Core pure mathematics 2

1. COMPLEX NUMBERS

1.1 Exponential form of complex numbers

1.2 Multiplying and dividing complex numbers

1.3 De Moivre's theorem

1.4 Trigonometric identities

1.5 Sums of series

1.6 $n$th roots of a complex number

1.7 Solving geometric problems

1.8 Mixed exercise 1

1.9 Review exercise for chapter 1

 

2. SERIES

2.1 The method of differences

2.2 Higher derivatives

2.3 Maclaurin series

2.4 Series expansions of compound functions

2.5 Mixed exercise 2

2.6 Review exercise for chapter 2

 

3. METHODS IN CALCULUS

3.1 Improper integrals

3.2 The mean value of a function

3.3 Differentiating inverse trigonometric functions

3.4 Integrating with inverse trigonometric functions

3.5 Integrating using partial fractions

3.6 Mixed exercise 3

3.7 Review exercise for chapter 3

 

4. VOLUMES OF REVOLUTION

4.1 Volumes of revolution around the $x$-axis

4.2 Volumes of revolution around the $y$-axis

4.3 Volumes of revolution of parametrically defined curves

4.4 Modelling with volumes of revolution

4.5 Mixed exercise 4

4.6 Review exercise for chapter 4

 

5. POLAR COORDINATES

5.1 Polar coordinates and equations

5.2 Sketching curves

5.3 Areas enclosed by a polar curve

5.4 Tangents to polar curves

5.5 Mixed exercise 5

5.6 Review exercise for chapter 5

 

6. HYPERBOLIC FUNCTIONS

6.1 Introduction to hyperbolic functions

6.2 Inverse hyperbolic functions

6.3 Identities and equations

6.4 Differentiating hyperbolic functions

6.5 Integrating hyperbolic functions

6.6 Mixed exercise 6

6.7 Review exercise for chapter 6

 

7. METHODS IN DIFFERENTIAL EQUATIONS

7.1 First-order differential equations

7.2 Second-order homogeneous differential equations

7.3 Second-order non-homogeneous differential equations

7.4 Using boundary conditions

7.5 Mixed exercise 7

7.6 Review exercise for chapter 7

 

8. MODELLING WITH DIFFERENTIAL EQUATIONS

8.1 Modelling with first-order differential equations

8.2 Simple harmonic motion

8.3 Damped and forced harmonic motion

8.4 Coupled first-order simultaneous differential equations

8.5 Mixed exercise 8

8.6 Review exercise for chapter 8

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