Mathematical Methods I
- Sciences
- 200 level
- 3 credit units
- 105 pages
- 4 units
This course is designed for undergraduate students in mathematics and physical sciences. It builds upon mathematical concepts from the 100 level, such as differentiation, integration, trigonometric identities, and exponential and logarithmic functions. The course focuses on providing a strong understanding of advanced mathematical methods, including limits, continuity, differentiability, partial differentiation, convergence of infinite series, Taylor and Maclaurin series, and numerical integration techniques. The course is essential for students pursuing careers in mathematics and engineering.
About this course
- Difficulty
- Intermediate
- Study hours
- 208 hours
- Maths
- Advanced
- Content
- Theoretical, problem solving
- Practical work
- No
- Graded exercises
- Tutor marked assignments
- Final examination
What you'll read
The real module and unit structure of MTH281, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
MTH281 · UNIT 2: PARTIAL DIFFERENTIATION
In general, the sums, differences, products and quotients of continuous functions (except, of course, at the zeros of the denominator in the case of a quotients).
What you should be able to do
- Compute limits and derivatives of mathematical functions.
- Apply partial differentiation to functions of several variables.
- Determine the convergence of infinite series.
- Use Taylor and Maclaurin series to approximate functions.
- Solve integration problems using numerical methods.
What it prepares you for
- Mathematician
- Engineer
- Data Analyst
- Statistician
- Financial Analyst
- Engineering
- Finance
- Data Science
- Research
- Academia
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module 1:
Unit 1: Limit, Continuity and Differentiability
Involves rigorous definitions of limits and continuity, requiring a strong foundation in basic calculus and real analysis.
- Module 1:
Unit 2: Partial Differentiation
Requires understanding of multivariable calculus and chain rule, making it challenging to apply in complex scenarios.
- Module 1:
Unit 3: Convergence of Infinite Series
Requires understanding of various convergence tests and their appropriate application, which can be difficult to master.
A suggested way through it
13 weeks, about 52 hours in total. Yours will differ.
- Week 1Module 1:
Unit 1: Limit, Continuity and Differentiability · 4 hours
Understand the definition of a limit and how to establish limits of functions.. Learn to determine the continuity of a function and identify points of discontinuity.. Practice differentiation of functions from first principles..
- Week 2Module 1:
Unit 1: Limit, Continuity and Differentiability · 4 hours
Apply Rolle's Theorem and the Mean-Value Theorem to solve problems.. Obtain nth differential coefficients of simple functions using Leibnitz's formula.. Solve problems related to maxima and minima of functions..
- Week 3Module 1:
Unit 2: Partial Differentiation · 4 hours
Understand functions of several independent variables and their properties.. Learn to compute first partial derivatives of functions with respect to different variables.. Apply the chain rule to find partial derivatives of composite functions..
- Week 4Module 1:
Unit 2: Partial Differentiation · 4 hours
Compute higher partial derivatives and verify the commutative property.. Calculate total derivatives and apply them to implicit differentiation.. Solve problems involving homogeneous functions and Euler's Theorem..
- Week 5Module 1:
Unit 2: Partial Differentiation · 4 hours
Apply Lagrange multiplier techniques to find minima and maxima of functions of several variables.. Carry out Taylor series expansion of functions of several variables.. Practice change of variables in partial differential equations..
- Week 6Module 1:
Unit 3: Convergence of Infinite Series · 4 hours
Understand the definition of convergence of infinite series.. Learn and apply theorems related to series convergence.. Test for convergence of series with positive terms using comparison tests..
- Week 7Module 1:
Unit 3: Convergence of Infinite Series · 4 hours
Test for convergence of alternating series.. Distinguish between absolute and conditional convergence.. Apply absolute convergence tests to determine convergence..
- Week 8Module 1:
Unit 3: Convergence of Infinite Series · 4 hours
Understand the concept of power series and their properties.. Perform operations with power series, including multiplication and rearrangement.. Determine the radius and interval of convergence for power series..
- Week 9Module 1:
Unit 4: Taylor and Maclaurin Series · 4 hours
Learn to carry out series expansion using Taylor's and Maclaurin's methods.. Apply Taylor's theorem to expand functions around a specific point.. Apply Maclaurin's theorem to expand functions around zero..
- Week 10Module 1:
Unit 4: Taylor and Maclaurin Series · 4 hours
Evaluate limits of indeterminate forms using Taylor and Maclaurin series.. Apply L'Hopital's rule to evaluate limits.. Solve mathematical problems using Taylor and Maclaurin series expansions..
- Week 11Module 1:
Unit 5: Numerical Integrations · 4 hours
Understand the concept of numerical integration and its applications.. Learn and apply the Trapezium rule for numerical integration.. Apply Simpson's rule for numerical integration..
- Week 12Module 1:
Unit 5: Numerical Integrations · 4 hours
Apply Simpson's rule to solve practical problems.. Use series expansion methods for numerical integration.. Compare and contrast different numerical integration techniques..
- Week 13Module 1:
Unit 5: Numerical Integrations · 4 hours
Review all units and prepare for final examination.. Work on assignments and tutor-marked assignments.. Solve additional problems to reinforce understanding..
Preparing for the exam
- Review all definitions and theorems related to limits, continuity, and differentiability.
- Practice solving problems involving partial derivatives and their applications.
- Master the different convergence tests for infinite series and apply them to various series.
- Understand the derivation and application of Taylor and Maclaurin series.
- Practice numerical integration techniques, including the Trapezium and Simpson's rules.
Questions students ask about this course
What is MTH281 about?
This course is designed for undergraduate students in mathematics and physical sciences. It builds upon mathematical concepts from the 100 level, such as differentiation, integration, trigonometric identities, and exponential and logarithmic functions. The course focuses on providing a strong understanding of advanced mathematical methods, including limits, continuity, differentiability, partial differentiation, convergence of infinite series, Taylor and Maclaurin series, and numerical integration techniques. The course is essential for students pursuing careers in mathematics and engineering.
How many units does MTH281 have?
MTH281, Mathematical Methods I, has 4 units across 1 module, over 105 pages of course material. You can read it one unit at a time.
How many credit units is MTH281?
MTH281 carries 3 credit units, at 200 level in Sciences.
Is MTH281 hard?
MTH281 is rated intermediate level, with advanced mathematical content. It is mostly theoretical and problem solving work.
How long does MTH281 take to study?
About 208 hours of study, spread across its 4 units.
How is MTH281 assessed?
MTH281 is assessed by graded exercises, tutor marked assignments and final examination.
What can I do with MTH281?
Mathematician, Engineer, Data Analyst, Statistician and Financial Analyst.