Syllabus

MA120 Arts

MA121 Calculus (part one)

• Functions and graphs: 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.
• Graphs, tangents, maxima and minima, concavity..
• Indefinite integration: integration by substitution.
• Integration by parts: introduction to logx and e^x, logarithmic differentiation, differentiation of a^x etc.
• Inverse trigonometric functions: partial fractions, trigonometric substitutions.
• Word problems, related rates.
• Implicit differentiation; first order differential equations: separable and linear equations.

MA122 Calculus (part two)

• Continuity and differentiability: differentiation from first principles
• Tangents to a graph, Newton's Method
• The Mean Value Theorem: application to increasing and decreasing functions, l'Hopital's Rule.
• Graphs, maxima and minima, concavity: word problems, related rates
• Riemann sums, the trapezoidal rule: the Fundamental Theorem of Calculus
• Definite integrals, areas between curves.
• The logarithmic function as an integral, and its properties: the exponential function
• Indefinite integration: reduction formulae, integration by substitution, integration by parts.
• Reduction formulae, partial fractions, inverse trigonometric functions, etc.
• Implicit differentiation; first order differential equations: separable and linear equations.

Texts

• G.B. Thomas & R.L. Finney, "Calculus and Analytic Geometry" (Addison Wesley)
• S.L. Salas, E. Hille & J.T. Anderson, "Calculus, One and Several Variables" (Wiley)
• E. Mendelson. Beginning Calculus. Schaum Outline.

MA123 Algebra (part one)

• Introduction to 2 by 2 and determinants
• Transpose, adjoint and inverse
• Characteristic equation, eigenvalues and eigenvectors
• Conics: ellipse, hyperbola and parabola.
• Linear equations
• The Principle of Induction.
• Applications: geometry, linear transformations, linear equations.

MA124 Algebra (part two)

• Complex numbers: de Moivre's Theorem, applications to trigonometry and roots of unity, solution of equations.
• Introduction to 3 x 3 matrices and determinants. Transpose, adjoint and inverse. Application to linear equations.
• Markov processes: transition matrices, steady states, recurrence relations, and commercial applications