First semester, 2011-2012
OBJECTIVE
To prepare students without A Level Mathematics
for the module CIVE1620 Engineering Mathematics.
SYLLABUS
Algebra and Functions: - Simplification of rational algebraic expressions including factorising and cancelling, and dividing one polynomial by another - Rational functions and partial fractions - The Remainder Theorem. Co-ordinate geometry in the (x,y)-plane: - Co-ordinate geometry of the circle, standard equation of the circle - Cartesian and parametric representations of curves and the conversion between them. Sequences and Series Expansions: - The expansion of (1+x)^n, the notations n! and (nk) - Binomial expansion of (1+x)^q where q is a rational number. Trigonometry: - The secant, cosecant and cotangent functions - Inverse trigonometric functions, their graphs and their restricted domains and their relationship with the sine cosine and tangent functions - Knowledge and use of double angle formulas, the formulas for sin(A +/- B), cos(A +/- B and tan(A +/- B) - Expression of a.cos q + b.sin q in the forms r.cos(q+a) and r.sin(q+a). Exponentials and logarithms: - Exponential growth and decay - The solution of equations of the form a^x=b. Differentiation: - The derivatives of the trigonometric functions - Application of differentiation to tangents and normals - Differentiation using the product, quotient and chain rules, and the formula dx/dy=1/(dy/dx) - Differentiation of functions defined implicitly or parametrically - Formation of simple differential equations. Integration: - Integration of sin x and cos x - Simple cases of integration by parts and using substitutions - Simple cases of integration using partial fractions - Analytical solution of first order differential equations with separable variables.General administrative information (PDF)
Complete notes for the course (PDF)
Problem Sheets: 1 (PDF) 2 (PDF) 3 (PDF) 4 (PDF) 5 (PDF)
Solutions: 1 (PDF) 2 (PDF) 3 (PDF) 4 (PDF) 5 (PDF)
Formula sheet handed out with exam paper
A worked example from lectures
Information from university module catalogue
2010 solutions (PDF) 2011 solutions (PDF)
Last updated December 13th 2011