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                                                                                                                                                      Teaching  Contact                                                                                                                                                                                                                                                                 Self-                                                                                                                                                   Placement                                                                                                                                                    Total 
                                                                                                                                                                                                        component                                                                                                                                                     type                                                                                                                       hours                                                                                                                                                  directed                                                                                                                                                hours                                                                                                                                                        student 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        study                                                                                                                                                                                                                                                                                                                learning 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        hours                                                                                                                                                                                                                                                                                                                hours 
                                                                                                                                                                                                        Linear                                                                                                                                                        Lecture 20                                                                                                                                                                                                                                                                        70                                                                                                                                                      0                                                                                                                                                            90 
                                                                                                                                                                                                        Algebra 
                                                                                                                                                                                                        lectures 
                                                                                                                                                                                                        Tutorial Tutorial 10                                                                                                                                                                                                                                                                                                                                                                                                                            10  0  20 
                                                                                                                                                                                                        Calculus                                                                                                                                                      Lecture 20                                                                                                                                                                                                                                                                        70                                                                                                                                                      0                                                                                                                                                            90 
                                                                                                                                                                                                        lectures 
                                                                                                                                                                                                        TOTALS:                                                                                                                                                                                                                                                                                  50                                                                                                                                                     150                                                                                                                                                     0                                                                                                                                                            200 
                                                                                                                                                                                             
                                                                                                                                                                                             
                                                                                                                                                                                             
                                                                                                                                                                                             
                                                                                                                                                                                             
                                                                                                                                                                                             
                  WHAT TYPES OF ASSESSMENT AND FEEDBACK CAN I EXPECT? 
                   
                  Assessments 
                   
                  Coursework and exam. 
                   
                  Assessment pattern: 
                   
                   Assessment         Assessment  Weighting Minimum  Pass/Fail? 
                   component          type                        qualifying 
                                                                  mark 
                   Calculus           Written        5 40 N/A 
                   coursework 1       assignment, 
                                      including 
                                      essay 
                   Calculus           Written        5 40 N/A 
                   coursework 2       assignment, 
                                      including 
                                      essay 
                   Examination (3     Written        80 40 N/A 
                   hours)             Exam 
                   Linear Algebra     Written        5 40 N/A 
                   coursework 1       assignment, 
                                      including 
                                      essay 
                   Linear Algebra     Written        5 40 N/A 
                   coursework 2       assignment, 
                                      including 
                                      essay 
                   
                  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