Syllabus

MA130 Commerce

MA131 Calculus (part one)

• Functions, graphs, asymptotes: informal limits
• Calculation of limits, introduction to continuity, limits as x tends to infinity, and asymptotes.
• Differentiation by rule: the Chain Rule.
• Review of trigonometry: Limits and differentiation of trigonometric functions.
• Derivatives and Applications
• Continuity and differentiability: differentiation from first principles
• Ranges of increase and decrease, stationary points, local maxima and minima, absolute maxima and minima, business applications.

MA132 Calculus (part two)

• Anti-derivatives
• Indefinite integration: integration by substitution.
• Integration by parts:
• Tangents to a graph, Newton's Method
• The Mean Value Theorem: application to increasing and decreasing functions,
• Riemann sums, the trapezoidal rule: Simpson's Rule; the Fundamental Theorem of Calculus
• Definite integrals, areas between curves.
• The logarithmic function as an integral, and its properties: the exponential function
• First order differential equation applications
• Implicit differentiation; first order differential equations: separable and linear equations.

MA133 Algebra (part one)

• Equations and applications.
• Introduction to 2 by 2 and determinants
• Transpose, adjoint and inverse
• Solutions of systems of linear equations - Gaussian Elimination, Business applications.
• General matrices, determiinants, inverse by cofactor and row reduction applications.
• Characteristic equation, eigenvalues and eigenvectors

Linear equations, Linear programming, graphical method.

MA134 Algebra (part two)

• Further Linear Programming, Simplex method.
• Mathematics of Finance, annuities, present and future value.
• Markov processes: transition matrices, steady states, recurrence relations, and commercial applications
• Cost-benefit analysis.

Texts:

• E. Mendelson. Beginning Calculus. Schaum Outline.
• F.S. Budnick Mathematics for Business Economics and McGraw-Hill the Social Sciences.