Summary of 2023 MATH161H0 Augmented Engineering Mathematics 1B

2023 MATH161H0 Augmented Engineering Mathematics 1B

MATH161

Summary of Course Content

MATH161 is a year-long Programme in Engineering Mathematics. The aim of the course is to further develop the concepts of differential and integral calculus and introduce elements of complex numbers and differential equations. The course commences with a revision of antiderivatives and then proceeds to finding the area under a curve. The Riemann sum is introduced and then related to the integration of a function. Definite and indefinite integrals are discussed. Further techniques of integration such as "u-substitution"; trigonometric integrals; integration by parts; trigonometric substitution and applications of integration are introduced. A study of the different types of improper integrals is made. This is followed by a study of the applications of integration in determining areas under curves; volumes of solids of revolution, surface areas of solids of revolutions and lengths of curves. Parametric curves and polar coordinates are then studied and followed by conic sections which looks at the properties of parabolas, circles , ellipses and hyperbolas. A basic study of differential equations is the made. Sequences and series are studied in some detail and then followed by Taylor and Maclaurin expansions of functions. The course is completed by a having a glimpse into complex numbers and basic complex functions.

Structure

All lectures and tutorials will be conducted on campus according to the timetable given below. The lecture and test schedule for the First Semester is attached. There are Tutorials Exercises based on the lectures which students need to complete to gauge their understanding of the content material. Tutors will be available to assist the students during the tutorial sessions. The programme for the second semester will be conveyed at a later date.