

Contents


Week 1: 
Preliminaries; linear functions and line equations, quadratic polynomials and parabolas, cartesian system 
Week 2: 
Preliminaries; circles and ellipse, inequalities, trigonometric functions, exponential and logarithmic functions 
Week 3: 
Limits; limits of polynomials, rational functions, trigonometric functions, exponential and logarithmic functions 
Week 4: 
Limits; limit at infinity, infinite limit, L'hospital's rule 
Week 5: 
Limits; continuity and intermediate value theorem 
Week 6: 
Derivatives; tangent lines, definition of derivative, product, quotient and chain rules 
Week 7: 
Derivatives; derivative of polynomials, rational functions, trigonometric functions, exponential and logarithmic functions 
Week 8: 
Derivatives; applications (increasing/decreasing functions, local  absolute extremum) 
Week 9: 
Derivatives; applications (computing local  absolute extremum), closed interval method 
Week 10: 
Derivatives; applications (curve sketching) 
Week 11: 
Integration; indefinite integral, definite integral and fundamental theorem of calculus 
Week 12: 
Integration; integrals of polynomials, basic trigonometric functions and exponential functions 
Week 13: 
Integration; substitution rule, integration by parts, integrals of basic rational functions 
Week 14: 
Integration; integrals of logarithmic functions, area 
Week 15*: 
 
Week 16*: 
Final 
Textbooks and materials: 

Recommended readings: 
Calculus, R. A. Adams and C. Essex, 7th Edition, Addison Wesley 

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

