Template:MATHS 150: 2007 Description

From MathsDept

MATHS 150 is the natural first year Mathematics course for students with a good mathematics background who are considering a major or a minor in Mathematics. In addition students planning a major in, for example, Physics, Economics, Statistics or Computer Science will find that their choices in those disciplines are greatly enhanced by a strong component of Mathematics, the more the better.

Course Outline The following topics are covered in this course:

• Sets, intervals and inequalities, the absolute value.
• Domain, range, and inverses of functions, including trigonometric, exponential and logarithmic functions.
• Limits and limit theorems, Squeeze Theorem, continuity, The Intermediate Value Theorem. Limits at infinity and asymptotes of functions.
• Tangents and rates of change, Derivatives and differentiability, differentiation rules, Chain Rule.
• Implicit differentiation, maxima and minima, the Extreme Value, Fermat's, Rolle's and the Mean Value Theorems.
• Concavity, graph sketching and optimization.
• Functions of two variables: limits and continuity, partial derivatives, local linearity.
• The Riemann Integral and the Fundamental Theorem of Calculus.
• Integration by substitution and by parts.
• First order differential equations, slope fields and Euler's method. Modelling with these.
• Vectors in IRn , norms, angles, the dot product and orthogonality.
• The Cauchy Schwartz inequality.
• Linear combinations of vectors, and vector and parametric vector equations of lines and planes in IR3.
• Normal vectors, and Cartesian equations of planes.
• Linear systems, augmented matrices and elementary row operations.
• Echelon forms, Gaussian elimination and back substitution, Homogeneous linear systems and some applications of linear systems.
• Operations on matrices, algebraic properties of matrices, matrix inverses and elementary matrices.
• Determinants and their properties, and applications including the cross product.

Revision Information about an intensive revision course held in the fortnight before the beginning of the first semester is available at Superstart