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01.2 Indices

01.3 Simplification and Factorisation

01.4 Arithmetic of Algebraic Fractions

01.5 Formulae and Transposition

02.2 Graphs of Functions and Parametric Form

02.3 One-to-One and Inverse Functions

02.4 Characterising Functions

02.5 The Straight Line

02.6 The Circle

02.7 Some Common Functions

03.2 Solving Quadratic Equations

03.3 Solving Polynomial Equations

03.4 Solving Simultaneous Linear Equations

03.5 Solving Inequalities

03.6 Partial Fractions

04.2 Trigonometric Functions

04.3 Trigonometric Identities

04.4 Applications of Trigonometry to Triangles

04.5 Applications of Trigonometry to Waves

05.2 Quadratic Functions and Modelling

05.3 Oscillating Functions and Modelling

05.4 Inverse Square Law Modelling

06.2 The Hyperbolic Functions

06.3 Logarithms

06.4 The Logarithmic Function

06.5 Modelling Exercises

06.6 Log-linear Graphs

07.2 Matrix Multiplication

07.3 Determinants

07.4 The Inverse of a Matrix

08.2 Solution by Inverse Matrix Method

08.3 Solution by Gauss Elimination

10.3 The Exponential Form of a Complex Number

10.4 De Moivre’s Theorem

11.2 Using a Table of Derivatives

11.3 Higher Derivatives

11.4 Differentiating Products and Quotients

11.5 The Chain Rule

11.6 Parametric Differentiation

11.7 Implicit Differentiation

12.2 Maxima and Minima

12.3 The Newton-Raphson Method

12.4 Curvature

12.5 Differentiation of Vectors

12.6 Case Study: Complex Impedance

13.2 Definite Integrals

13.3 The Area Bounded by a Curve

13.4 Integration by Parts

13.5 Integration by Substitution and Using Partial Fractions

13.6 Integration of Trigonometric Functions

14.2 The Mean Value and the Root-Mean-Square Value

14.3 Volumes of Revolution

14.4 Lengths of Curves and Surfaces of Revolution

15.2 Calculating Centres of Mass

15.3 Moment of Inertia

16.2 Infinite Series

16.3 The Binomial Series

16.4 Power Series

16.5 Maclaurin and Taylor Series

18.2 Partial Derivatives

18.3 Stationary Points

18.4 Errors and Percentage Change

19.2 First Order Differential Equations

19.3 Second Order Differential Equations

19.4 Applications of Differential Equations

22.2 Applications of Eigenvalues and Eigenvectors

22.3 Repeated Eigenvalues and Symmetric Matrices

22.4 Numerical Determination of Eigenvalues and Eigenvectors

25.2 Applications of PDEs

25.3 Solution Using Separation of Variables

25.4 Solution Using Fourier Series

28.2 Differential Vector Calculus

28.3 Orthogonal Curvilinear Coordinates

29.2 Surface and Volume Integrals

29.3 Integral Vector Theorems

30.2 Gaussian Elimination

30.3 LU Decomposition

30.4 Matrix Norms

30.5 Iterative Methods for Systems of Equations

31.2 Numerical Integration

31.3 Numerical Differentiation

31.4 Nonlinear Equations

32.2 Linear Multistep Methods

32.3 Predictor-Corrector Methods

32.4 Parabolic PDEs

32.5 Hyperbolic PDEs

37.2 The Binomial Distribution

37.3 The Poisson Distribution

37.4 The Hypergeometric Distribution

38.2 The Uniform Distribution

38.3 The Exponential Distribution

40.2 Interval Estimation for the Variance

41.2 Tests Concerning a Single Sample

41.3 Tests Concerning Two Samples

44.2 Two-Way Analysis of Variance

44.3 Experimental Design

45.2 Non-parametric Tests for Two Samples