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: 2012/13 Semester 1, Available to all students (SV1)

Learn enabled: Yes 
Quota: None 
Location 
Activity 
Description 
Weeks 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
King's Buildings  Lecture  Th A, JCMB  111  12:10  13:00      King's Buildings  Lecture  Th A, JCMB  111   12:10  13:00     King's Buildings  Lecture  Th A, JCMB  111    13:10  14:00    King's Buildings  Lecture  Th A, JCMB  111      12:10  13:00  King's Buildings  Tutorial  Teaching Studio 3217, JCMB  111     11:10  12:00 or 12:10  13:00  
First Class 
Week 1, Monday, 12:10  13:00, Zone: King's Buildings. Th A, JCMB 
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
Up to 15% Continuous Assessment, the remainder examination. 
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.)
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 

