PHY1035 : Algebra, Multivariable Calculus & Differential Equations

• Offered for Year: 2020/21
• Module Leader(s): Dr Gerasimos Rigopoulos
• Lecturer: Professor Tamara Rogers
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
Semesters
 Semester 1 Credit Value: 10 Semester 2 Credit Value: 10 ECTS Credits: 10

Aims

To lay the mathematical foundations for more advanced mathematics needed to describe
physical systems. Students will learn how to solve simple differential equations and how known computational tools of the calculus of functions of a single variable generalize to functions of many variables.

Outline Of Syllabus

Complex numbers, arithmetic, Argand diagram, polar form, de Moivre's theorem, powers and roots of unity.

Vectors: sums, products (scalar, dot, cross), equations of lines and planes, orthogonality, norm.

Linear algebra: row operations, solution of linear equations, Gaussian elimination, matrix operations, determinants, inverting matrices, eigenvectors, quadratic forms.

A general introduction to differential equations: Partial and ordinary; linear and non-linear; homogeneous and non- homogeneous. First-order ordinary differential equations (ODEs): direct integration; separation of variables, homogeneous equations, general linear first order ODEs. Second-order linear ODEs: Constant coefficients, inhomogeneous equations. Partial differentiation of multivariable functions: stationary points, chain rule. Integration of multivariable functions: Double and triple integration, change of variables, polar, spherical and cylindrical coordinates.

Teaching Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture91:009:00Present in Person
Guided Independent StudyAssessment preparation and completion301:0030:00Completion of in course assessment
Structured Guided LearningLecture materials361:0036:00Non-Synchronous Activities
Scheduled Learning And Teaching ActivitiesLecture91:009:00Synchronous On-Line Material
Structured Guided LearningStructured non-synchronous discussion181:0018:00Non Synchronous Discussion to Support Learning
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Office Hour or Discussion Board Activity
Guided Independent StudyIndependent study941:0094:00Preparation time for lectures, background reading, coursework review
Total200:00
Jointly Taught With
Code Title
MAS1609Algebra, Multivariable Calculus & Differential Equations
Teaching Rationale And Relationship

Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Alternatives will be offered to students unable to be present-in-person due to the prevailing C-19 circumstances.
Student’s should consult their individual timetable for up-to-date delivery information.

Assessment Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A60In class test
Other Assessment
Description Semester When Set Percentage Comment
Written exercise1M30N/A
Written exercise2M10N/A
Assessment Rationale And Relationship

The course assessments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.