The syllabus for the finale examination will be the material covered in all the lectures on the course. The questions will be based on the topics after linear algebra, but answering them will involve knowledge of the linear algebra in the course.

The topics on which questions will be asked and the sections in Apostol, Calculus Volume II (Second Edition, Wiley Reprint 2017) or M. Hirsch, S. Smale, R. L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd Edition, Academic Press, 2004. which roughly correspond to this material are as below.

• Differential Calculus of vector fields:: Apostol - Chapter 8: Sections 8.1 - 8.22.
• Applications of Differential calculus:: Apostol - Chapter 9: Sections 9.9 - 9.15.
• Multiple Integrals: Apostol - Chapter 11: Sections 11.1 - 11.12 and 11.26 - 11.33.
• Line Integrals: Apostol - Chapter 10: Sections 10.1 - 10.16.
• Green’s theorem: Apostol - Chapter 11: Sections 11.19 - 11.23.
• Linear Ordinary Differential Equations: Hirsch-Smale-Devaney: Chapter 2: 2-1 - 2.6, Chapter 3: 3.1 - 3.4, Chapter 4: Section 4.1.

The examination will be for 3 hours; 50% of the total marks of the course will be based on the final examination.