MAST20026 Real Analysis Notes | Assignment Help | Syllabus
University: University Of Melbourne
“This topic introduces the area of mathematical analysis by providing a thorough theoretical foundation as well as a few examples. Many key conclusions are carefully proven, and students are exposed to proof techniques such as mathematical induction and contradiction proof.
The difference between real and rational numbers is stressed, and it is used to justify strict concepts of sequence convergence and divergence, such as the Cauchy criteria. These concepts are expanded to include the theory of infinite series, as well as common convergence and divergence tests. The Mean Value Theorem and Taylor’s Theorem are applications of a similar approach of continuity and differentiability of functions with a single variable. The Riemann integral’s definitions and characteristics allow for a formal demonstration of the Fundamental Theorem of Calculus. The convergence characteristics of sequences and series are investigated, with applications to power series representations of basic functions and Taylor series production. Fourier series are a kind of representation for periodic functions.
Learning outcomes that are expected
After completing this course, students should be able to:
Acquire a sense of mathematical rigor, be able to utilize evidence by induction, proof by contradiction, and epsilon-delta proofs as both a theoretical and approximation technique;
Understand the Riemann integral and improper integrals, as well as their theory and applications.
Know how to calculate the convergence and divergence of infinite series;
Have a thorough understanding of power series expansions and Taylor polynomial approximations in theory and practice; and
Recognize the significance of Fourier series in the representation of periodic functions.
Skills that are universal
Students will have the chance to acquire general abilities that will help them in any future professional path, in addition to acquiring particular skills that will help them in their future jobs in science. These are some of them:
analytical skills: the ability to construct and express logical arguments and work in abstract or general terms to increase the clarity and efficiency of analysis; collaborative skills: the ability to work in a team; problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies; problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies; problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies; problem-solving skills: the ability to engage with unfamiliar problems and identify relevant
Ability to fulfill regular deadlines while managing conflicting obligations is referred to as time management abilities.”
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