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A foundational paper covering epsilon-delta limit proofs, continuity of piecewise functions, first- and second-order differential equations, systems of linear equations solved by Gaussian elimination, determinant properties, and integration via partial fractions and power series.

Applies core calculus to real-world models: piecewise sensor functions and the Chain Rule, exact and integrating-factor differential equations for drug concentration, matrix inversion for pricing systems, and Taylor series applied to concentration estimates and traffic-flow integrals.

The most advanced paper in the series, combining Laplace transforms for second-order differential equations, eigenvalue and diagonalization problems in a production-systems context, and Maclaurin series approximation with error analysis — all set within realistic modelling scenarios.

Connects calculus to engineering practice: continuity, differentiability and the derivative from first principles, variation of parameters for non-homogeneous differential equations, optimisation and integration applications, and boundary value problems modelling heat flow along a cooling fin.

An advanced paper combining integration by substitution and improper integrals, formal proofs within inner product spaces (Cauchy-Schwarz, Triangle inequality, Pythagorean Theorem), second-order differential equations solved by reduction of order, and singular value decomposition of a symmetric matrix.

This test covers Sampling Design and Bias, Confidence Interval for a Mean, One-Sample Hypothesis Test for a Proportion, and Conditional Probability and Bayes' Theorem

This test covers Two-Sample Inference for Means, Chi-Square Test of Independence, One-Way ANOVA, and Simple Linear Regression and Inference

This test covers Descriptive Statistics and Distribution Shape, Confidence Interval for a Proportion, Paired t-Test, and Discrete Random Variables and Expected Value

This test covers Inference for Two Proportions, Chi-Square Goodness-of-Fit Test, Two-Way ANOVA Concepts and Interaction, and Multiple Regression

Part A of the ME 2222 Thermodynamics examination focuses on the foundational laws of thermodynamics and their direct engineering applications. Students will demonstrate their understanding of energy conservation, steady-flow systems, and the Second Law concept of entropy. The three questions progressively build from conceptual definitions through mathematical derivations to quantitative problem solving, reflecting the analytical depth expected at this level of mechanical engineering study. Part A carries a total of 40 marks and students are expected to complete it within approximately 80 minutes, leaving clear, well-structured workings for each calculation.