# 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

• 35 강의
• 07:33:31
• 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
• 17. 1 - Complex Numbers Exam Questions pt. 1 00:17:15
• 18. 1 - Complex Numbers Exam Questions pt. 2 00:12:39
• 19. 1 - Complex Numbers Exam Questions pt. 3 00:12:47
• 20. 1 - Complex Numbers Exam Questions pt. 4 00:14:25
• 21. 2 - Roots of Quadratic Equations Exam Questions pt .1 00:16:47
• 22. 2 - Roots of Quadratic Equations Exam Questions pt. 2 00:16:34
• 23. 3 - Numerical Solutions of Equations Exam Questions pt. 1 00:10:26
• 24. 3 - Numerical Solutions of Equations Exam Questions pt. 2 00:11:05
• 25. 3 - Numerical Solutions of Equations Exam Questions pt. 3 00:11:56
• 26. 4 - Coordinate Systems Exam Questions pt. 1 00:12:50
• 27. 4 - Coordinate Systems Exam Questions pt. 2 00:13:35
• 28. 4 - Coordinate Systems Exam Questions pt. 3 00:22:27
• 29. 5&6 - Matrices & Transformations Using Matrices pt. 1 00:16:50
• 30. 5&6 - Matrices & Transformations Using Matrices pt. 2 00:19:00
• 31. 5&6 - Matrices & Transformations Using Matrices pt. 3 00:09:14
• 32. 7 - Series pt. 1 00:17:06
• 33. 7 - Series pt. 2 00:14:55
• 34. 8 - Proof by Mathematical Induction pt. 1 00:20:06
• 35. 8 - Proof by Mathematical Induction pt. 2 00:19:33

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수강생 – 20-03-27:

심화 수학 정말 어렵게 느껴지는 과목입니다.

그것에 비해 강의 시간이 너무 짧은 것이 아닌가 생각이 들었습니다.

하지만 기우에 불과했습니다.

정말 짧은 시간에 컴팩트한 강의로 쉽게 수업을 들을 수 있었습니다.

반복도 여러번 했습니다.

정말 돈이 아깝지 않은 강의입니다.

역시 케임브리지 대학 출신이라는 생각을 했습니다.

선생님 정말 감사합니다. 