LO4 Examine how differential and integral calculus can be used to solve engineering and manufacturing sector problems

Qualification

Pearson BTEC Higher Nationals for England (2024)

Unit number and title

4002. Engineering Mathematics

Assignment title

Calculus

Assessor

Engineering Team

Academic year

1

Unit Code

A/651/0708

Assignment

3 of 3

Verification Date

2^nd September 2024

Issue Date

2^nd September 2024

Final Submission Date

No later than 31st August 2025

Submission Format

All text elements of your submission should be word processed, mathematical solutions can be handwritten (neatly) and scanned into your document.

Assignment Format

• Organisation: Use clear headings, paragraphs, and sub-sections, to ensure clarity and ease of reading.
• Referencing: Support your work with research. Use Harvard referencing or an approved alternative. Ensure accuracy to avoid plagiarism.
• Bibliography: Include a bibliography listing all referenced sources at the end, following the same referencing style.

Assignment Structure

Your assignment MUST include the following sections:

• Cover Page: Your Course, Name, Unit Name and Assignment number/name
• Contents Page: List tasks or questions with page numbers.
• References: List all sources used, but do not use Wikipedia.

Submission Requirements

By submitting your assignment, you confirm the following:

• Originality: The work is your own, with all sources properly cited.
• Plagiarism: You acknowledge that plagiarism and collusion are forms of academic misconduct and are strictly prohibited.
• Plagiarism Detection: Your assignment will be submitted to TurnItIn, a plagiarism detection service, that compares your work against databases, online sources, and other students` work.
• False Declaration: Making a false declaration is academic misconduct.

Professional Conversation

• Selected assignments will require a video conference to assess understanding before final grades are issued.

 Vocational Scenario or Context

You work as a Test Engineer for a global manufacturer of electrical and mechanical components and systems. Your Line Manager is responsible for delegating to you and your colleagues the testing of theory, principles, and hypotheses from several worldwide company divisions. She has asked you to undertake a series of such evaluations.

Task 1

Differentiate each of the following voltage functions with respect to time and hence determine the ‘rate of change’ for each of the functions when time (t) is 5 seconds.

a) �� = (��² + 6)²

b) �� = (3��³ − 4�� + 6)³

c) �� = �������� (2��)

d) �� = 4��^−0.5��

e) �� = sin(2��³ + 4�� − 2)

f) �� = cos(3��⁴ − 5�� + 4)

Task 2

PART 1

For the circuit shown below, assuming zero charge on the capacitor at t = 0, the current flowing may be quantified as…

E  -t 

i = e RC

R

Integrate this equation with respect to t and hence find the charge stored in the capacitor one second after the switch is closed.

PART 2

The current (����) through a 10 mH inductor (L) has a relationship with time (t) as follows;

                                                                          1

���� = �� ∫ cos(100��) ����

Determine the inductor current when the time is 0.9 seconds.

Task 3

PART 1

Determine the area under the following exponential growth curve between 2 seconds and 4 seconds;

4

�� = �(1 − ��^−��) ����

2

PART 2

Determine the area under the following exponential decay curve between 2 seconds and 4 seconds;

4

�� = �(��^−��) ����

2

Task 4

PART 1

Locate the co-ordinates of the turning point for the following function and determine whether it is a maxima or minima;

�� = 3��² − 5�� 

PART 2

Find the maxima and minima values for the function;

�� = ��³ − 4�� + 6

Sources of information to support you with this Assignment

Bird J. (2021) Higher Engineering Mathematics. 9th Ed. Routledge.

Bird J. (2019) Science and Mathematics for Engineering. 6th Ed. Routledge.

Glyn J. and Dyke P. (2020) Modern Engineering Mathematics. 6th edition. Pearson. Made Easy Editorial Board (2022) Engineering Mathematics for GATE 2023 and ESE 2023 (Prelims) – Theory and Previous Year Solved Papers. India: Made Easy Publications

Pvt Ltd.

Rattan K.S., Klingbeil N.W., and Baudendistel C.M. (2021) Introductory Mathematics for Engineering Applications. 2nd Ed. Wiley.

Ram M. (2021) Recent Advances in Mathematics for Engineering. CRC Press. Teodorescu P., Stanescu N., and Pandrea N. (2013) Numerical Analysis with Applications in Mechanics and Engineering. Wiley-IEEE Press.

Ram M. (2020) Mathematics in Engineering Sciences: Novel Theories, Technologies, and Applications. 1st Edition. CRC Press.

Sobot, R. (2022) Engineering Mathematics by Example. 1st Ed. Springer.

Stroud, K.A. and Booth, D.J. (2020) Engineering Mathematics. 8th Ed. Bloomsbury Publishing

Urbano M. (2019) Introductory Electrical Engineering with Math Explained in Accessible Language. Wiley.

Vick B. (2020) Applied Engineering Mathematics. CRC Press.