Welcome to Mathematics for Natural Sciences A¶

These notes are designed for you to follow the content in NSCI0005.

In these notes we will cover:

Complex numbers
- Definitions and extending the real numbers
- Cartesian and polar form
- Exponential form and Euler formula
- Finding complex roots
- de Moivre’s theorem
- Relationship between trignometric functions and hyperbolic functions
Sequences, series and convergences
- Sequences and recurrence relations
- Series as summing a sequence
- Limits of series and infinities
- Series convergence tests - Preliminary, Ratio, Comparison
Vectors and Matrices
- Vector notation
- Vector equation of a line
- Scalar and vector equations of a plane
- Matrix algebra
- Matrix determinants
- Matrix inverses
Differentiation and Integration
- Arc length
- Solids of revolution - surface area and volume
- Reduction formulae
- Partial differentiation
- Multi-variable chain rule
- Stationary points and saddles
1st and 2nd order differential equations (ODEs)
- Seperable 1st order systems of ODEs
- Integrating factor method for 1st order systems
- Seperable partial differential equations (PDEs)
- Homogeneous 2nd order systems
- Inhomogeneous 2nd order systems