 ## Maths

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### IN2 Integration of polynomials

How do you integrate a polynomial where x is raised to a power? We saw this in the previous section on antidifferentiation. But how do you integrate a linear expression in brackets where the whole...

### IN3.1 Integration of functions of the form m over (ax+b)

How do you integrate a logarithm? How do you integrate an exponential function? How do you integrate a trigonometric function?

### IN3.3 Integration of exponential functions

How do you integrate a logarithm? How do you integrate an exponential function? How do you integrate a trigonometric function?

### IN3.4 Integration of trigonometric functions

How do you integrate a logarithm? How do you integrate an exponential function? How do you integrate a trigonometric function?

### IN5 Area under a curve

An area under a curve might be above the axis (and therefore positive). But sections might also be below the axis (and therefore negative).

### IN6 Integration by substitution

An expression that is composed of two functions (say an algebraic expression nested within a trigonometric expression) can be complicated to integrate. You can simplify this by substituting a single...

### IN7 Integration using partial fractions

How do you integrate an expression when there is an algebraic expression in the numerator and denominator of a fraction? Integrating using partial fractions helps you to solve this problem.

### IN8 Integration by parts

If you can consider your expression to be a product (i.e. Multiplication x) of two functions, you can integrate this using Integration by parts. This reflects the product rule in...

### IN9 Double integrals

Integrating will find the area between the curve and the x-axis (horizontal axis). We learned in IN4 Definite integrals how to limit this to a section of the x axis.

### Integration

Integration is vital in engineering. It is the key mathematical tool for finding the centre of mass or the surface area of a body. Integration is also called antidifferentiation.

### Laplace transforms

Transforms are another means of solving some differential equations that may prove too difficult to solve using other methods.

### M1 Matrices: Introduction

A matrix is an array of numbers. This module discusses matrices, their order, row and column matrices, square matrices and the identity matrix.

### M10 Eigenvalues and eigenvectors

Eigenvalues and eigenvectors are used to understand how buildings, structures and automobiles react in real life. They also provide insights into many mathematical areas.

### M2 Addition and subtraction of matrices

Matrices of the same shape (same number of rows and columns) may be added/subtracted by adding/subtracting the corresponding elements.

### M3 Matrix multiplication

To multiply two matrices A and B, the number of columns in A must equal the number of rows in B.

### M4 Determinant of a matrix

The determinant of a matrix can only be calculated for a square matrix and is used in many aspects of mathematics/engineering/physics.

### M5 Special matrices

It is helpful to understand the definition of a number of different types of “special” matrices.

### M6 Systems of equations

Systems of linear equations may be solved using elementary row operations. This is sometimes called Gaussian elimination.