Ma10192 Mathematics 1
Diary of Lectures 2015/16 (Semester 1)
Numbers in [] refer to on-line lecture notes
(Lec 1) Mon 28 Sept
- Ch.1: Functions and equations
- Polynomials [1.1]
(Lec 2) Wed 30 Sept
- Exponentials and logorithms [1.2]
(Lec 3) Thu 1 Oct
(Lec 4) Mon 5 Oct
- Inverse trig functions [1.3.3]
- Polar coordinates [1.3.4]
(Lec 5) Tue 6 Oct
- Application: harmonic form [1.3.5]
- Approximation: bisection method [1.4]
significant figures/decimal places
(Lec 6) Thu 8 Oct
- Ch.2: Differentiation
- Definition [2.1]
- Standard functions: polynomials, exponentials [2.3]
(Lec 7) Mon 12 Oct
- Standard functions (cont): log, sin, cos.
(Lec 8) Wed 14 Oct
- Rules for differentiation [2.4]:
- linearity, product & quotient rule, chain rule.
(Lec 9) Thu 15 Oct
- Derivatives of inverse functions [2.5]
- Parametric differentiation [2.6]
(Lec 10) Mon 19 Oct
- Implicit differentiation [2.7]
- Maxima & Minima (=extrema) [2.8]
(Lec 11) Wed 21 Oct
- Examples of finding local and global extrema.
- Asymptotes [2.9]
(Lec 12) Thu 22 Oct
- L'Hopital's Rule
- Newton's method [2.10]
(Lec 13) Mon 26 Oct
- Taylor polynomials and series [2.11]
(Lec 14) Wed 28 Oct
(Lec 15) Thu 29 Oct
- Ch.3: Integration
- Definition as antideriative and as area [3.1-3]
- Fundamental Theorem of Calculus [3.4]
(Lec 16) Mon 2 Nov
- Integration by substitution [3.5.1]
- Integration by parts [3.5.2, 3.6]
Wed 4 Nov
(Lec 17) Thu 5 Nov
- Integration of rational functions [3.7]:
- method of partial fractions
(CT) Fri 6 Nov
(Lec 18) Mon 9 Nov
(Lec 19) Wed 11 Nov
- Integrating trig products [3.8]
- Trig substitutions [3.9]
- Hyperbolic sin/cos [3.10]
(Lec 20) Thu 12 Nov
- Hyperbolic substitution
- Area between curves [3.11]
(Lec 21) Mon 16 Nov
- Improper integrals [3.13]
(Lec 22) Wed 18 Nov
- Numerical integration [3.12]:
- Trapezium Rule, Simpson's Rule
- Ch.4: Ordinary Differential Equations
- Separation of variables [4.1]
(Lec 23) Thu 19 Nov
- Linear equations [4.2]:
- homogeneous case
- integrating factors [4.2.1]
(Lec 24) Mon 23 Nov
- variation of parameters [4.2.2]
- method of undetermined coefficients [4.2.3]
(Lec 25) Wed 25 Nov
- method of undetermined coefficients (cont.)
- Partial derivatives [5.1]
- Chain rule for partial derivatives [5.3]
(Lec 26) Thu 26 Nov
- Critical points of functions of two variables [5.1]
(Lec 27) Mon 30 Nov
- Exact differential equations [5.4]
(Lec 28) Wed 2 Dec
- Numerical methods for ODEs [4.3]
(Lec R1) Thu 3 Dec
(Lec R2) Mon 7 Dec
- Question and answer session
Wed 9 & Thu 10 Dec
Back to Ma10192 home page.