Here are the topics we plan to cover in ENGR121 in 2020 Tri 2, with week numbers. There are ten weeks of topics listed; the sixth and twelfth week are reserved for catching up if necessary, and revising otherwise:

(1) Sets, numbers and functions

Sets, intersection, union, laws of set theory, numbers, intervals, inequalities, functions (many-to-one,composition, parametric).

(2) Functions and logic

Inverse functions, continuous functions, periodic functions, logic – or, and, not, nor, nand, truth tables, boolean algebra, logical equivalence, logic circuits, disjunctive normal form.

(3) Algebraic techniques

Indices, Polynomials, laws of indices, factorising, quadratic formula, complete the square, Binomial theorem, gGraphing of functions, asymptotes, common engineering functions

(4) Trig functions, sequences

Degrees/radians, sine, cosine, tangent, trig identities, waves, inverse trig functions, trig equations.

(5) Sequences, series, limits

Summation notation, series, arithmetic & geometric series, binomial theorem, power series, rates of change, limits, continuity, definition of derivatives.

(6) Introduction to differentiation, Catch up/revision

(7) Differentiation

Existence of derivatives, common derivatives, product rule, quotient rule, chain rule, implicit differentiation.

(8) Integration

Integration as area under curve, trapezium rule, limits, common integrals, sums, lots of practice. Trig functions, average-value, piecewise continuous functions.

(9) Vectors

Vectors, linear combinations, linear independence, dot product, cross product.

(10) Matrix algebra

Matrices (size, addition, multiplication), transformations

Special matrices, identity, inverse, determinant, solution of simultaneous equations.

(11) Probability

Sample spaces, definitions, rules, permutations, combinations.

(12) Catch up/revision