

Contents


Week 1: 
Introduction and Preliminaries (Real numbers, Intervals, Absolute value, Cartesian coordinates, Equations of lines, Parabolas, Circles, Ellipses, Functions)

Week 2: 
Introduction and Preliminaries (Polynomials, Trigonometry and the Trigonometric Functions), Introduction to the concept of limit 
Week 3: 
Limits and Continuity 
Week 4: 
The Derivative, Differentiation Rules 
Week 5: 
Chain Rule, Derivatives of Trigonometric Functions, HigherOrder Derivatives 
Week 6: 
The MeanValue 'Theorem, Implicit Differentiation, Antiderivatives and InitialValue Problems Midterm I 
Week 7: 
lnverse Functions, Exponential and Logarithmic Functions 
Week 8: 
The Inverse Trigonometric Functions, Related Rates, Indeterminate Forms 
Week 9: 
Extreme Values, Concavity and Inflections 
Week 10: 
Sketching the Graph of a Function, ExtremeValue Problems 
Week 11: 
Integration, Riemann Sum, Definite Integral, The Fundamental Theorem of Calculus, The Method of Substitution 
Week 12: 
Techniques of Integration: Integration by Parts, Integrals of Rational Functions, Inverse Substitutions Midterm II 
Week 13: 
Areas of Plane Regions, Improper Integrals 
Week 14: 
Improper Integrals, Applications of Integration 
Week 15*: 
 
Week 16*: 
Final exam 
Textbooks and materials: 
: Calculus, R. A. Adams and C. Essex, 7th Edition, Addison Wesley 
Recommended readings: 
Howard Anton Calculus: A new Horizon, 6th Edition, Wiley 1999. Calculus and Analytic Geometry, Thomas and Finney, 6th Edition 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

