Overview (MA2730,2812,2815) lecture 1 Overview (MA2730,2812,2815) lecture 1 Contents of the teaching and assessment blocks MA2730: Analysis I Lecture slides for MA2730 Analysis I Analysis — taming infinity Maclaurin and Taylor series. Simon Shaw Sequences. people.brunel.ac.uk/~icsrsss Improper Integrals.
[email protected] Series. College of Engineering, Design and Physical Sciences Convergence. bicom & Materials and Manufacturing Research Institute Brunel University LATEX 2ε assignment in December. Question(s) in January class test. Question(s) in end of year exam. September 21, 2015 Web Page: http://people.brunel.ac.uk/~icsrsss/teaching/ma2730 Shaw bicom, mathematics, CEDPS, IMM, CI, Brunel Shaw bicom, mathematics, CEDPS, IMM, CI, Brunel MA2730, Analysis I, 2015-16 MA2730, Analysis I, 2015-16 Overview (MA2730,2812,2815) lecture 1 Overview (MA2730,2812,2815) lecture 1 Lecture 1 Lecture 1 MA2730: topics for Lecture 1 Functions — Level 1 revision What is a function? How do we define a function? What ingredients do we need? A function is a triple: Lecture 1 A rule, for example f(x)= x2 + sin(√x). A domain, for example. Revision of functions and factorials (from Level 1) D = [0, ) R. ∞ ⊆ Maclaurin polynomials — some intuition A range, for example. Taylor polynomials R = [ 1, ) R − ∞ ⊆ Definitions and formality We then write f : D R with rule f(x)= x2 + sin(√x). → Examples and exercises Often the range is replaced with the co-domain. The co-domain is The introductory material covered in this lecture can be found in usually R. Usually the domain is taken to be the largest subset of The Handbook in Chapter 1 and Section 1.1.