Engineering Tripos Part IB, 2P8: The Engineer in Business (Compulsory), 2020-21
Lecturer and Course Leader
Lecturer
Lecturer
Timing and Structure
Weeks 1-8, Lent Term. 8 x 1-hour sessions including: 3 x 1-hour sessions on economics, 2 x 1-hour sessions on strategy, 3 x 1-hour sessions on marketing. The first three lectures will be delivered live on Zoom.
Aims
The aims of the course are to:
- provide students with a basic understanding of how businesses work, and to give them the language to work effectively with those who work in non-technical roles within a business.
Objectives
As specific objectives, by the end of the course students should be able to:
- gain a preliminary, concise and multi-faceted understanding of issues in running businesses.
Content
The module is structured around three major fields of studies that complement each other, namely economics, marketing, and strategy.
- The sessions on economics aim to introduce the economic nature of the firm, why and how firms grow or contract, and the nature of economic regulation facing firms.
- The sessions on strategy aim to examine how firms develop and maintain competitive advantage; and to help students to develop skills that will allow them to make robust strategic business decisions in the face of uncertainty and complexity.
- The sessions on marketing aim to help students understand core questions in marketing and how marketing contributes to business strategy and firm performance; and to help students to develop strategic and analytical skills in planning and evaluating marketing decisions in the business world.
The Engineer in Business
Sessions on economics (3 x 1-hour sessions):
The economic nature of the firm (1 session)
The theory of the firm (1 session)
The regulation of the firm (1 session)
Sessions on strategy (2 x 1-hour sessions):
What is strategy and how to analyse industries? (1 session)
Types of competitive advantage: Cost leadership and differentiation strategies (1 session)
Sessions on marketing (3 x 1-hour sessions):
Demystifying marketing (1 session)
Strategic brand management (1 session)
Marketing communication in the digital age (1 session)
Further notes
Assessment
A set of multiple-choice questions to be completed over 30 minutes of examination time. The 2019 paper is in proposed format.
Examples papers
Booklists
Please refer to the Booklist for Part IB Courses for complete references to this module, this can be found on the associated Moodle course.
Some helpful references on Economics Sessions:
|
Sloman, J., Garrett, D., Guest, J. and Jones, E. (2019) |
Economics for Business, 8th Edition, Pearson. Chapters 3 (Business Organisations), 13 (Alternative Theories of the Firm), 15 (Growth Strategy), 20 (Reasons for Government Intervention in the Market) and 21 (Government and the Firm). |
E-book via
|
Some helpful references on Strategy Sessions:
|
Magretta, J. (2002) |
“Why Business Models Matter.” Harvard Business Review, 80(5): pp. 86-92 |
E-article via |
|
Porter, M. (1996) |
“What is Strategy?” Harvard Business Review, 74(6): pp. 61-78 |
E-article via |
|
Porter, M. (2008) |
“The Five Competitive Forces that Shape Strategy.” Harvard Business Review, 86(1): pp. 78-93 |
E-article via |
|
MacMillan, I. C. McGrath, G. (1997) |
“Discovering New Points of Differentiation.” Harvard Business Review, 75(4): pp. 133-145 |
E-article via |
Some helpful references on Marketing Sessions:
|
Kotler, P. et al. (2016) |
Marketing Management. 3rd European ed. Harlow: Prentice Hall/Pearson Education ‘Introduction to Marketing.’ ‘The Changing Marketing.’ ‘Managing digital technology in marketing.’ ‘Digital and global brand management strategies.’ |
E-book via Printed books at: HF5415.13.K67 M3 2016 |
|
Day, G. S. (1994) |
"The Capabilities of Market-Driven Organizations." Journal of Marketing, 58(4): pp. 37-52 |
E-article via |
|
Rust, R., Zeithaml, V.A. and Lemon, K. N. (2004) |
“Customer-Centered Brand Management.” Harvard Business Review, 82(9), 110-118 |
E-article via |
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
KU3
Appreciate the social, environmental, ethical, economic and commercial considerations affecting the exercise of their engineering judgement.
D2
Understand customer and user needs and the importance of considerations such as aesthetics.
D3
Identify and manage cost drivers.
S1
The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.
S2
Extensive knowledge and understanding of management and business practices, and their limitations, and how these may be applied appropriately to strategic and tactical issues.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
Last modified: 15/01/2021 20:54
Engineering Tripos Part IB, 2P8: The Engineer in Business (Compulsory), 2019-20
Lecturer
Lecturer
Lecturer
Timing and Structure
Weeks 1-8, Lent Term. 8 x 1-hour sessions including: 3 x 1-hour sessions on economics, 3 x 1-hour sessions on marketing, 2 x 1-hour sessions on strategy
Aims
The aims of the course are to:
- provide students with a basic understanding of how businesses work, and to give them the language to work effectively with those who work in non-technical roles within a business.
Objectives
As specific objectives, by the end of the course students should be able to:
- gain a preliminary, concise and multi-faceted understanding of issues in running businesses.
Content
The module is structured around three major fields of studies that complement each other, namely economics, marketing, and strategy.
- The sessions on economics aim to introduce the economic nature of the firm, why and how firms grow or contract, and the nature of economic regulation facing firms.
- The sessions on marketing aim to help students understand core questions in marketing and how marketing contributes to business strategy and firm performance; and to help students to develop strategic and analytical skills in planning and evaluating marketing decisions in the business world.
- The sessions on strategy aim to examine how firms develop and maintain competitive advantage; and to help students to develop skills that will allow them to make robust strategic business decisions in the face of uncertainty and complexity.
The Engineer in Business
Sessions on economics (3 x 1-hour sessions):
The economic nature of the firm (1 session)
The theory of the firm (1 session)
The regulation of the firm (1 session)
Sessions on marketing (3 x 1-hour sessions):
Demystifying marketing (1 session)
Strategic brand management (1 session)
Marketing communication in the digital age (1 session)
Sessions on strategy (2 x 1-hour sessions):
What is strategy and how to analyse industries? (1 session)
Types of competitive advantage: Cost leadership and differentiation strategies (1 session)
Further notes
Assessment
A set of multiple-choice questions to be completed over 30 minutes of examination time. A sample paper has been uploaded on the Moodle site.
Examples papers
Booklists
Please see the Booklist for Part IB Courses for complete references for this module.
Some helpful references on Economics Sessions:
|
Sloman, J., Garrett, D., Guest, J. and Jones, E. (2016) |
Economics for Business, 7th Edition, Pearson. Chapters 3 (Business Organisations), 14 (Alternative Theories of the Firm), 15 (Growth Strategy), 20 (Reasons for Government Intervention in the Market) and 21 (Government and the Firm). |
E-book via
|
Some helpful references on Marketing Sessions:
|
Kotler, P. et al. (2016) |
Marketing Management. 3rd European ed. Harlow: Prentice Hall/Pearson Education ‘Introduction to Marketing.’ ‘The Changing Marketing.’ ‘Managing digital technology in marketing.’ ‘Digital and global brand management strategies.’ |
E-book via Printed books at: HF5415.13.K67 M3 2016 |
|
Day, G. S. (1994) |
"The Capabilities of Market-Driven Organizations." Journal of Marketing, 58(4): pp. 37-52 |
E-article via |
|
Rust, R., Zeithaml, V.A. and Lemon, K. N. (2004) |
“Customer-Centered Brand Management.” Harvard Business Review, 82(9), 110-118 |
E-article via |
Some helpful references on Strategy Sessions:
|
Magretta, J. (2002) |
“Why Business Models Matter.” Harvard Business Review, 80(5): pp. 86-92 |
E-article via |
|
Porter, M. (1996) |
“What is Strategy?” Harvard Business Review, 74(6): pp. 61-78 |
E-article via |
|
Porter, M. (2008) |
“The Five Competitive Forces that Shape Strategy.” Harvard Business Review, 86(1): pp. 78-93 |
E-article via |
|
MacMillan, I. C. McGrath, G. (1997) |
“Discovering New Points of Differentiation.” Harvard Business Review, 75(4): pp. 133-145 |
E-article via |
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
KU3
Appreciate the social, environmental, ethical, economic and commercial considerations affecting the exercise of their engineering judgement.
D2
Understand customer and user needs and the importance of considerations such as aesthetics.
D3
Identify and manage cost drivers.
S1
The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.
S2
Extensive knowledge and understanding of management and business practices, and their limitations, and how these may be applied appropriately to strategic and tactical issues.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
Last modified: 16/05/2019 12:27
Engineering Tripos Part IB, 2P8: The Engineer in Business (Compulsory), 2018-19
Lecturer
Lecturer
Lecturer
Timing and Structure
Weeks 1-8, Lent Term. 8 x 1-hour sessions including: 3 x 1-hour sessions on economics, 3 x 1-hour sessions on marketing, 2 x 1-hour sessions on strategy
Aims
The aims of the course are to:
- provide students with a basic understanding of how businesses work, and to give them the language to work effectively with those who work in non-technical roles within a business.
Objectives
As specific objectives, by the end of the course students should be able to:
- gain a preliminary, concise and multi-faceted understanding of issues in running businesses.
Content
The module is structured around three major fields of studies that complement each other, namely economics, marketing, and strategy.
- The sessions on economics aim to introduce the economic nature of the firm, why and how firms grow or contract, and the nature of economic regulation facing firms.
- The sessions on marketing aim to help students understand core questions in marketing and how marketing contributes to business strategy and firm performance; and to help students to develop strategic and analytical skills in planning and evaluating marketing decisions in the business world.
- The sessions on strategy aim to examine how firms develop and maintain competitive advantage; and to help students to develop skills that will allow them to make robust strategic business decisions in the face of uncertainty and complexity.
The Engineer in Business
Sessions on economics (3 x 1-hour sessions):
The economic nature of the firm (1 session)
The theory of the firm (1 session)
The regulation of the firm (1 session)
Sessions on marketing (3 x 1-hour sessions):
Demystifying marketing (1 session)
Strategic brand management (1 session)
Marketing communication in the digital age (1 session)
Sessions on strategy (2 x 1-hour sessions):
What is strategy and how to analyse industries? (1 session)
Types of competitive advantage: Cost leadership and differentiation strategies (1 session)
Further notes
Assessment
A set of multiple-choice questions to be completed over 30 minutes of examination time. A sample paper has been uploaded on the Moodle site.
Examples papers
Booklists
Please see the Booklist for Part IB Courses for complete references for this module.
Some helpful references on Economics Sessions:
|
Sloman, J., Garrett, D., Guest, J. and Jones, E. (2016) |
Economics for Business, 7th Edition, Pearson. Chapters 3 (Business Organisations), 14 (Alternative Theories of the Firm), 15 (Growth Strategy), 20 (Reasons for Government Intervention in the Market) and 21 (Government and the Firm). |
E-book via
|
Some helpful references on Marketing Sessions:
|
Kotler, P. et al. (2016) |
Marketing Management. 3rd European ed. Harlow: Prentice Hall/Pearson Education ‘Introduction to Marketing.’ ‘The Changing Marketing.’ ‘Managing digital technology in marketing.’ ‘Digital and global brand management strategies.’ |
E-book via Printed books at: HF5415.13.K67 M3 2016 |
|
Day, G. S. (1994) |
"The Capabilities of Market-Driven Organizations." Journal of Marketing, 58(4): pp. 37-52 |
E-article via |
|
Rust, R., Zeithaml, V.A. and Lemon, K. N. (2004) |
“Customer-Centered Brand Management.” Harvard Business Review, 82(9), 110-118 |
E-article via |
Some helpful references on Strategy Sessions:
|
Magretta, J. (2002) |
“Why Business Models Matter.” Harvard Business Review, 80(5): pp. 86-92 |
E-article via |
|
Porter, M. (1996) |
“What is Strategy?” Harvard Business Review, 74(6): pp. 61-78 |
E-article via |
|
Porter, M. (2008) |
“The Five Competitive Forces that Shape Strategy.” Harvard Business Review, 86(1): pp. 78-93 |
E-article via |
|
MacMillan, I. C. McGrath, G. (1997) |
“Discovering New Points of Differentiation.” Harvard Business Review, 75(4): pp. 133-145 |
E-article via |
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
KU3
Appreciate the social, environmental, ethical, economic and commercial considerations affecting the exercise of their engineering judgement.
D2
Understand customer and user needs and the importance of considerations such as aesthetics.
D3
Identify and manage cost drivers.
S1
The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.
S2
Extensive knowledge and understanding of management and business practices, and their limitations, and how these may be applied appropriately to strategic and tactical issues.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
Last modified: 04/04/2019 09:22
Engineering Tripos Part IB, 2P8: Introductory Business Economics, 2017-18
Lecturer
Timing and Structure
Weeks 1-8, Lent Term. 8 lectures. Compulsory Section for Paper 8.
Aims
The aims of the course are to:
- Introduce students to some basic concepts, categories and tools of economics, both as general background and in preparation for other economics courses in the Engineering Tripos.
Content
The course consists of eight lectures
- Introduction to Economics
- Microeconomics: Demand, Supply and Market Equilibrium
- Microeconomics: Costs and the Firm
- Microeconomics: Market Structure
- Macroeconomics: Introduction
- Macroeconomics: the Components of Aggregate Demand
- Macroeconomic: Policy
- Review
Booklists
Please see the Booklist for Part IB Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
KU3
Appreciate the social, environmental, ethical, economic and commercial considerations affecting the exercise of their engineering judgement.
D2
Understand customer and user needs and the importance of considerations such as aesthetics.
D3
Identify and manage cost drivers.
S1
The ability to make general evaluations of commercial risks through some understanding of the basis of such risks.
S2
Extensive knowledge and understanding of management and business practices, and their limitations, and how these may be applied appropriately to strategic and tactical issues.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
Last modified: 28/11/2017 06:59
[node:field-syllabus-course-year:parent:name], Engineering Tripos Part IB, 2017-18
Lecturer
Timing and Structure
1 or 2 lectures per week in weeks 1-4. 6 lectures.
Aims
The aims of the course are to:
- Show how concepts of probability can be applied to engineering applications.
Objectives
As specific objectives, by the end of the course students should be able to:
- Explain and use simple ideas of probability, mean, variance, etc.
- Manipulate random variables and probability density functions.
- Solve simple statistical problems of engineering importance.
Content
Probability and Statistics
- Probability.
- Conditional probability and independence.
- Permutations and combinations.
- Binomial and Poisson distributions.
- Expectation of a discrete random variable.
- Variance and standard deviation.
- Probability density function for a continuous random variable.
- Mean and variance.
- Normal and exponential distribution.
- Tests of significance and confidence intervals
Further Information
Further information, including details of each lecture and hand-outs are available here: http://mlg.eng.cam.ac.uk/teaching/1BP7
Booklists
Please see the Booklist for Part IB Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
Last modified: 06/06/2017 14:15
Engineering Tripos Part IB, 2P7: Linear Algebra, 2025-26
Lecturer
Timing and Structure
Weeks 4 & 8 Lent Term 1 lecture/week; weeks 5-7 Lent Term 2 lectures/week. 8 lectures
Aims
The aims of the course are to:
- Introduce the ideas and techniques of Linear Algebra, and illustrate some of their applications in engineering.
Objectives
As specific objectives, by the end of the course students should be able to:
- For all objectives, complete calculations by hand for small problems, or by using Matlab for larger problems (the IB Computing Course deals with this in detail).
- Solve a set of linear equations using Gaussian elimination, and complete the LU factorisation of a matrix.
- Understand, and be able to calculate bases for the four fundamental subspaces of a matrix.
- Calculate the least squares solution of a set of linear equations.
- Orthogonalize a set of vectors, complete the QR factorisation of a matrix, and be able to use this to find the least squares solution of a set of linear equations.
- Find the eigenvalues and eigenvectors of a matrix, and complete the A = SL S-1 or A = QL QT factorisations as appropriate.
- Find the SVD of a matrix, and to understand how this can be used to calculate the rank of the matrix, and to provide a basis for the each of its fundamental subspaces.
Content
- Solution of the matrix equation Ax = b: Gaussian elimination, LU factorization, the four fundamental subspaces of a matrix.
- Least squares solution of Ax = b for an m x n matrix with n independent columns: Gram-Schmidt orthogonalization, QR decomposition.
- Solution of Ax = l x, eigenvectors and eigenvalues.
- Singular Value Decomposition.
Booklists
Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 05/06/2025 11:17
Engineering Tripos Part IB, 2P7: Linear Algebra, 2024-25
Lecturer
Timing and Structure
Weeks 4 & 8 Lent Term 1 lecture/week; weeks 5-7 Lent Term 2 lectures/week. 8 lectures
Aims
The aims of the course are to:
- Introduce the ideas and techniques of Linear Algebra, and illustrate some of their applications in engineering.
Objectives
As specific objectives, by the end of the course students should be able to:
- For all objectives, complete calculations by hand for small problems, or by using Matlab for larger problems (the IB Computing Course deals with this in detail).
- Solve a set of linear equations using Gaussian elimination, and complete the LU factorisation of a matrix.
- Understand, and be able to calculate bases for the four fundamental subspaces of a matrix.
- Calculate the least squares solution of a set of linear equations.
- Orthogonalize a set of vectors, complete the QR factorisation of a matrix, and be able to use this to find the least squares solution of a set of linear equations.
- Find the eigenvalues and eigenvectors of a matrix, and complete the A = SL S-1 or A = QL QT factorisations as appropriate.
- Find the SVD of a matrix, and to understand how this can be used to calculate the rank of the matrix, and to provide a basis for the each of its fundamental subspaces.
Content
- Solution of the matrix equation Ax = b: Gaussian elimination, LU factorization, the four fundamental subspaces of a matrix.
- Least squares solution of Ax = b for an m x n matrix with n independent columns: Gram-Schmidt orthogonalization, QR decomposition.
- Solution of Ax = l x, eigenvectors and eigenvalues.
- Singular Value Decomposition.
Booklists
Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 30/07/2024 08:50
Engineering Tripos Part IB, 2P7: Linear Algebra, 2023-24
Lecturer
Timing and Structure
Weeks 4 & 8 Lent Term 1 lecture/week; weeks 5-7 Lent Term 2 lectures/week. 8 lectures
Aims
The aims of the course are to:
- Introduce the ideas and techniques of Linear Algebra, and illustrate some of their applications in engineering.
Objectives
As specific objectives, by the end of the course students should be able to:
- For all objectives, complete calculations by hand for small problems, or by using Matlab for larger problems (the IB Computing Course deals with this in detail).
- Solve a set of linear equations using Gaussian elimination, and complete the LU factorisation of a matrix.
- Understand, and be able to calculate bases for the four fundamental subspaces of a matrix.
- Calculate the least squares solution of a set of linear equations.
- Orthogonalize a set of vectors, complete the QR factorisation of a matrix, and be able to use this to find the least squares solution of a set of linear equations.
- Find the eigenvalues and eigenvectors of a matrix, and complete the A = SL S-1 or A = QL QT factorisations as appropriate.
- Find the SVD of a matrix, and to understand how this can be used to calculate the rank of the matrix, and to provide a basis for the each of its fundamental subspaces.
Content
- Solution of the matrix equation Ax = b: Gaussian elimination, LU factorization, the four fundamental subspaces of a matrix.
- Least squares solution of Ax = b for an m x n matrix with n independent columns: Gram-Schmidt orthogonalization, QR decomposition.
- Solution of Ax = l x, eigenvectors and eigenvalues.
- Singular Value Decomposition.
Booklists
Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 30/05/2023 15:14
Engineering Tripos Part IB, 2P7: Linear Algebra, 2022-23
Lecturer
Timing and Structure
Weeks 4 & 8 Lent Term 1 lecture/week; weeks 5-7 Lent Term 2 lectures/week. 8 lectures
Aims
The aims of the course are to:
- Introduce the ideas and techniques of Linear Algebra, and illustrate some of their applications in engineering.
Objectives
As specific objectives, by the end of the course students should be able to:
- For all objectives, complete calculations by hand for small problems, or by using Matlab for larger problems (the IB Computing Course deals with this in detail).
- Solve a set of linear equations using Gaussian elimination, and complete the LU factorisation of a matrix.
- Understand, and be able to calculate bases for the four fundamental subspaces of a matrix.
- Calculate the least squares solution of a set of linear equations.
- Orthogonalize a set of vectors, complete the QR factorisation of a matrix, and be able to use this to find the least squares solution of a set of linear equations.
- Find the eigenvalues and eigenvectors of a matrix, and complete the A = SL S-1 or A = QL QT factorisations as appropriate.
- Find the SVD of a matrix, and to understand how this can be used to calculate the rank of the matrix, and to provide a basis for the each of its fundamental subspaces.
Content
- Solution of the matrix equation Ax = b: Gaussian elimination, LU factorization, the four fundamental subspaces of a matrix.
- Least squares solution of Ax = b for an m x n matrix with n independent columns: Gram-Schmidt orthogonalization, QR decomposition.
- Solution of Ax = l x, eigenvectors and eigenvalues.
- Singular Value Decomposition.
Booklists
Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 24/05/2022 14:09
Engineering Tripos Part IB, 2P7: Linear Algebra, 2021-22
Lecturer
Timing and Structure
Weeks 4 & 8 Lent Term 1 lecture/week; weeks 5-7 Lent Term 2 lectures/week. 8 lectures
Aims
The aims of the course are to:
- Introduce the ideas and techniques of Linear Algebra, and illustrate some of their applications in engineering.
Objectives
As specific objectives, by the end of the course students should be able to:
- For all objectives, complete calculations by hand for small problems, or by using Matlab for larger problems (the IB Computing Course deals with this in detail).
- Solve a set of linear equations using Gaussian elimination, and complete the LU factorisation of a matrix.
- Understand, and be able to calculate bases for the four fundamental subspaces of a matrix.
- Calculate the least squares solution of a set of linear equations.
- Orthogonalize a set of vectors, complete the QR factorisation of a matrix, and be able to use this to find the least squares solution of a set of linear equations.
- Find the eigenvalues and eigenvectors of a matrix, and complete the A = SL S-1 or A = QL QT factorisations as appropriate.
- Find the SVD of a matrix, and to understand how this can be used to calculate the rank of the matrix, and to provide a basis for the each of its fundamental subspaces.
Content
- Solution of the matrix equation Ax = b: Gaussian elimination, LU factorization, the four fundamental subspaces of a matrix.
- Least squares solution of Ax = b for an m x n matrix with n independent columns: Gram-Schmidt orthogonalization, QR decomposition.
- Solution of Ax = l x, eigenvectors and eigenvalues.
- Singular Value Decomposition.
Booklists
Please refer to the Booklist for Part IB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P8
Ability to apply engineering techniques taking account of a range of commercial and industrial constraints.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 01/10/2021 17:22
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