Syllabus

MA150 Engineering

MA151 Analysis (part one)

 
• Functions, relations and graphs. Inequalities, absolute value. Polynomials, rational functions, trigonometric functions.
• Limits and continuity, the derivative, methods of differentiation, maxima and minima
• The Mean Value Theorem and its applications, l'Hopital's Rule, Newton's Method
• Taylor's Theorem, Taylor expansions of elementary functions

MA152  Analysis (part two)

• Integration, the Fundamental Theorem of Calculus
• Applications: area, arc length, volumes of revolution
• Methods of integration, the trapezoidal rule, Simpson's rule
• Polar coordinates, areas in polar coordinates
• Differential 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)

MA153 Algebra (part one)

• 2 by 2 and 3 by 3 matrices, equations in up to 3 variables, determinants, inverse matrices
• Geometric transformations of R^2, standard equations for conics
• Eigenvalues and eigenvectors, diagonalisation of matrices, reduction of the general second degree equation to standard form

MA154 Algebra (part two)

• Polynomials over a field, the Remainder Theorem, roots and coefficients of a polynomial, complex roots of a real polynomial
• Complex numbers, de Moivre's Theorem with trigonometric applications, the Argand diagram, nth roots of unity
• Systems of linear equations, the Gaussian (row reduction) technique
• Row operations, inverse of a matrix by row reduction

Texts

• J.B. Fraleigh & R.A. Beauregard, "Linear Algebra" (Addison Wesley)
• F. Ayres, "Matrices" (Schaum Outline)
• F. Ayres, "Modern Algebra" (Schaum Outline)