Syllabus

MA100 1st Science (pass)

MA101 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.
• Indefinite integration: integration by substitution.
• Functions and graphs; informal limits.
• Graphs, tangents, maxima and minima, concavity.
• Word problems, related rates.
• Integration by parts: introduction to logx and e^x, logarithmic differentiation, differentiation of a^x etc.
• Inverse trigonometric functions: partial fractions, trigonometric substitutions.
• Definite integrals, areas between curves: introduction to the Fundamental Theorem of the Calculus.
• Implicit differentiation; first order differential equations: separable and linear equations.

MA102 Calculus (part two)

• Inequalitie: inequalities involving absolute values
• Definition of a limit (using epsilon and delta), limits of sums and constant multiples.
• 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
• The logarithmic function as an integral, and its properties: the exponential function
• Definite integrals, areas between curves.
• Indefinite integration: reduction formulae
• 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)

MA103 Algebra (part one)

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

MA104 Algebra (part two)

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