In Term 1, students will learn fundamental concepts such as number systems, algebra, and geometry. They will explore various types of functions, including inverse, composite, polynomial, rational, circular, exponential, logarithmic, and hyperbolic functions, as well as continuous and discontinuous functions. Students will gain skills in graphing functions and apply differentiation techniques, covering basic rules, parametric and implicit differentiation, higher derivatives, and optimization. They will also cover integration techniques, including definite and indefinite integrals, partial fractions, integration by parts, and substitution. Linear algebra will be introduced, covering systems of linear equations, Gaussian elimination, matrices, and eigenvalue problems.
In Term 2, students will study vectors, their physical meanings, and different coordinate systems, including Cartesian, cylindrical, and spherical coordinates. They will learn to manipulate complex numbers and explore their application in solving ordinary differential equations (ODEs). The course also covers ordinary differential equations, from first-order types to second-order ODEs with constant coefficients, including Laplace transforms. Students will delve into functions of multiple variables, covering partial differentiation, vector calculus, and integration techniques. The module concludes with sequences, series, and tests for convergence, including the Taylor series of common functions.
