Undergraduate Course: Several Variable Calculus and Differential Equations (MATH08063)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 8 (Year 2 Undergraduate) 
Availability  Available to all students 
SCQF Credits  20 
ECTS Credits  10 
Summary  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. 
Course description 
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.

Information for Visiting Students
Prerequisites  None 
Course Delivery Information

Academic year 2014/15, Available to all students (SV1)

Quota: None 
Course Start 
Semester 1 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Lecture Hours 44,
Seminar/Tutorial Hours 11,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
138 )

Additional Information (Learning and Teaching) 
Students must pass exam and course overall.

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

Additional Information (Assessment) 
Coursework 15%, Examination 85% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)  Several Variable Calculus and Differential Equations (MATH08063)  3:00   Resit Exam Diet (August)  Several Variable Calculus and Differential Equations (MATH08063)  3:00  
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.

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.)

Additional Information
Graduate Attributes and Skills 
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 

