Basic differentiation rules
3. Product and quotient rules
4. Chain rule
5. Implicit differentiation
6. Derivatives of inverse function

Application of differentiation

1. Extrema on an interval
2. Rolle' theorem and mean value theorem
3. Increasing and decreasing functions and the first derivative test
4. Concavity and second derivative test
5. Limits at infinity
6. Optimization problem
7. Differentials

Integration

1. Antiderivatives and indefinite integration
2. Riemann sums and definite integrals
3. Fundamental theorem of calculus
4. Substitution
5. Indefinite form and L'Hopital rule
6. The natural logarithmic function

Application of integration

1. Area of a region between two curves
2. volume by disk method
3. volume by shell method
4. surfaces of revolution

Integration Techniques and improper integrals

1. Integration by parts
2. Trigonometric integrals
3. Trigonometric substitution
4. Partial fractions
5. Numerical integration
6. Improper integrals

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Course Details：

1. Teaching Materials：Self DevelopedProvided by Textbook Authors