MODULE SPECIFICATION – UNDERGRADUATE PROGRAMMES KEY FACTS Module name Calculus and Linear Algebra (Maths 2) Module code AS2051 School Cass Business School Department or equivalent UG Programme UK credits 20 ECTS 10.0 Level 5 Delivery location (partnership programmes only)

MODULE SUMMARY Module outline and aims To provide additional mathematical tools required for core statistical and actuarial modules [Calculus] To set up a framework for treating functions of several real variables and consider further methods for solving ordinary differential equations. [Linear Algebra] To introduce the elementary features of linear algebra. Content outline Functions of several variables: Differentiation: definition of partial derivative for function of several variables, chain rules, differential, transformation of partial derivatives. Method of Lagrange multipliers. Integration: standard coordinate systems in R2 and R3, integration in R2 and R3, iterated integrals, change of variables, Jacobians. Differential Equations: Ordinary differential equations: linear; constant coefficient order greater than two; variable coefficient, one solution of the complementary function known, variation of parameters, introduction to solution in series. Laplace Transforms: Introduction to Laplace Transforms; inversion by partial fractions; application to solution of ordinary differential equations. Linear Algebra Vector spaces, linear combinations and subspaces, spanning sets, linear independence and bases, dimension. Linear transformations, isomorphisms, matrix representation, change of basis and similar matrices. Eigenvalues and eigenvectors of matrices, diagonalisation of symmetric matrices. The Cayley-Hamilton Theorem. Inner products, orthonormal bases, the Gram-Schmidt process, orthogonal transformations.

WHAT WILL I BE EXPECTED TO ACHIEVE? On successful completion of this module, you will be expected to be able to: Knowledge and understanding: - Demonstrate an understanding of the calculus of several variables and associated

applications. - Demonstrate an understanding of vector spaces and linear transformations Skills: - Improve manipulative skills in the application of calculus - Use tolls for thinking logically - Solve relevant linear ODEs - Apply methods of linear algebra Values and attitudes: - Understand the importance of formal proofs and abstract definitions in the formulation

and solution of mathematical problems. HOW WILL I LEARN? Lectures and tutorials. Teaching pattern: Teaching component

Teaching type

Contact hours

Self-directed study hours

Placement hours

Total student learning hours

Linear Algebra lectures

Lecture 20 70 0 90

Tutorial Tutorial 10 10 0 20 Calculus lectures

Lecture 20 70 0 90

TOTALS: 50 150 0 200

WHAT TYPES OF ASSESSMENT AND FEEDBACK CAN I EXPECT? Assessments Coursework and exam. Assessment pattern: Assessment component

Assessment type

Weighting Minimum qualifying mark

Pass/Fail?

Calculus coursework 1

Written assignment, including essay

5 40 N/A

Calculus coursework 2

Written assignment, including essay

5 40 N/A

Examination (3 hours)

Written Exam

80 40 N/A

Linear Algebra coursework 1

Written assignment, including essay

5 40 N/A

Linear Algebra coursework 2

Written assignment, including essay

5 40 N/A

Assessment criteria Assessment Criteria are descriptions of the skills, knowledge or attributes students need to demonstrate in order to complete an assessment successfully and Grade-Related Criteria are descriptions of the skills, knowledge or attributes students need to demonstrate to achieve a certain grade or mark in an assessment. Assessment Criteria and Grade-Related Criteria for module assessments will be made available to students prior to an assessment taking place. More information will be available from the module leader. Feedback on assessment Following an assessment, students will be given their marks and feedback in line with the Assessment Regulations and Policy. More information on the timing and type of feedback that will be provided for each assessment will be available from the module leader.

Assessment Regulations The Pass mark for the module is 40%. Any minimum qualifying marks for specific assessments are listed in the table above. The weighting of the different components can also be found above. The Programme Specification contains information on what happens if you fail an assessment component or the module.

INDICATIVE READING LIST Calculus, T.M. Apostol (Blaisdell, 1957). Salas and Hille's Calculus: One and Several Variables, (Wiley, 1995). Advanced Engineering Mathematics, E Kreyszig (Wiley, 1988). 3000 Solved Problems in Linear Algebra, S. Lipschutz (McGraw-Hill, 1989) Schaum series. Schaum's Outline of Theory and Problems of Linear Algebra, S. Lipschutz (McGraw Hill, 1991). Linear Algebra done right, S. Axler (Springer, 1997). Algebra, P M Cohn (vol 1, Wiley, 1974). A Survey of Modern Algebra, S MacLane and G Birkhoff (Collier-MacMillan, 1965). Mathematical Methods for Physics and Engineers by K. F. Riley, M. P. Hobson & S. J. Bence. Student Solution Manual for Mathematical Methods for Physics and Engineers by K. F. Riley, M. P. Hobson & S. J. Bence. Version: 2.0 Version date: July 2013 For use from: 2013-14

Appendix: see http://www.hesa.ac.uk/content/view/1805/296/ for the full list of JACS codes and descriptions CODES HESA Code Description Price Group 24 Mathematics C

JACS Code Description Percentage (%) N323 The application of statistical

concepts within the financial industry.

100