This assessment requires students to apply differentiation and integration techniques to analyse real-world mathematical models. It involves interpreting the derivative as a rate of change of a physical phenomenon, applying differentiation rules, and solving elementary differential equations relevant to a simplified mathematical model. Additionally, students will also apply integration techniques to determine accumulated quantities, and analyse systems governed by integral equations in practical contexts.

• Interpret derivative as rate of change: Accurately applying differentiation rules to analyse and interpret derivatives in real-world contexts.
• Develop and analyse mathematical models: Constructing well-defined mathematical models involving rates of change and elementary differential equations, demonstrating correct application of differentiation and integration techniques.
• Achieving task objectives: Successfully solving the given problems, meeting the expected learning outcomes with precise and accurate solutions.
• Providing well-structured and justified solutions: Presenting solutions in a clear, logical, and organised manner, supported by appropriate mathematical reasoning and step-by-step calculations.
• Demonstrating a systematic problem-solving approach: Breaking down complex problems into manageable steps, applying suitable mathematical techniques, while clearly explaining the reasoning behind each step.
• Explains key assumptions and interpretations: Clearly articulates assumptions made in the problem-solving process and provides insightful interpretations of the mathematical results in context.

This assessment evaluates students’ ability to analyse signals and control systems using Fourier and Laplace transforms. It focuses on transforming time-domain functions into the frequency domain, understanding control system components, and applying Laplace transform techniques for system analysis using simulation software.

• Correctly applying Fourier transforms to convert time-domain functions into their frequency-domain representations.
• Accurately analysing signal characteristics, such as frequency components, bandwidth, and dominant frequencies.
• Explaining the fundamental principles of automatic control systems, including open-loop and closed-loop configurations.
• Identifying and describing typical control system building blocks (e.g., sensors, controllers, actuators) and their roles.
• Correctly applying forward and inverse Laplace transforms to analyse dynamic systems.
• Implementing and simulating a simple control system effectively using industry-standard software.
• Using appropriate mathematical notation, diagrams, and structured explanations.
• Presenting simulation results with clear annotations and interpretation.

In this assessment, students will apply Fourier and Laplace transforms to analyse control systems. They will:

• Perform Fourier transforms to obtain frequency-domain representations of time-domain signals.
• Apply forward and inverse Laplace transforms to analyse control systems in the s-domain and simulate results using software.
• Work collaboratively or independently and communicate your solutions professionally through a structured report or presentation.

Submission should include calculations, simulation results, and explanations demonstrating their understanding.

• Correct application of Fourier transforms to given time-domain signals.  
• Accurate interpretation of frequency-domain representations.
• Correct application of forward and inverse Laplace transforms.
• Analysis of control system behaviour in the s-domain.
• Use of simulation software to simulate and analyse simple control systems.
• Clarity and professionalism in presenting solutions.
• Proper use of figures, graphs, and simulation outputs.
• Effective distribution of tasks and evidence of teamwork. 

This is a take-home assessment designed to reinforce students' overall understanding of the unit and their ability to apply mathematical concepts in practice. It assesses students' ability to:

• Interpret the derivative as a rate of change of a physical quantity and apply differentiation rules to investigate rates of change in real-world scenarios.
• Use differentiation and integration techniques to construct and analyse simple mathematical models involving rates of change and elementary differential equations.
• Explain the principles of automatic control systems and identify typical control system building blocks.
• Apply forward and inverse Laplace transforms to analyse control systems in the s-domain, using simulation software to validate results.

Students are required to provide detailed calculations, justifications, and interpretations of their results. The submission should be structured professionally, incorporating mathematical reasoning, graphical representations, and simulation outputs where applicable.

• Correct interpretation of derivatives as rates of change in real-world scenarios.
• Correct application of differentiation and integration techniques in constructing mathematical models.
• Clear explanation of control system principles.
• Correct application of forward and inverse Laplace transforms.
• Analysis of control systems in the s-domain with appropriate justifications.
• Use of simulation software to implement a simpler control system and interpretation of results.
• Effective use of equations, graphs, and simulation outputs.  
• Justified assumptions and interpretations of results.