### SYLLABUS:

Approximately we will cover one item per lecture. It is your responsibility to keep track of the pace of the course.
**Week 1:**

**Chapter I. Numbers and Functions**
- Numbers and Functions
- Implicit functions, Inverse functions

**Week 2:**

**Chapter II. Derivatives (1)**
- The tangent to a curve
- Instantaneous velocity
- Rates of change

**Chapter III. Limits and continuous functions**
- The concept of limits

**Week 3:**
- Properties and computations of limits (section 6, section 7); When limits fail to exist (section 8)
- One-sided limits (left and right limits), limits involving infinity (section 5, section 9)
- The Sandwich Theorem and applications (section 11)

**Week 4:**
- Continuity
- Two limits in trigonometry
- Asymptotes

**Week 5:**

**Chapter IV. Derivatives (2)**
- The definition of derivatives
- Differentiation rules: product rule and quotient rule, chain rule

**Week 6:**
- Implicit differentiation
- Derivatives of inverse functions
- Related rates

**Week 7:**

**Chapter V. Max/min problems, graph sketching**
- The Intermediate Value Theorem
- Increasing/decreasing functions
- Maxima/minina

**Week 8:**
- General strategy for graph sketching
- Convexity, concavity
- Optimization problems
- Parametrized curves

**Week 9:**
- L'Hospital's rule

**Chapter VI. Exponentials, logarithms**
- Exponential functions and logarithms
- Derivatives of exponential functions and logarithms

**Week 10**
- Limits involving exponentials and logarithms
- Exponential growth and decay

**Chapter VII. The integral**
- Area under a graph

**Week 11**
- The definition of an integral
- The Fundamental Theorem of Calculus

**Week 12**
- Indefinite Integrals, properties of integrals
- Substitution Method
- Thanksgiving break

**Week 13:**

**Chapter VIII. Applications of Definite Integrals**
- Area between graphs
- Computing volumes by slicing

**Week 14:**
- Volumes of solids of revolution I
- Volumes of solids of revolution II
- Arc length(the length of a curve)

**Week 15**
- Work
- Review for the final