An introduction to the basic concepts and techniques of calculus for students who have not studied mathematics at tertiary level.This covers fundamentals of differentiation and integration

• LO 1 : Differentiate simple functions from first principles  

• LO 2: Use standard derivatives in combination with the product, quotient and chain  

• LO 3 : Use the first and second derivatives to find maximum and minimum values of a function 

• LO 4 : Evaluate the accuracy of different experiments, both with respect to experimental set-ups and methods of measurement. 

• LO 5 : Apply differentiation to practical problems.  

• LO 6 : Use standard integrals to solve polynomial and trigonometric functions  

• LO 7  Apply partial fractions, substitution and integration parts. 

• LO 8 : Solve simple differential equation 

The Engineering Council sets the overall requirements for the AHEP (Accreditation for Higher Education Programmes). It is the standard used by the UK engineering profession to assess the competence and commitment of individual engineers and technicians and is in its 4th iteration. Link: ahep-fourth-edition 

The module will be delivered through a blend of online teaching and learning material, guided study, and on-campus face-to-face classes (tutorials, feedback sessions). Extensive notes for pre/post lecture reading will be provided together with suggested further reading.

A weekly module map will be made available to you on the module detailing teaching and learning content and activities each week, indicative time commitment and relationship to the module assessment. 

Subject-Specific Skills: 

• Applying calculus to real engineering problems 

• Use of computational techniques for differentiation and integration 

• Group working. 

SUMMATIVE ASSSSMENT  

The module is assessed via an exam in the summer exam period.   

THE OPPORTUNITY FOR REASSESSMENT IN THIS MODULE: 

Opportunities for re-assessment is only permitted provided you have not failed more credit than in the resit rule adopted by your programme.  If the amount of credit you have failed is more than permitted by the relevant resit rule, you may be permitted to repeat study if you are within the threshold set for the Repeat rule adopted by your programme.  You will be notified of your eligibility to resit/repeat any modules after the Examining Board in the Summer period. 

All resit assessments will be held in the Resit Examination period, prior to the start of the following academic session. 

Reassessment will be via successful completion of the failed components. For group components, the remit of the reassessment will be set by the module leader while also mapped against the module learning outcomes.  

• Introduction to the ideas of the differential calculus.
• Definition of derivative.
• Differentiation from first principles.
• Differentiation of trigonometric functions. Logarithmic and exponential functions and their derivatives (all done without proof).
• Use of product, quotient and chain (function of a function) rules.
• Simple application to optimization problems. (Maximum and minimum values)
• Integration of polynomial functions and easy trigonometric functions.
• Integration by use of partial fractions.
• Definite integrals
• Bounded area problems
• Integration by parts and by substitution.
• Simple differential equations
• Using calculus in computations