General
- Information about evaluation is here.
From the "Courses of Study" booklet.
Online access to Apostol's book.
Online access to Goldberg's book.
Online access to Ross' book.
From the "Courses of Study" booklet.
Online access to Apostol's book.
Online access to Goldberg's book.
Online access to Ross' book.
Assignments and Notes regarding the Number System
A good resource to revise all the basics about numbers.
Assignment on inequalities
Lecture Notes
Lecture notes on polynomial growth, induction, binomial coefficients and exponential growth
Lecture Notes on Sequences and Series - part 1
Lecture notes on properties of least upper bound
Slightly more general than required for this course.
Lecture notes on limits of sequences of real numbers
Assignments and notes introducing functions
Introduction to continuous functions.
For extra reading.
Continuous functions as uniform limits
Study of Convergence of Power series with some examples
A Wikipedia page that gives many examples of series (including power series). For extra reading.
Continuity of the inverse of a monotone continuous function.
A notion of distance between continuous functions
Computing areas of certain regions in the plane.
Proof of the well-known formulas for integrals of polynomials
Brief solutions.
Axiomatic formulation of integration
Mean Value Theorem, Indefinite Integral and Differentiation
Little-o notation and the properties of differentiation.
Multiple derivatives and Taylor series. Pathological examples.
Important special functions and their properties.
Exponential, Sine, Cosine and the Complex numbers.
The Natural Logarithm.
Solutions and some remarks.