Module manager: Dr Alison Parker, Prof Steven Tobias
Email: A.E.Parker@leeds.ac.uk, S.M.Tobias@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2013/14
Good grade in A-level Mathematics or equivalent.
| MATH1050 | Calculus and Mathematical Analysis |
| MATH1055 | Numbers and Vectors |
| MATH1060 | Introductory Linear Algebra |
| MATH1331 | Linear Algebra with Applications |
| MATH1400 | Modelling with Differential Equations |
This module is not approved as an Elective
This module introduces students to several fundamental topics of mathematics. Calculus is an essential tool in many areas of mathematics. This module consolidates basic calculus material from A-level, extends the syllabus to include more advanced techniques, and introduces elements of the analysis required to formalise the subject. These techniques lead to methods for solving simple ordinary differential equations. Linear algebra provides a basis for wide areas of mathematics and this module provides the essential foundation for this topic. Students will complement theoretical work with projects and assignments using the mathematical computer package Maple.
On completion of this module, students should:
- be able to differentiate functions of one variable and determine the location and nature of turning points;
- be able to compute the Taylor series of functions of one variable;
- be comfortable with the calculus of several variables;
- be able to use a variety of methods to integrate simple functions;
- be aware of the analytical basis of calculus as expressed in rigorous definitions and theorems such as the Fundamental Theorem of Calculus;
- be able to solve systems of equations by row reduction;
- be able to manipulate matrices and vectors and understand their basic properties;
- appreciate the value and limitations of computational methods, and be able to perform simple computational tasks using Maple;
- have demonstrated problem solving and modelling, communication, and group-working skills.
- Functions and their inverses. Continuity and discontinuity. Graphs of functions.
- Differentiation. Calculations from first principles. Non-differentiability.
- Chain rule, product rule, extrema, Taylor series.
- Intermediate value, Rolle's and Mean Theorems.
- Functions of several variables.
- Partial derivatives, directional derivatives, multivariable chain rule.
- Stationary points of functions of two variables. Conditions for a stationary point. Criteria for extrema. Lagrange multipliers.
- Gradients of scalar functions. Tangent planes.
- Implicit differentiation. Change of variables. Solution of exact equations.
- Integration. Areas under curves. Riemann integration. Calculations from first principles.
- Definite and indefinite integrals. Integration techniques.
- Fundamental theorem of the calculus.
- Systems of equations. Gaussian elimination. Echelon form.
- Vectors and matrices. Inverses. Transposes.
- Determinants. Computation. Cramer's rule.
- Introduction to MAPLE as a tool for numerical, graphical and symbolic computation.
- Vectors in 2 and 3 dimensions. Dot and cross products. Geometrical interpretation.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Workshop | 8 | 1 | 8 |
| Lectures | 55 | 1 | 55 |
| Tutorial | 11 | 1 | 11 |
| Private study hours | 176 | ||
| Total Contact hours | 74 | ||
| Total hours (100hr per 10 credits) | 250 | ||
Studying and revising of course material.
Completing of assignments and assessments.
Weekly tutorials. Examples sheets marked and returned with feedback.
!!! In order to pass the module, students must pass the examination. !!!
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | 5% midterm exam in lecture | 5 |
| Written Work | Example sheets and project work | 20 |
| Total percentage (Assessment Coursework) | 25 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 3.0 Hrs 0 Mins | 75 |
| Total percentage (Assessment Exams) | 75 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 2/13/2014
Errors, omissions, failed links etc should be notified to the Catalogue Team