MA12002: Applied mathematics 1A
[Page last updated: 23 October 2023]
| Academic Year: | 2023/24 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 15 [equivalent to 30 CATS credits] |
| Notional Study Hours: | 300 |
| Level: | Certificate (FHEQ level 4) |
| Period: |
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| Assessment Summary: | CWSI 20%, EXCB 80% |
| Assessment Detail: |
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| Supplementary Assessment: |
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| Requisites: | |
| Learning Outcomes: |
By the end of the unit, you will be able to:
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| Synopsis: | You will develop core skills in applied mathematics, including statistics and computer programming. You will explore calculus in two and three dimensions and key mathematical methods for solving linear differential equations. Examples will be chosen from physics, engineering and other sciences. You will develop a solid foundation in probability theory leading to applications in statistics. You will learn Python programming, including the design and analysis of algorithms. |
| Content: | Programming:
Introduction to programming: fundamental concepts such as iteration vs recursion; implementing mathematical algorithms based on pseudocode. Elements of the Python language: variables and scope, basic data types; control structures: conditionals, loops, functions, and subroutines. Understanding and analysing algorithms: common design patterns such as divide-and-conquer and dynamic programming. Complexity analysis: complexity of common algorithms for sorting and searching, Big-O notation, the master theorem for divide-and-conquer algorithms. Principles of software design and testing.
Probability & Statistics:
Sample space, events as sets, unions, and intersections. Axioms and laws of probability. Equally likely events. Sampling methods: with or without ordering and replacement. Conditional probability. Partition theorem. Bayes' theorem. Independence of events. Bernoulli trials. Discrete random variables (RVs). Probability mass function (PMF). Bernoulli, Geometric, Binomial and Poisson distributions. Joint and marginal discrete distributions. Definition of continuous random variables (RVs), cumulative distribution functions (CDFs) and probability density functions (PDFs). Some common continuous distributions including uniform, exponential and normal. Independence of RVs (including joint distribution as a product of marginals). Expectation of RVs. Properties of expectation. Expectation of product of independent RVs. Variance and properties. Standard deviation. Moments, covariance, correlation. Sums of independent random variables. Key application: Random walks. Statement of the law of large numbers.
Multivariable calculus & differential equations:
Visualisation and analysis of space in rectangular, polar, cylindrical, and spherical co-ordinate systems, arc length, surfaces of revolution. Visualisation and parameterisation of three-dimensional surfaces (planes, paraboloids, spheres, cylinders, cones). Partial derivatives, critical points, chain rule. Jacobians and change of variables, double integrals over rectangular and non-rectangular domains, triple integrals, surface area and volume, the Riemann interpretation. Key applications. Dynamics and differential equations: first-order linear and nonlinear differential equations, integrating factors, separable equations. Review of complex numbers and Euler's formula. Second-order linear constant-coefficient equations: characteristic equations, real and complex roots, general real solutions, inhomogeneous problems. Key applications. |
| Course availability: |
MA12002 is Compulsory on the following courses:Department of Mathematical Sciences
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Notes:
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