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Analysis grew out of calculus, which leads to the study of limits of functions, sequences and series. It is one of the fundamental topics underlying much of mathematics including differential equations, dynamical systems, differential geometry, topology and Fourier analysis. This unit introduces the field of mathematical analysis both with a careful theoretical framework as well as selected applications. It shows the utility of abstract concepts and teaches an understanding and construction of proofs in mathematics. This unit will be useful to students of mathematics, science and engineering and in particular to future school mathematics teachers, because we shall explain why common practices in the use of calculus are correct, and understanding this is important for correct applications and explanations. The unit starts with the foundations of calculus and the real numbers system. It goes on to study the limiting behaviour of sequences and series of real and complex numbers. This leads naturally to the study of functions defined as limits and to the notion of uniform convergence. Returning to the beginnings of calculus and power series expansions leads to complex variable theory: elementary functions of complex variable, the Cauchy integral theorem, Cauchy integral formula, residues and related topics with applications to real integrals.

Classes

3x1-hr lectures; 1x1-hr tutorial; and 1x1-hr practice class/wk

Assessment

2 x in-class quizzes (20%); a take-home assignment (10%); and a final exam (70%)

Textbooks

As set out in the Intermediate Mathematics Handbook

(MATH1X21 or MATH1931 or MATH1X01 or MATH1906) and (MATH1X23 or MATH1933 or MATH1X03 or MATH1907) and (MATH1XX2)

ProhibitionsMATH2923 or MATH3068 or MATH2962

Faculty: Science

Semester 2

05 Aug 2019

Department/School: Mathematics and Statistics Academic Operations

Study Mode: Normal (lecture/lab/tutorial) day

Census Date: 31 Aug 2019

Unit of study level: Intermediate

Credit points: 6.0

EFTSL: 0.125

Available for study abroad and exchange: Yes

Faculty/department permission required? No

Location

Camperdown

More details

Unit of Study coordinator: Dr Daniel Hauer

HECS Band: 2

Leadership for good starts here

ABN: 15 211 513 464

CRICOS Number: 00026A

TEQSA: PRV12057