Offered to students admitted to Year 1 in  ALL 

Major/Minor  ALL 
Course Type  
Offer in 2022  2023  Y N 
Course Code  MATH1851 
Date  2023/03/25 06:25 
Enquiry for Course Details 
MATH1851 Calculus and ordinary differential equations (6 credits)  Academic Year  2022  

Offering Department  Mathematics  Quota  700  
Course Coordinator  Prof Y K Lau (1st sem); Dr X Zhang (2nd sem), Mathematics < yklau@maths.hku.hk; xzhang@maths.hku.hk >  
Teachers Involved 
(Dr L Xu,Mechanical Engineering) (Dr X Zhang,Mathematics) (Dr Y Chen,Mechanical Engineering) (Prof K W Chow,Mechanical Engineering) (Prof Y K Lau,Mathematics) 

Course Objectives  In this course, students will be introduced to fundamental concepts of calculus and ordinary differential equations with a view on applications in different engineering fields. A concrete foundation of mathematics that underpins the various engineering subjects will be built. Mathematical concepts and principles, as well as some typical engineering applications, would be emphasized so that students could enhance their mathematical skills in solving engineering problems, and be well prepared in learning a higher level of applied mathematics required in different engineering disciplines.  
Course Contents & Topics 
 Differential and integral calculus (single variable) [limits and continuity, derivatives, (higherorder) derivatives of elementary functions, derivatives by implicit differentiation, the mean value theorem, L'H\^{o}pital's rule, parametric representation of curves, polar coordinates, indefinite integrals, integration by parts, partial fractions decomposition, definite integrals, the fundamental theorem of calculus, and their applications]  Ordinary differential equations [first order equations, integrating factors and linear equations, Bernoulli equations, separable equations, homogeneous equations, exact differential equations, higherorder homogeneous linear equations with constant coefficients, characteristic polynomials, methods of undetermined coefficients and variation of parameters, higherorder inhomogeneous linear ordinary differential equations, choice of particular solutions and physical implication of resonance, CauchyEuler equations, and their applications]  Laplace transforms [Laplace transforms of elementary functions, inverse Laplace transforms, transforms of derivatives and integrals, derivatives of Laplace transform, first and second shifting theorems, convolutions, partial fractions, solution of linear differential equations (initial value problems) using Laplace transforms] 

Course Learning Outcomes 
On successful completion of this course, students should be able to:


Prerequisites (and Corequisites and Impermissible combinations) 
Level 2 or above in Module 1, or Module 2 of HKDSE Mathematics or equivalent, or Pass in MATH1011. (This course is exclusively for Engineering students.) 

Course to PLO Mapping  
Offer in 2022  2023  Y 1st sem 2nd sem  Examination  Dec May  
Offer in 2023  2024  Y  
Course Grade  A+ to F  
Grade Descriptors 


Course Type  Lecturebased course  
Course Teaching & Learning Activities 


Assessment Methods and Weighting 


Required/recommended reading and online materials 
(Textbook) Introduction to Calculus and Differential Equations (Pearson) G.B. Thomas, et al.: Thomas' Calculus (Pearson Education, 2005, 11th ed.) R.K. Nagle, et al.: Fundamentals of Differential Equations and Boundary Value Problems (Pearson Education, 2008, 5th ed.) 

Course Website  http://moodle.hku.hk/  
Additional Course Information 
There will be no 'makeup' for a missed test or assignment under normal circumstances. Students are advised not to take MATH1851 and MATH1853 together in the same semester. This course is offered by the Department of Mathematics and the Faculty of Engineering. Timetable: https://hkumath.hku.hk/~math/Timetable/Timetable2223_S1.pdf https://hkumath.hku.hk/~math/Timetable/Timetable2223_S2.pdf 
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