Further pure mathematics 1

1. VECTORS

1.1 Vector product

1.2 Finding areas

1.3 Scalar triple product

1.4 Straight lines

1.5 Solving geometrical problems

1.6 Mixed exercise 1

1.7 Review exercise for chapter 1

 

2. CONIC SECTIONS 1

2.1 Parametric equations

2.2 Parabolas

2.3 Rectangular hyperbolas

2.4 Tangents and normals

2.5 Loci

2.6 Mixed exercise 2

2.7 Review exercise for chapter 2

 

3. CONIC SECTIONS 2

3.1 Ellipses

3.2 Hyperbolas

3.3 Eccentricity

3.4 Tangents and normals to an ellipse

3.5 Tangents and normals to a hyperbola

3.6 Loci

3.7 Mixed exercise 3

3.8 Review exercise for chapter 3

 

4. INEQUALITIES

4.1 Algebraic methods

4.2 Using graphs to solve inequalities

4.3 Modulus inequalities

4.4 Mixed exercise 4

4.5 Review exercise for chapter 4

 

5. THE t-FORMULAE

5.1 The $t$-formulae

5.2 Applying the $t$-formulae to trigonometric identities

5.3 Solving trigonometric equations

5.4 Modelling with trigonometry

5.5 Mixed exercise 5

5.6 Review exercise for chapter 5

 

6. TAYLOR SERIES

6.1 Taylor series

6.2 Finding limits

6.3 Series solutions of differential equations

6.4 Mixed exercise 6

6.5 Review exercise for chapter 6

 

7. METHODS IN CALCULUS

7.1 Leibnitz's theorem and nth derivatives

7.2 L'Hospital's rule

7.3 The Weierstrass substitution

7.4 Mixed exercise 7

7.5 Review exercise for chapter 7

 

8. NUMERICAL METHODS

8.1 Solving first-order differential equations

8.2 Solving second-order differential equations

8.3 Simpson's rule

8.4 Mixed exercise 8

8.5 Review exercise for chapter 8

 

9. REDUCIBLE DIFFERENTIAL EQUATIONS

9.1 First-order differential equations

9.2 Second-order differential equations

9.3 Modelling with differential equations

9.4 Mixed exercise 9

9.5 Review exercise for chapter 9

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