Mathematical Methods Iii
- Sciences
- 300 level
- 3 credit units
- 194 pages
- 7 units
This course, Mathematical Methods 111, provides essential methods for solving mathematical problems encountered in scientific disciplines. It explores functions of several variables, Jacobian applications, and functional dependence. The course also covers multiple, line, and improper integrals, along with an introduction to tensor calculus. Students will learn techniques for solving complex integrals and differential equations using methods like Fourier and Laplace transforms.
About this course
- Difficulty
- Intermediate
- Study hours
- 90 hours
- Maths
- Advanced
- Content
- Theoretical, problem solving
- Practical work
- No
- Assignments
- Tutor Marked Assignments
- Final Examination
What you'll read
The real module and unit structure of MTH381, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
MTH381 · UNIT 2: VECTOR FIELD THEORY
Show that the functions v( x) = e ax and u( x) = ebx are linearly dependent on the interval. 0 < x < 1 .
What you should be able to do
- Apply Jacobian transformations to change variables in multiple integrals
- Determine linear dependence or independence of functions
- Solve line, multiple, and improper integrals
- Apply Fourier and Laplace transforms to solve differential equations
- Evaluate complex integrals using Cauchy's Integral Theorem and Residue Theorem
What it prepares you for
- Data Analyst
- Financial Analyst
- Aerospace Engineer
- Electrical Engineer
- Software Engineer
- Engineering
- Physics
- Finance
- Computer Science
- Data Science
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module 2:
Unit 1: Functions of Complex Variables
Requires understanding of complex number properties and operations, including polar forms and conjugates.
- Module 2:
Unit 2: Integration of Complex Plane
Involves complex integration techniques and application of Cauchy's integral theorem.
- Module 3:
Unit 1: Residue Integration Method
Requires understanding of Laurent series and application of the Residue Theorem to evaluate complex integrals.
A suggested way through it
13 weeks, about 41 hours in total. Yours will differ.
- Week 1Module 1: Functions of Several Variables
Unit 1: Some Basic Concepts · 2 hours
Review basic concepts of functions of several variables.. Practice evaluating functions with multiple inputs..
Unit 2: Vector Field Theory · 2 hours
Study the definition and properties of Jacobians.. Solve problems involving Jacobian transformations..
- Week 2Module 2:
Unit 1: Functions of Complex Variables · 3 hours
Understand the representation of complex numbers.. Perform arithmetic operations with complex numbers..
- Week 3Module 2:
Unit 1: Functions of Complex Variables · 3 hours
Study the polar form of complex numbers.. Practice multiplication and division in polar form..
- Week 4Module 2:
Unit 1: Functions of Complex Variables · 3 hours
Learn about curves and regions in the complex plane.. Understand concepts related to sets in the complex plane..
- Week 5Module 2:
Unit 1: Functions of Complex Variables · 3 hours
Study limits, derivatives, and analytic functions.. Understand the Cauchy-Riemann equations..
- Week 6Module 2:
Unit 1: Functions of Complex Variables · 3 hours
Practice applying the Cauchy-Riemann equations.. Solve problems involving Laplace's equation and harmonic functions..
- Week 7Module 2:
Unit 1: Functions of Complex Variables · 3 hours
Study exponential and trigonometric functions.. Understand hyperbolic functions..
- Week 8Module 2:
Unit 2: Integration of Complex Plane · 3 hours
Study line integrals in the complex plane.. Understand the definition and existence of complex line integrals..
- Week 9Module 2:
Unit 2: Integration of Complex Plane · 3 hours
Learn about integration methods.. Understand the use of the representation of the path..
- Week 10Module 2:
Unit 2: Integration of Complex Plane · 3 hours
Study Cauchy's Integral Theorem.. Understand the independence of path and deformation of path..
- Week 11Module 2:
Unit 2: Integration of Complex Plane · 3 hours
Learn about the existence of indefinite integrals.. Understand Cauchy's Integral Formula..
- Week 12Module 2:
Unit 2: Integration of Complex Plane · 3 hours
Study derivatives of analytic functions.. Understand Morera's Theorem and Liouville's Theorem..
- Week 13Module 3:
Unit 1: Residue Integration Method · 4 hours
Understand residues and their formulas.. Study the Residue Theorem.. Practice evaluating real integrals..
Preparing for the exam
- Create detailed concept maps linking key theorems and techniques from each module.
- Practice solving a variety of complex integrals using different methods (e.g., Residue Theorem, direct integration).
- Focus on understanding the conditions under which each theorem (e.g., Cauchy's Integral Theorem) is applicable.
- Review and practice applying Fourier and Laplace transforms to solve differential equations.
- Work through all examples in the course material and attempt similar problems from recommended textbooks.
- Allocate specific time slots for reviewing each module and completing practice problems.
- Prioritize understanding the underlying principles rather than memorizing formulas.
- Form study groups to discuss challenging concepts and practice problem-solving together.
- Review all Tutor-Marked Assignments (TMAs) and identify areas for improvement.
- Create a summary sheet of key formulas and theorems for quick reference during the exam.
Questions students ask about this course
What is MTH381 about?
This course, Mathematical Methods 111, provides essential methods for solving mathematical problems encountered in scientific disciplines. It explores functions of several variables, Jacobian applications, and functional dependence. The course also covers multiple, line, and improper integrals, along with an introduction to tensor calculus. Students will learn techniques for solving complex integrals and differential equations using methods like Fourier and Laplace transforms.
How many units does MTH381 have?
MTH381, Mathematical Methods Iii, has 7 units across 4 modules, over 194 pages of course material. You can read it one unit at a time.
How many credit units is MTH381?
MTH381 carries 3 credit units, at 300 level in Sciences.
Is MTH381 hard?
MTH381 is rated intermediate level, with advanced mathematical content. It is mostly theoretical and problem solving work.
How long does MTH381 take to study?
About 90 hours of study, spread across its 7 units.
How is MTH381 assessed?
MTH381 is assessed by Assignments, Tutor Marked Assignments and Final Examination.
What can I do with MTH381?
Data Analyst, Financial Analyst, Aerospace Engineer, Electrical Engineer and Software Engineer.