Undergraduate Course: Several Variable Calculus and Differential Equations (MATH08063)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Course type  Standard 
Availability  Available to all students 
Credit level (Normal year taken)  SCQF Level 8 (Year 2 Undergraduate) 
Credits  20 
Home subject area  Mathematics 
Other subject area  None 
Course website 
None 
Taught in Gaelic?  No 
Course description  Students taking this course should have either passed 'Calculus and its Applications' or be taking 'Accelerated Algebra and Calculus for Direct Entry' :
A several variable calculus course, and a first methods course for differential equations. 
Information for Visiting Students
Prerequisites  None 
Displayed in Visiting Students Prospectus?  No 
Course Delivery Information

Delivery period: 2013/14 Semester 1, Available to all students (SV1)

Learn enabled: Yes 
Quota: None 

Web Timetable 
Web Timetable 
Course Start Date 
16/09/2013 
Breakdown of Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Lecture Hours 44,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
139 )

Additional Notes 
Students must pass exam and course overall.

Breakdown of Assessment Methods (Further Info) 
Written Exam
85 %,
Coursework
15 %,
Practical Exam
0 %

Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)  Several Variable Calculus and Differential Equations (MATH08063)  3:00  
Summary of Intended Learning Outcomes
1. Calculation dot product, cross product, arclength and curvature.
2. Knowledge of limits and continuity for functions of several variables.
3. Calculating first and second order partial derivatives from formulae, and from first principles.
4. Calculating the gradient function, and the derivative map.
5. Using the chain rule to calculate partial derivatives of composite functions.
6. Identifying local extrema and critical points. Use the Hessian matrix to investigate the form of a surface at a critical point. Identify when the Hessian is positive definite, in two and three dimensions, using the subdeterminant criterion.
7. Using the Lagrange multiplier method to find local extrema of functions, under one constraint only.
8. Calculating easy double integrals. Change the order of integration in double integrals, for easy regions.
9. Calculating line integrals and surface integrals for easy functions. Use Green's Theorem in the plane.
10. Computation of grad, div, curl.
11. Use of Stokes' and divergence theorem in simple explicit cases.
12. Knowledge of direction fields and ability to classify differential equations.
13. Solution of first order linear ODE by separation, integrating factor and also numerically via Euler¿s method
14. Solution of any secondorder linear homogeneous equation or system with constant coefficient, and inhomogeneous equation with trig or exponential or constant or periodic rhs, or by variation of parameters, or by series expansions. 
Assessment Information
See 'Breakdown of Assessment Methods' and 'Additional Notes' above. 
Special Arrangements
None 
Additional Information
Academic description 
Not entered 
Syllabus 
Week 1: Vectors and Vector functions: Book 1, Chapters 13 & 14.
Week 24: Partial derivatives: Book 1, Chapter 15.
Week 47: Multiple integrals and Vector Calculus: Book 1, Chapters 16 & 17.
Week 89: First order differential equations: Book 2, Chapters 1 & 2.
Week 1011: Second order differential equations and series solutions: Book 2, Chapters 3 & 5. 
Transferable skills 
Not entered 
Reading list 
Students are expected to have a personal copies of :
Book 1: Calculus, International Metric Edition 6e by James Stewart. (This book is also relevant for Y1 courses.)
Or
Essential Calculus : Early Transcendentals, International Metric Edition, 2nd Edition
Book 2: Elementary Differential Equations and Boundary Value Problems, 9th Edition by William E. Boyce and Richard C. DiPrima (This book is also relevant for Y3 courses.)

Study Abroad 
Not entered 
Study Pattern 
Not entered 
Keywords  SVCDE 
Contacts
Course organiser  Dr Tom Mackay
Tel: (0131 6)50 5058
Email: T.Mackay@ed.ac.uk 
Course secretary  Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk 

