MA137 Mathematical Analysis Notes | Assignment Help | Syllabus
Country: United Kingdom
University: The University Of Warwick
Many mathematical issues cannot be solved directly. As a result, approximate solutions are sought, with the error between the actual and approximate answers estimated. Indeed, a series of approximate solutions that converge to an exact solution may be used to show the presence of a solution. In mathematical analysis, the study of limiting processes is a fundamental topic. It entails quantifying the concept of limit as well as exact formulations of intuitive concepts such as infinite sums, functions, continuity, and calculus. In term one, you’ll learn about the concepts of mathematicians like as Cauchy, Dirichlet, Weierstrass, Bolzano, D’Alembert, Riemann, and others about sequences and series, and in term two, you’ll learn about continuity and differentiability.
1. Decimal expressions and real numbers; geometric series; and fraction conversion of repeating decimals.
2. The completeness axiom and the convergence of a nonrecurring decimal in the form of an ascending sequence that is limited above converges to a real number.
3. The completeness axiom as the primary distinction between rationals and reals; irrationals may be approximated by rationals and vice versa.
Inequalities are number four.
5. Sequence and subsequence are defined formally.
6. Cauchy sequences and the Cauchy criteria; limit of a series of real numbers
(a) Positively numbered series
Alternating series (b)
8. The number e may be written as lim(1+(1/n)n or 1 + 1 + (1/2!) + (1/3!) + ……
9. Sets that are bounded and unbounded. Infs and sups.
11. Continuous function properties
12. Consistent Boundaries
14. Differentiable function properties
15. Derivatives of higher order
Power Series, No. 16
Taylor’s Theorem (#17)
18. Analysis’s Classical Functions
Upper and Lower Limits (19.)
The student should be able to do the following by the conclusion of the module:
Find out what the symbol ‘infinity’ means.
Learn how to calculate basic limits and what it means for a series to converge or diverge.
When does it make sense to add an unlimited amount of numbers?
Understand the terms “continuity” and “distinctiability.”
Determine the characteristics of several continuous and differentiable functions.
Give an example of when a function may be represented by a power series.
Create their own problem-solving strategies.
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