Undergraduate Course: Mathematics for Science and Engineering 1b (MATH08061)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 8 (Year 1 Undergraduate) 
Availability  Not available to visiting students 
SCQF Credits  20 
ECTS Credits  10 
Summary  **THIS COURSE IS FOR RETAKING STUDENTS ONLY**
AP's, GP's, limits, power series, radius of convergence.
Basic differentiation: rate of change, simple derivatives, rules of differentiation, maxima/minima. Derivatives of powers, polynomials, rational functions, circular functions. Chain rule. Differentiation of exponential and related functions, differentiation of inverse functions, parametric and implicit differentiation, higher derivatives. Partial differentiation, directional derivatives, chain rule, total derivative, exact differentials. L'Hopital's rule. Taylor's Theorem and related results. Maclaurin series.
Basic integration: antiderivatives, definite and indefinite integrals.
Fundamental Theorem of Calculus. Substitution. Area, arclength, volume, mean values, rms values and other summation applications of integration. Integration by parts. Limits and improper integrals.
Differential equations. General and particular solutions, boundary values.
Separable differential equations. First order linear differential equations with constant coefficients. 
Course description 
This syllabus is for guidance purposes only :
AP's, GP's, limits, power series, radius of convergence.
Differentiation.
Rates of change, definition of derivative, slope, speed, acceleration, maximum and minimum values.
Techniques of differentiation. Rules. Derivatives of powers, polynomials, rational functions, circular functions. Chain rule. Differentiation of exponential and related functions, parametric and implicit differentiation, higher derivatives.
Integration, basics and Fundamental Theorem of Calculus.
Techniques of integration.
Applications of Integration. Volumes of solids of revolution, mean values, rms, arclength and surface area.
Improper integrals
Taylor's Theorem and related results. Maclaurin series, L'H\^opital's rule, interpolation.
Calculus of vectors.
Partial Differentiation, directional derivatives, chain rule, total derivative, exact differentials.
ODE's. Classification of DE's. Ordinary/Partial, independent/dependent variables, order, linear/nonlinear, homogeneous/nonhomogeneous.
Solving DE's. General and particular solutions, boundary values.
First order ODE's. Separable, linear, exact solutions.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  Students MUST NOT also be taking
Calculus and its Applications (MATH08058)

Other requirements  This course is restricted to students for whom it is a compulsory part of their Degree Programme.
AGrade at Higher Mathematics OR BGrade at Alevel Mathematics OR equivalent 
Course Delivery Information

Academic year 2015/16, Not available to visiting students (SS1)

Quota: 50 
Course Start 
Semester 2 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Lecture Hours 33,
Seminar/Tutorial Hours 21,
Supervised Practical/Workshop/Studio Hours 10,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
129 )

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

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20%, Examination 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)  Mathematics for Science and Engineering 1b (MATH08061)  3:00   Resit Exam Diet (August)  Mathematics for Science and Engineering 1b  3:00  
Learning Outcomes
Series :
1. Ability to sum arithmetic and geometric series
2. Understanding the nature of power series and the radius of convergence
3. Ability to undertake simple calculations using the geometric, binomial, exponential and trigonometric series
4. Ability to construct Maclaurin and Taylor series
Differentiation :
1. Understanding and application of derivative as a rate of change; understanding its graphical interpretation
2. Ability to differentiate polynomials in standard form and all powers of x, including higher derivatives
3. Ability to use the product, quotient and chain rules
4. Ability to use differentiation to solve optimisation problems
5. Ability to differentiate and integrate each of the trigonometric functions.
6. Ability to differentiate inverse functions including those for sin and tan
7. Understanding of simple calculus properties of hyperbolic functions
8. Ability to differentiate implicit functions
9. Ability to calculate simple partial derivatives
10. Ability to calculate directional derivatives
11. Ability to perform differentiation following the motion
12. Ability to construct and use differential expressions
13. Ability to understand the notation used in thermodynamic
Integration :
1. Ability to evaluate an integral by antidifferentiation
2. Understanding an integral as a sum
3. Ability to integrate polynomials in standard form and all powers of x
4. Ability to use simple rearrangements (trigonometric and partial fractions) and simple substitution
5. Ability to construct integrals using the summation definition, with applications
6. Ability to integrate squares and products of sin and cos
7. Ability to integrate 1/(ax+b) and f'/f; ability to differentiate and integrate exp(x)
8. Ability to evaluate integrals in terms of inverse circular and hyperbolic functions
9. Ability to use integration by parts
10. Ability to use substitutions of various types
11. Ability to calculate arclengths and areas for parametric functions
Differential equations: ability :
1. to identify and solve separable differential equations
2. to solve linear homogeneous firstorder differential equations with constant coefficients
3. to find particular solutions for linear differential equations with constant coefficients, for simple righthand sides
4. to fit initial and boundary conditions
Limits and Continuity: ability :
1. to use L'Hopital's Rule
2. to use the limits of combinations of log, polynomial and exponential functions
3. to evaluate 'improper' integrals

Reading List
Students will be assumed to have acquired their personal copy of :
"Modern Engineering Mathematics", 4th Edition by Glyn James.
ISBN: 9781780166476 CU.James: Modern Maths Pack 2011.
Note that this is a special edition for Edinburgh University Students.
It is only available from Blackwell's bookshop on South Bridge in Edinburgh.
It includes essential access to the online assessment and resource system.

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  mse1b 
Contacts
Course organiser  Dr Antony Maciocia
Tel: (0131 6)50 5994
Email: A.Maciocia@ed.ac.uk 
Course secretary  Ms Marieke Blair
Tel: (0131 6)50 5048
Email: M.Blair@ed.ac.uk 

