# Examine how sequences and series can be used to solve engineering problems.

Unit 8 Further Engineering Mathematics, Pearson BTEC International Level 3 qualifications in Applied Science

Assignment - Using sequences and series to solve engineering problems

Learning Outcome 1: Examine how sequences and series can be used to solve engineering problems.

Assignment Brief:

You are undergoing a work placement as a Mechanical Engineer and are tasked with demonstrating your problem-solving skills using mathematical sequences and series relevant to engineering scenarios.

Engineering Problem Solving with Sequences and Series:

1. Exploring Mathematical Sequences:

• Identify and analyze provided sequences (e.g., Arithmetic Progression, Geometric Progression) within engineering contexts.
• Determine key parameters such as first term, common difference/ratio, specific terms, and summations.
2. Engineering Cost Estimations:

• Estimate the cost of drilling using tunnelling machine data and cost-per-metre variations derived from mathematical sequences.
3. Motor Speed Analysis:

• Calculate and present motor speed variations as a Geometric Progression, determining common ratio and tabulating speeds.
4. Depreciation Analysis:

• Utilize depreciation rates (derived from sequences) to forecast the value of a CNC machine center over time.
5. Binomial Expansion and Pascal`s Triangle:

• Apply Pascal`s Triangle and the Binomial Theorem to expand and evaluate binomial expressions within engineering calculations.
6. Maclaurin Series and Exponential Functions:

• Derive Maclaurin series expansions for exponential functions (e.g., ex) and calculate values using specific terms.
7. Pendulum Oscillation Calculations:

• Apply the oscillation time period formula to calculate expected percentage errors based on length measurement variations.

Conclusion:

This assignment emphasizes the practical application of mathematical sequences and series in solving diverse engineering problems. By addressing these tasks, you will showcase your ability to apply mathematical concepts to real-world engineering scenarios effectively.