SYLLABUS:

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