Course structure:

Topic Weeks
1 Preliminaries 1 - 2
2 Integration 2 - 5
3 Complex numbers 5 - 8
4 Analysis of real numbers and real-valued functions 8 - 10


The table below provides more-detailed outlines of the lectures.
Note that for future lectures, the outlines might change a bit.
(You may need to press F5 (reload) to get the latest version.)
The numbers in italics indicate sections in Riley's book where you can find more
about the material in any given section or subsection - but do try other books too.

Week Monday 13am W103 Thursday 12am W103 Friday 12am W103
  1 1 Preliminaries
1.1 Algebra
1.1.1 Algebraic manipulation 1.1
1.1.2 Binomial theorem 1.5-1.6		 Diagnostic test 1.1.3 Proof by induction 1.7.2
1.2 Trigonometry 1.2
1.2.1 Pythagoras
1.2.2 Trig functions
  2 1.2.3 Addition formula for cosine
1.2.4 Addition formula for sine;
  examples
1.2.5 Derivatives 2.1.1-2.1.3 		1.2.6 Inverse trig functions

2 Integration 2.2
2.1 Two ideas of integration 2.2.1-2.2.2 		2.2 Fundamental theorem of calculus 2.2.2
2.3 Natural log and exponential
2.3.1 Definition of ln(x)
2.3.2 Exponential as inverse log
  3  Properties of the exponential
2.3.3 Derivative of ex; examples
2.4 Hyperbolic functions 3.7
  Definitions of sinh, cosh etc 		  Properties of sinh and cosh;
  inverse hyperbolic functions
 2.5 Basic idea of integration
2.6 Methods of integration
2.6.1 Useful indefinite integrals 2.2.3
2.6.2 Integration by parts 2.2.8, 2.2.9
 Recurrence relations
  4   Integration by parts (continued)
Recurrence relations: the Gamma function
2.6.3 Integration by substitution 2.2.7
 Examples 		2.6.4 Partial fractions 1.4, 2.2.6
  Clearing fractions and the cover-up rule 		  Partial fractions: more on the cover-up rule;
  examples
  5 2.6.5 Powers of trig functions 2.2.4
 2.7 Line integrals 2.7.1 Arc length
2.7.2 Work done by a force
3 Complex numbers 3
3.1 What are complex numbers? 3.1
  Addition and multiplication 3.2.1, 3.2.3
3.2 Conjugate and modulus 3.2.2, 3.2.4
  6 3.2.1 More properties
3.3 Polar representation of complex numbers 3.3
3.2.3 		  Polar representation of complex numbers (ctd)
  Geometry of addition and multiplication
  De Moivre's theorem 3.4
  examples 3.4.1
  7 3.4 Complex functions
3.4.1 Exponential 3.3
 3.4.2 Trig and hyperbolic functions 3.7
3.4.3 The derivative of eiθ 		3.5 Equations in a complex variable
3.5.1 Transcendental equations
3.5.2 Algebraic equations 3.4.2, 3.4.3
  8   Algebraic equations (ctd)
  Examples of algebraic equations
 3.5.3 The fundamental theorem of algebra 3.1
4 Analysis of real numbers and real-valued
functions
4.1 Various types of real number 		  Various types of real number (ctd)
  Irrationality of sqrt(2) 1.7.2
4.2 Limits of functions of a real variable 4.7
  9   Limits of functions of a real variable (ctd)
   The pinching theorem;
    the case of sin(x)/x 		  The calculus of limits theorem 4.7 (i)-(iii);
    examples
4.3 Continuous functions
  The intermediate value theorem
10 4.4 Differentiable functions 2.1.1
  examples and counterexamples 		4.5 Two important theorems:
  (a) Rolle's Theorem   (b) The Mean Value Theorem
4.6 L'Hopital's rule 4.7 (v);
  examples.
 4.6 L'Hopital's rule (ctd);