Undergraduate Course: Mathematics for Science and Engineering 1b (MATH08061)
|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
|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: anti-derivatives, definite and indefinite integrals.
Fundamental Theorem of Calculus. Substitution. Area, arc-length, 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.
This syllabus is for guidance purposes only :
AP's, GP's, limits, power series, radius of convergence.
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.
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)
|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.
A-Grade at Higher Mathematics OR B-Grade at A-level Mathematics OR equivalent
Course Delivery Information
|Academic year 2015/16, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
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
|Additional Information (Learning and Teaching)
Students must pass exam and course overall.
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 20%, Examination 80%
||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|
| 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
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
1. Ability to evaluate an integral by anti-differentiation
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 arc-lengths and areas for parametric functions
Differential equations: ability :
1. to identify and solve separable differential equations
2. to solve linear homogeneous first-order differential equations with constant coefficients
3. to find particular solutions for linear differential equations with constant coefficients, for simple right-hand 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
|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 on-line assessment and resource system.
|Graduate Attributes and Skills
|Course organiser||Dr Antony Maciocia
Tel: (0131 6)50 5994
|Course secretary||Ms Marieke Blair
Tel: (0131 6)50 5048
© Copyright 2015 The University of Edinburgh - 18 January 2016 4:23 am