MTH5105 - Differential and Integral Analysis - 2023/24
Topic outline
-
-
-
142.0 KB
-
361.7 KB
-
-
-
11.1 MB
-
-
WEEK 1 LECTURES
We will be reviewing "Continuity" and covering a rigorous introduction to "Differentiation".
WEEK 1 TASKS
- Familiarise yourself with the QMPlus page
- By the end of the week, start solving the problems in course worksheet 1
-
101.5 KB
-
122.9 KB
-
80.2 KB
-
The due/cutoff date for this assignment is February 6th 5pm.
Only a SINGLE PDF submission on QMPlus will be accepted. Emailed submissions will not be accepted under any circumstances.
If you have a problem uploading your submission, you will have to submit an EC claim.
Please put your name and your student number on your submission.
Tidyness and clarity of the presentation of your answers counts!
-
113.5 KB
-
WEEK 2 LECTURES
We will be covering the properties of differentiation and the mean value theorem.
WEEK 2 TASKS
- By the end of the week, start solving the problems in coursework sheet 2
- Complete the coursework sheet 1
- Prepare your solutions to the first assignment (under the week 1 tab)
-
85.4 KB
-
113.3 KB
- By the end of the week, start solving the problems in coursework sheet 2
-
WEEK 3 LECTURES
We will be covering the Taylor's theorem.
WEEK 3 TASKS
- By the end of the week, start solving the problems in coursework sheet 3
- Complete the coursework sheet 2
- Submit solutions to the first assignment (under the week 1 tab)
-
92.7 KB
-
121.2 KB
-
60.7 KB
-
The due/cut-off date for this assignment is February 20th 17.00hrs.
Only a SINGLE PDF submission on QMPlus will be accepted. Emailed submissions will not be accepted under any circumstances.
If you have a problem uploading your submission, you will have to submit an EC claim.
Please put your name and your student number on your submission.
Tidyness and clarity of the presentation of your answers counts!
-
69.4 KB
- By the end of the week, start solving the problems in coursework sheet 3
-
This is a second module in real analysis following on from the Convergence and Continuity module. We will explore in a rigorous way the main concepts, methods and results from the calculus of derivatives and integrals.
We formalize the definitions of differentiability and integrability and prove their basic algebraic properties.
We then explore some important results in real analysis and calculus such as the Mean Value Theorem and the Fundamental Theorem of Calculus.
We discuss Taylor’s Theorem and Improper integrals, widely used in probability and statistics, and close with the introduction of sequences of functions and their convergence.
-
WEEK 4 LECTURES
We will be covering the inverse function theorem.
- By the end of the week, start solving the problems in coursework sheet 4
- Complete the coursework sheet 3
- Start preparing your solutions to the second assignment (under the week 3 tab)
-
98.8 KB
-
129.4 KB
- By the end of the week, start solving the problems in coursework sheet 4
-
WEEK 5 LECTURES
This week we will be covering the basics of Riemann integration.
- By the end of the week, start solving the problems in coursework sheet 5
- Complete the coursework sheet 4
- Submit solutions to the second assignment (under the week 3 tab)
-
113.3 KB
-
157.7 KB
-
58.4 KB
-
The due/cut-off date for this assignment is March 12th Tuesday 5pm.
Only PDF submissions on QMPlus will be accepted.
Emailed submissions will not be accepted under any circumstances.
If you have a problem uploading your submission, you will have to submit an EC claim.
Remember to include your name and student number on your submission.
Tidyness and clarity of the presentation of your answers counts!
-
108.8 KB
- By the end of the week, start solving the problems in coursework sheet 5
-
-
104.5 KB
-
145.2 KB
-
-
-
WEEK 8 LECTURES
We will be covering basic properties of the Riemann integral.- By the end of the week, start solving the problems in coursework sheet 7
- Complete the coursework sheet 6
- Submit solutions to the third assignment (under the week 5 tab)
-
58.8 KB
-
74.3 KB
-
83.5 KB
-
The due date for this assignment is March 26th Tuesday 5pm.
Only PDF submissions on QMPlus will be accepted.
Emailed submissions will not be accepted under any circumstances.
If you have a problem uploading your submission, you will have to submit an EC claim.
Remember to include your name and student number on your submission.
Tidyness and clarity of the presentation of your answers counts!
-
112.0 KB
- By the end of the week, start solving the problems in coursework sheet 7
-
WEEK 9 LECTURES
We will be covering the Fundamental Theorem of Calculus.
- By the end of the week, start solving the problems in coursework sheet 8
- Complete the coursework sheet 7
- Start preparing the fourth assignment (under the week 8 tab)
-
46.7 KB
-
71.4 KB
- By the end of the week, start solving the problems in coursework sheet 8
-
-
63.3 KB
-
72.1 KB
-
94.2 KB
-
114.9 KB
-
8.2 MB
-
-
We will cover power series.
- By the end of the week, start solving the problems in coursework sheet 10
- Complete the coursework sheet 9
- Start preparing the fifth assignment (under the week 10 tab)
-
110.4 KB
-
143.5 KB
- By the end of the week, start solving the problems in coursework sheet 10
-
-
ACADEMIC CONTENT
This module covers:
- Differentiable functions, the algebra of derivatives and key theorems.
- Integration involving the Riemann integral; the Fundamental Theorem of Calculus; applications.
- Sequences of functions; pointwise and uniform convergence; the Weierstrass M-test; term-by-term integration of power series.
DISCIPLINARY SKILLS
At the end of this module, students should be able to:
- Define the derivative and state the properties of the derivative including the chain rule and inverse function rule.
- State and use key theorems concerning differentiable functions, such as Rolle's Theorem, the Mean Value Theorem and Taylor's Theorem.
- Define the Riemann integral, and state its properties.
- State the Fundamental Theorem of Calculus and apply it to the calculation of limits.
- Apply Taylor's Theorem to some well-known functions.
- Distinguish pointwise and uniform convergence.
- Apply the Weierstrass M-test to determine if an infinite series of functions converges uniformly.
ATTRIBUTES
At the end of this module, students should have developed with respect to the following attributes:
- Grasp the principles and practices of their field of study.
- Acquire substantial bodies of new knowledge.
- Explain and argue clearly and concisely.
- Acquire and apply knowledge in a rigorous way.
- Connect information and ideas within their field of study.
-
-
-
137.9 KB
-
You are encouraged to seek help in the Learning Cafe. All staff are there to help you with your questions.
I will be there for approximately for 2 hours per week, on Mondays and Fridays.
-
-
-