Undergraduate Course: Several Variable Calculus and Differential Equations (MATH08063)
|School||School of Mathematics
||College||College of Science and Engineering
||Availability||Available to all students
|Credit level (Normal year taken)||SCQF Level 8 (Year 2 Undergraduate)
|Home subject area||Mathematics
||Other subject area||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
|Displayed in Visiting Students Prospectus?||No
Course Delivery Information
|Delivery period: 2013/14 Semester 1, Available to all students (SV1)
||Learn enabled: Yes
|Course Start Date
|Breakdown of Learning and Teaching activities (Further Info)
Lecture Hours 44,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
Students must pass exam and course overall.
|Breakdown of Assessment Methods (Further Info)
|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, arc-length 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 second-order 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.
|See 'Breakdown of Assessment Methods' and 'Additional Notes' above.|
||Week 1: Vectors and Vector functions: Book 1, Chapters 13 & 14.
Week 2-4: Partial derivatives: Book 1, Chapter 15.
Week 4-7: Multiple integrals and Vector Calculus: Book 1, Chapters 16 & 17.
Week 8-9: First order differential equations: Book 2, Chapters 1 & 2.
Week 10-11: Second order differential equations and series solutions: Book 2, Chapters 3 & 5.
||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.)
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.)
|Course organiser||Dr Tom Mackay
Tel: (0131 6)50 5058
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427
© Copyright 2013 The University of Edinburgh - 10 October 2013 4:51 am