SMA 2119
CALCULUS III
Prerequisite: SMA 1218: Calculus II
Course purpose
The aim of the course is to extend the tools and techniques of single variable calculus to functions
of several variables.
Expected Learning Outcomes
By the end of the course, the learner should be able to:
1. Calculate and interpret first and second partial derivatives, directional derivatives and
gradients for functions of several variables.
2. Evaluate double integrals using rectangular coordinates.
3. Change the order of integration for double integrals.
4. Apply double integrals to solve application problems.
Course description
Sequences and series: convergence tests. Single variable analysis: function series and power
series (Taylor's and Maclaurin's theorems), Special functions and their power series (binomial,
logarithmic, exponential, trigonometric and hyperbolic functions). Several variables analysis:
Differentiability, Partial derivatives, inverse and implicit function theorems, iterated integrals,
Jacobians, change of order of integration, change of variable in multiple integrals, Improper
integrals and their convergence. Applications of multiple integrals.
Mode of delivery: Lectures, Tutorials, Self-study, exercises, group discussions, presentations
Instructional Materials/Equipment: White board, markers, flip chart, hand-outs, LCD projector,
a computer installed with appropriate software.
Course assessment
Assignments
Continuous Assessment Tests
Final Examination
Total
10%
20%
70%
100%
Core textbook
1. Hughes-Halliet, D., Gleason, A.M., McCallum, W.G., et al. (2017). Calculus:
Multivariable. 7th Edition. Hoboken: Wiley.
2. Hass, J., Heil, C., Weir, M.D. (2018). Thomas’ Calculus, 14th Edition. Boston: Pearson.
Other textbooks
1. Lipsman, R.L., Rosenberg, J.M. (2017). Multivariable Calculus with MATLAB: With
Applications to Geometry and Physics. Springer.
2. Hass, J., Heil, C., Weir, M.D. (2018). Thomas’ Calculus. 14th Edition. Boston: Pearson.
3. Hughes-Hallet, D., Gleason, A.M., Lock, P.F., et al., (2014). Applied Calculus. 5th Edition.
Hoboken, NJ: John Wiley and Sons.
Course Journals
1. Journal of Mathematics Research