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