|
Week |
lecture/tutorial no. |
Topics |
Remark |
|
1
(10/7/06-14/7/06) |
- |
Briefing |
¡¡ |
|
L1 |
Definition of functions; the graphs of a real
function; transformation of functions |
¡¡ |
|
L2 |
Sums, differences, products and quotients;
composition of functions; monotone functions; odd and even functions;
injective functions; surjective functions; bijective functions |
¡¡ |
|
L3 |
Inverse functions; polynomials; rational functions |
¡¡ |
|
2
(17/7/06-21/7/06) |
L4 |
The absolute value function; real-valued n-th root
functions; trigonometric functions and their inverses I |
¡¡ |
|
L5 |
Trigonometric functions and their inverses II |
¡¡ |
|
T1* |
Tutorial 1 |
¡¡ |
|
L6 |
Exponential and logarithmic functions; hyperbolic
functions and their inverses I |
¡¡ |
|
3
(24/7/06-28/7/06) |
L7 |
Hyperbolic functions and their inverses II |
¡¡ |
|
L8 |
Limits of real functions; one-sided limits |
¡¡ |
|
T2* |
Tutorial 2 |
¡¡ |
|
L9 |
Properties of limits; limits at infinity and
infinities limits I |
¡¡ |
|
4
(31/7/06-4/8/06) |
L10 |
Limits at infinity and infinities limits II; the
precise definition of a limit I |
¡¡ |
|
L11 |
The precise definition of a limit II; continuity I |
¡¡ |
|
T3* |
Tutorial 3 |
¡¡ |
|
L12 |
Continuity II |
¡¡ |
|
5
(7/8/06-11/8/06) |
L13 |
Derivatives |
¡¡ |
|
L14 |
Differentiation formulas |
¡¡ |
|
T4* |
Tutorial 4 |
¡¡ |
|
L15 |
The chain rule; higher order derivatives; implicit
differentiation |
¡¡ |
|
6
(14/8/06-18/8/06) |
L16 |
The mean value theorem |
¡¡ |
|
L17 |
L¡¯Hopotal Rule; differentialbility of inverses;
some applications of derivatives I |
¡¡ |
|
T5* |
Tutorial 5 |
¡¡ |
|
L18 |
Some applications of derivatives II |
¡¡ |
|
7
(21/8/06-25/8/06) |
L19 |
Some applications of derivatives III; Taylor¡¯s
theorem I |
¡¡ |
|
L20 |
Taylor¡¯s theorem II |
¡¡ |
|
T6* |
Tutorial 6 |
¡¡ |
|
L21 |
Riemann integral; basic properties of the definite
integral |
¡¡ |
|
8
(28/8/06-2/9/06)
¡¡ |
semester break |
¡¡
¡¡
¡¡
¡¡ |
|
9
(4/9/06-8/9/06)
¡¡ |
L22 |
Areas of bounded regions; fundamental theorem of
calculus I |
¡¡ |
|
L23 |
Fundamental theorem of calculus II;
antidifferentiation and indefinite integral |
|
|
TEST I |
TEST I (7 Sept 06,
Thursday) |
¡¡ |
|
L24 |
Techniques of integration I |
¡¡ |
|
10
(11/09/06-15/09/06)
¡¡ |
L25 |
Techniques of integration II |
¡¡ |
|
L26 |
Improper integrals; the logarithms and the
exponential functions |
¡¡ |
|
T7* |
Tutorial 7 |
¡¡ |
|
L27 |
Another look at the integral; applications of the
definite integral I |
¡¡ |
|
11
(18/9/06-22/9/06)
¡¡ |
L28 |
Applications of the definite integral II |
¡¡ |
|
L29 |
Infinite series. Series with positive terms. |
¡¡ |
|
TEST |
TEST II (21 Sept 06,
Thursday, Venue: DPA) |
¡¡ |
|
L30 |
Integral test. Comparison tests |
¡¡ |
|
12
(25/9/06-29/9/06) |
L31 |
Definition; Matrix algebra; Types of matrces. |
¡¡ |
|
L32 |
System of Linear Equations |
¡¡ |
|
T8* |
Tutorial 8 |
¡¡ |
|
L30 |
Inverse of a Matrix; Determinants |
¡¡ |
|
13
(2/10/06-6/10/06)
¡¡ |
L31 |
Cramer's rule; |
|
|
L32 |
Revision and exercise |
|
|
T9* |
Tutorial 9 |
|
|
L33 |
Revision and exercise |
|
|
14
(9/10/06-13/10/06)
¡¡ |
L34 |
Revision and exercise |
|
|
L35 |
Revision and exercise |
|
|
T10* |
Tutorial 10 |
|
|
L36 |
Revision and exercise |
|
|
15
(16/10/06-20/10/06) |
L37 |
Revision and exercise |
|
|
L38 |
Revision and exercise |
|
|
T11* |
Tutorial 11 |
|
|
T39 |
Revision and exercise |
|