A-level Further Mathematics for Year 13 - Course 1: Differential Equations, Further Integration, Curve Sketching, Complex Number

开始时间: 04/22/2022 持续时间: 2-4 weeks

所在平台: Edx

课程主页: https://www.edx.org/course/further-mathematics-year-13-course-1

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课程详情

This course by Imperial College London is designed to help you develop the skills you need to succeed in your A-level further maths exams.

You will investigate key topic areas to gain a deeper understanding of the skills and techniques that you can apply throughout your A-level study. These skills include:

* Fluency – selecting and applying correct methods to answer with speed and efficiency

* Confidence – critically assessing mathematical methods and investigating ways to apply them

* Problem solving – analysing the ‘unfamiliar’ and identifying which skills and techniques you require to answer questions

* Constructing mathematical argument – using mathematical tools such as diagrams, graphs, the logical deduction, mathematical symbols, mathematical language, construct mathematical argument and present precisely to others

* Deep reasoning – analysing and critiquing mathematical techniques, arguments, formulae and proofs to comprehend how they can be applied

Over eight modules, you will be introduced to

• Analytical and numerical methods for solving first-order differential equations
• The nth roots of unity, the nth roots of any complex number, geometrical applications of complex numbers.
• Coordinate systems and curve sketching.
• Improper integrals, integration using partial fractions and reduction formulae
• The area enclosed by a curve defined by parametric equations or polar equations, arc length and the surface area of revolution.
• Solving second-order differential equations
• The vector product and its applications
• Eigenvalues, eigenvectors, diagonalization and the Cayley-Hamilton Theorem.

Your initial skillset will be extended to give a clear understanding of how background knowledge underpins the A -level further mathematics course. You’ll also be encouraged to consider how what you know fits into the wider mathematical world.

课程大纲

An understanding of the content of the course A-Level Further Mathematics for Year 12: Course 1 and Course 2 is required

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