Module Specifications..
Current Academic Year 2023  2024
Please note that this information is subject to change.
 
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Description This module aims to ensure that students will have an understanding of the theory of the Calculus of Several Variables suitable for their studies in Physics. Where appropriate, theorems will be explained using arguments based on Physics rather than on formal mathematical proofs. Furthermore, it aims to develop students abilities to perform the calculations that arise in applications, especially in applications to Physics. Infinite dimensional vector spaces, in teh context of Fourier Series, will be considered also. Students will attend lectures on the course material and will work, independently, to solve problems on topics related to the course material. The students will have an opportunity to review their solutions, with guidance, at weekly tutorials.  
Learning Outcomes 1. Reformulate concepts from physics in the language of vector calculus. 2. Perform the calculations that arise when the calculus of several variables is used to solve problems. 3. Demonstrate an understanding of concepts by use of examples or counterexamples. 4. State and apply selected definitions and theorems. 5. Calculate trigonometric Fourier Series of elementary functions defined on finite intervals and sketch the periodic extensions of such functions.  
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml 

Indicative Content and Learning Activities
VECTORS IN 3SPACE Vectors as directed line segments, their addition and scalar multiplication. Frames of reference and coordinates. The inner product, cross product and their applications. FUNCTIONS OF ONE OR MORE VARIABLES Parametrized curves. Level sets and their parametrizations. DIFFERENTIAL CALCULUS Limits, continuity, partial differentiation. The chain rule. The gradient, divergence, curl and their physical interpretations. Max/Min problems and Lagrange multipliers. Taylor's formula. INTEGRAL CALCULUS Line integrals, multiple integrals, surface integrals. The integral theorems. Change of variable formula for multiple integrals. FOURIER SERIES Function spaces. Orthogonal projections onto finite dimensional spaces. Calculation of Trigonometric Fourier Series, Bessel's inequality, Parseval's identity. Fourier Transforms.  
 
Indicative Reading List  
Other Resources None  
Programme or List of Programmes
 
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