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MA259 Multivariable Calculus

Lecturer: Dr. Mario Micallef

Term(s): 1

Status for Mathematics students: Core

Commitment: 30 lectures

Assessment: 85% by examination, 15% by assignments

Prerequisites: MA131 Analysis I and II OR MA137 Mathematical Analysis

Leads To: MA209 Variational Principles, MA3D9 Geometry of Curves and Surfaces, MA3G7 Functional Analysis I, MA3G8 Functional Analysis II, MA3H5 Manifolds, MA3J3 Bifurcations Catastrophes and Symmetry.


• Continuous Vector-Valued Functions
• Some Linear Algebra
• Differentiable Functions
• Inverse Function Theorem and Implicit Function Theorem
• Vector Fields, Green’s Theorem in the Plane and the Divergence Theorem in R3
• Maxima, minima and saddles

Learning Outcomes:

  • Demonstrate understanding of the basic concepts, theorems and calculations of multivariate analysis.
  • Demonstrate understanding of the Implicit and Inverse Function Theorems and their applications.
  • Demonstrate understanding of vector fields and Green’s Theorem and the Divergence Theorem.
  • Demonstrate the ability to analyse and classify critical points using Taylor expansions.


1. R. Abraham, J. E. Marsden, T. Ratiu. Manifolds, Tensor Analysis, and Applications. Springer, second edition, 1988.
2. T. M. Apostol. Mathematical Analysis. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., second edition, 1974.
3. R. Coleman. Calculus on normed vector spaces, Springer 2012. [available online via Warwick's library]
4. J. J. Duistermaat, J. A. C. Kolk. Multidimensional Real Analysis I : Differentiation, CUP, 2004 [available online via Warwick's library]
5. T. W. Körner. A Companion to Analysis: A Second First and First Second Course in Analysis, volume 62 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2004.
6. J. E. Marsden and A. Tromba. Vector Calculus. Macmillan Higher Education, sixth edition, 2011.

Additional Resources

Year 1 regs and modules
G100 G103 GL11 G1NC

Year 2 regs and modules
G100 G103 GL11 G1NC

Year 3 regs and modules
G100 G103

Year 4 regs and modules

Archived Material
Past Exams
Core module averages