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JC1504: ADVANCED MATHEMATICS I-2 (2022-2023)

Last modified: 31 Jul 2023 11:19


Course Overview

This course deals with the theory of sequences and series, and discusses their applications to the theory of functions.  It also gives an introduction to differential equations and the theory of functions of several variables.  It provides the necessary mathematical background for further study in mathematics, computing science and other subjects.

Course Details

Study Type Undergraduate Level 1
Session Second Sub Session Credit Points 20 credits (10 ECTS credits)
Campus Offshore Sustained Study No
Co-ordinators
  • Professor Benjamin Martin

What courses & programmes must have been taken before this course?

  • Any Undergraduate Programme (Studied)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

This course is a continuation of Advanced Mathematics I-1. It further develops the theory of integration of a function of one variable. It introduces sequences and series and studies the notion of convergence.  It also provides a first introduction to partial differentiation and ordinary differential equations, which are fundamental in applications of Mathematics to other sciences.

Syllabus

  • Improper integrals.
  • Sequences and series of numbers; convergence and divergence.
  • Tools for determining convergence of a series: comparison test, alternating series test, absolute convergence, ratio test.
  • Vectors and vector-valued functions.
  • Multivariable calculus: partial and directional derivatives, linear approximation, representation of a function of two variables by a surface, the chain rule, maxima, minima and saddle-points.
  • First order ordinary differential equations: Separations of variables and integrating factors.

Second order ordinary differential equations: Theory and applications of linear equations with constant coefficients.


Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

Summative Assessments

Homework Exercises

Assessment Type Summative Weighting 20
Assessment Weeks Feedback Weeks

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Solutions provided

Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualAnalyseAbility to determine appropriate techniques to solve various ordinary differential equations of 1st- and 2nd order
ConceptualAnalyseAbility to determine appropriate techniques to compute improper integrals
ConceptualAnalyseAbility to determine appropriate techniques to decide whether a series converges
ConceptualAnalyseAbility to determine appropriate techniques to decide whether a sequence converges
ConceptualAnalyseAbility to determine appropriate techniques to solve problems using partial differentiation
ConceptualUnderstandAbility to state and understand the main definitions and theorems of the course
FactualUnderstandUnderstand what it means for a series to converge
FactualUnderstandUnderstand the concept of partial differentiation
FactualUnderstandUnderstand what it means for a sequence to converge

Exam

Assessment Type Summative Weighting 80
Assessment Weeks Feedback Weeks

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Students have opportunity to discuss script

Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualAnalyseAbility to determine appropriate techniques to decide whether a series converges
ConceptualAnalyseAbility to determine appropriate techniques to decide whether a sequence converges
ConceptualAnalyseAbility to determine appropriate techniques to solve problems using partial differentiation
ConceptualAnalyseAbility to determine appropriate techniques to solve various ordinary differential equations of 1st- and 2nd order
ConceptualAnalyseAbility to determine appropriate techniques to compute improper integrals
ConceptualUnderstandAbility to state and understand the main definitions and theorems of the course
FactualUnderstandUnderstand what it means for a series to converge
FactualUnderstandUnderstand the concept of partial differentiation
FactualUnderstandUnderstand what it means for a sequence to converge

Formative Assessment

There are no assessments for this course.

Resit Assessments

Maximum of resit exam and resit exam with carried forward in-course assessment marks

Assessment Type Summative Weighting 100
Assessment Weeks Feedback Weeks

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualUnderstandUnderstand what it means for a series to converge
ConceptualAnalyseAbility to determine appropriate techniques to decide whether a sequence converges
FactualUnderstandUnderstand what it means for a sequence to converge
ConceptualUnderstandAbility to state and understand the main definitions and theorems of the course
ConceptualAnalyseAbility to determine appropriate techniques to compute improper integrals
ConceptualAnalyseAbility to determine appropriate techniques to decide whether a series converges
ConceptualAnalyseAbility to determine appropriate techniques to solve various ordinary differential equations of 1st- and 2nd order
FactualUnderstandUnderstand the concept of partial differentiation
ConceptualAnalyseAbility to determine appropriate techniques to solve problems using partial differentiation

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