MA101-4-FY-CO:
Calculus

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Full Year
Undergraduate: Level 4
Current
Thursday 03 October 2024
Friday 27 June 2025
30
27 March 2024

 

Requisites for this module
(none)
(none)
(none)
EC115

 

EC251, EC368, EC371, EC372, EC383, MA105, MA108, MA200, MA202, MA203, MA222, MA225, MA318

Key module for

BSC N233 Actuarial Science (Including Placement Year),
BSC N233DT Actuarial Science (Including Placement Year),
BSC N323 Actuarial Science,
BSC N323DF Actuarial Science,
BSC N323DT Actuarial Science,
BSC N324 Actuarial Science (Including Year Abroad),
BSC N325 Actuarial Science (Including Foundation Year),
BA 0F66 Economics (Including Placement Year),
BA L100 Economics,
BA L102 Economics (Including Foundation Year),
BA L106 Economics (Including Year Abroad),
BSC 0E45 Economics (Including Placement Year),
BSC L101 Economics,
BSC L103 Economics (Including Foundation Year),
BSC L107 Economics (Including Year Abroad),
MECNL130 Economics,
MECNLA30 Economics (Including Placement Year),
MECNLA31 Economics (Including Year Abroad),
BSC L1G2 Economics and Mathematics (Including Placement Year),
BSC LG11 Economics and Mathematics,
BSC LG18 Economics and Mathematics (Including Foundation Year),
BSC LG1C Economics and Mathematics (Including Year Abroad),
BSC L1G1 Economics with Mathematics,
BSC L1G3 Economics with Mathematics (Including Placement Year),
BSC L1G8 Economics with Mathematics (Including Foundation Year),
BSC L1GC Economics with Mathematics (Including Year Abroad),
BSC GN13 Finance and Mathematics,
BSC GN15 Finance and Mathematics (Including Placement Year),
BSC GN18 Finance and Mathematics (Including Foundation Year),
BSC GN1H Finance and Mathematics (Including Year Abroad),
BA 5A84 Financial Economics (Including Placement Year),
BA L111 Financial Economics,
BA L118 Financial Economics (Including Foundation Year),
BA L195 Financial Economics (Including Year Abroad),
BSC 0Q64 Financial Economics (Including Placement Year),
BSC L114 Financial Economics,
BSC L117 Financial Economics (Including Foundation Year),
BSC L194 Financial Economics (Including Year Abroad),
MECNL131 Financial Economics,
MECNLB31 Financial Economics (Including Placement Year),
MECNLB32 Financial Economics (Including Year Abroad),
BA 9O47 International Economics (Including Placement Year),
BA L115 International Economics,
BA L160 International Economics (Including Foundation Year),
BA L163 International Economics (Including Year Abroad),
BSC 5H18 International Economics (Including Placement Year),
BSC L116 International Economics,
BSC L161 International Economics (Including Foundation Year),
BSC L162 International Economics (Including Year Abroad),
MECNL132 International Economics,
MECNLC32 International Economics (Including Placement Year),
MECNLC33 International Economics (Including Year Abroad),
BA 9L11 Management Economics (Including Placement Year),
BA L108 Management Economics,
BA L190 Management Economics (Including Foundation Year),
BA L192 Management Economics (Including Year Abroad),
BSC 5M00 Management Economics (Including Placement Year),
BSC L109 Management Economics,
BSC L191 Management Economics (Including Foundation Year),
BSC L193 Management Economics (Including Year Abroad),
MECNL133 Management Economics,
MECNL134 Management Economics (Including Placement Year),
MECNL135 Management Economics (Including Year Abroad),
BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
MMATG198 Mathematics,
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
BSC G1G4 Mathematics with Computing (Including Year Abroad),
BSC G1G8 Mathematics with Computing (Including Foundation Year),
BSC G1GK Mathematics with Computing,
BSC G1IK Mathematics with Computing (Including Placement Year),
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC G1F5 Mathematics with Physics (Including Foundation Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad),
BSC I1G3 Data Science and Analytics,
BSC I1GB Data Science and Analytics (Including Placement Year),
BSC I1GC Data Science and Analytics (Including Year Abroad),
BSC I1GF Data Science and Analytics (Including Foundation Year),
BA L1R0 Economics with a Modern Language,
BA R112 Economics with Language Studies,
BA R113 Economics with Language Studies (Including Foundation Year),
MSCIN399 Actuarial Science and Data Science,
MSCIG199 Mathematics and Data Science,
BSC N333 Actuarial Studies,
BSC N333DT Actuarial Studies,
BSC N334 Actuarial Studies (Including Placement Year),
BSC N334DT Actuarial Studies (Including Placement Year),
BSC N335 Actuarial Studies (Including Year Abroad)

Module description

This module introduces the important concepts from the field of calculus which underpins the mathematics utilised in various areas throughout maths as well as in other closely related disciplines, such as physics, biology, economics, statistics, data science and computer science. Students will cover various topics from differentiation, integration, power series, as well as introducing multivariate calculus through partial differentiation and double integration.


For students outside of the School, an appropriate A level in Mathematics (or equivalent) is required for this module. If you are unsure whether you meet this criteria please contact maths@essex.ac.uk before attempting to enrol.

Module aims

The aims of this module are:



  • To reinforce concepts of calculus, its applications and associated topics that students will have met prior to University and;

  • To extend them to allow students to engage with concepts met in an undergraduate mathematics degree.

Module learning outcomes

By the end of this module, students will be expected to be able to:



  1. Understand and be able to apply standard techniques for calculating univariate derivatives and integrals, such as the product rule, chain rule and integration by parts, as well as their multivariate analogues.

  2. Have a conceptual understanding of differentiation and integration through an introduction to the notion of limits and continuity.

  3. Have a conceptual understanding of the connection between integration and differentiation through the Fundamental Theorem of Calculus and notion of the anti-derivative.

  4. Be able to write and construct simple derivations and proofs, such as finding derivatives from first principles, deriving identities such as trigonometric or hyperbolic identities and the rules of differentiation.

  5. Have a conceptual and practical understanding of the applications of techniques in calculus such as classifying fixed points, solving differential equations and calculating power series expansions.

Module information

The syllabus of this modules covers material from univariate and multivariate calculus, and includes topics in:



  • Pre-calculus

    • Such as function notation, combining functions, inverse functions, piece-wise defined functions, absolute function.



  • Limits & Continuity

    • Introduction to the idea of limits and continuity.



  • Differentiation (univariate)


Reminder of properties and rules of differentiation, methods of differentiation. Calculating and classifying stationary points. Calculating the derivative from First Principles. Finding limits through l’Hopital’s rules.



  • Integration

  • Differential Equations

    • Introduction to differential equations and methods for solving certain first and second order differential equations.



  • Power Series

    • Taylor and Maclaurin expansions.



  • Multivariate Calculus
    Including an introduction to partial differentiation and double integration

Learning and teaching methods

Teaching in the School will be delivered using a range of face to face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.

Bibliography*

This module does not appear to have any essential texts. To see non - essential items, please refer to the module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Assignment 3     
Coursework   Assignment 4     
Coursework   Assignment 1     
Coursework   Assignment 2     
Exam  Main exam: In-Person, Open Book (Restricted), 150 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 150 minutes during September (Reassessment Period) 

Exam format definitions

  • Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
  • In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
  • In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
  • In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework Exam
40% 60%

Reassessment

Coursework Exam
40% 60%
Module supervisor and teaching staff
Dr Joseph Bailey, email: jbailef@essex.ac.uk.
Dr Joseph Bailey & Tahani Al-Karkhi
jbailef@essex.ac.uk

 

Availability
Yes
Yes
No

External examiner

No external examiner information available for this module.
Resources
Available via Moodle
Of 40 hours, 40 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.

 

Further information
Mathematics, Statistics and Actuarial Science (School of)

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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