# A레벨_Further Mathematics(AS)_Further Pure 1 > A레벨

## 과정소개

교재 : edexcel / 수강기간 : 30일

Further Pure Mathematics 1

Further Pure Mathematics 1 extends
horizontally from Pure Mathematics 1&2 to cover a wide range of topics
suitable for those who are looking to progress to a highly numerate course in a
STEM field. It serves as an introduction to more formal aspects of mathematics
which are later built upon in Further Pure Mathematics 2&3

**Chapter 1: Complex Numbers**

Imaginary and complex numbers are
introduced, along with their algebra and their applications to solving
polynomials. Through Argand diagrams, the geometry of complex numbers is also
introduced, and their relationship to vectors is made clear.

**Chapter 2: Roots of Quadratic Equations**

The concept of using the roots of quadratic
equations – without explicitly calculating them – is introduced, and new
equations are formed by manipulating expressions involving these roots.

**Chapter 3: Numerical Solutions of Equations**

The majority of functions cannot be solved
analytically, and thus numerical methods must be used to find their roots. This
chapter introduces three basic methods to estimate the roots of equations:
Interval Bisection; Linear Interpolation; and the Newton-Raphson method.

**Chapter 4: Coordinate Systems**

Curves related to Conic Sections were
studied as far back as the Ancient Greeks. Using the (relatively) modern
Cartesian coordinate system, this chapter investigates two such curves: The
Parabola and the Rectangular Hyperbola. Alongside their algebraic properties,
their geometric characteristics are also developed, with the parabola being
derived as a locus of points defined by a focus and a directrix.

**Chapter 5: Matrices**

At the most fundamental level a Matrix is
just an array of numbers, but the fact they connect in powerful ways to almost
all areas of mathematics makes their study essential. In this chapter, the
algebra of Matrices is introduced, including finding inverses and determinants,
and the non-commutative nature of their multiplication is appreciated.

**Chapter 6: Transformations using Matrices**

All linear transformations can be
represented using matrices. Linear transformations are using throughout
mathematics, and the sciences in general, making matrices indispensable tools.
This chapter we looks at the geometric effects of matrices including
reflections and rotations, inverse transformations, and how the determinant of
a matrix represents its scaling factor.

**Chapter 7: Series**

Sigma notation for summations is introduced
and standard results up to the sum of cubes are used to find both general
formulae and evaluate explicit sums which are linear combinations of these
standard results.

**Chapter 8: Proof**

Here we look at a powerful and formal
method of proof known as Proof by Induction. Ironically, it is actually a form
of deductive reasoning. Firstly the concept of logic of Proof by Induction is
introduced, then it is applied to four different cases: Proving the validity of
summation formulae; proving the divisibility of integer sequences; proving
general term expressions derived from recurrence relations; and proving results
involving the repeated multiplication of matrices.

## 강의목록

- 16 강의
- 02:44:01

- 1. Complex Numbers 1-1 00:11:07
- 2. Complex Numbers 1-2 00:09:43
- 3. Complex Numbers 1-3 00:09:45
- 4. Roots of Quadratic Equations 2-1 00:11:38
- 5. Numerical Solutions of Equations 3-1 00:10:37
- 6. Numerical Solutions of Equations 3-2 00:13:13
- 7. Coordinate Systems 4-1 00:09:17
- 8. Coordinate Systems 4-2 00:08:54
- 9. Matrices 5-1 00:08:16
- 10. Matrices 5-2 00:10:31
- 11. Transformation using Matrices 6-1 00:06:52
- 12. Transformation using Matrices 6-2 00:09:27
- 13. Transformation using Matrices 6-3 00:09:02
- 14. Series 7-1 00:12:05
- 15. Proof by Mathematical Induction 8-1 00:12:34
- 16. Proof by Mathematical Induction 8-2 00:11:00