Calculus and Linear Algebra
| Code | School | Level | Credits | Semesters |
| MTHS1001 | Mathematical Sciences | 1 | 40 | Full Year UK |
- Code
- MTHS1001
- School
- Mathematical Sciences
- Level
- 1
- Credits
- 40
- Semesters
- Full Year UK
Summary
The course consolidates core GCE mathematical topics in the differential and integral calculus of a function of single variable and used to solve some classes of differential equations. Basic theory is extended to more advanced topics in the calculus of several variables. In addition, the basic concepts of complex numbers, vector and matrix algebra are established and extended to provide an introduction to vector spaces. Students are introduced to different types of proof, such as direct proof, proof by contradiction and proof by induction, as well as theorems and tests for determining the limits of sequences and series. An emphasis in the course is to develop general skills and confidence in applying the methods of calculus and developing techniques and ideas that are widely applicable and used in subsequent modules. Students will be use a computer package to plot graphs and implement basic algorithms. Major topics include:
- Differential and integral calculus of a single variable;
- Differential equations;
- Differential calculus of several variables;
- Multiple integrals;
- Complex numbers;
- Matrix algebra;
- Vector algebra and vector spaces;
- Logic and proof;
- Limits of sequences;
- Limits of series;
- Use of a computer package.
Target Students
Available to Natural Sciences and Liberal Arts students taking the Mathematics pathway. Not available to Single Honours and Joint Honours students from the School of Mathematical Sciences.
Classes
- Two 1-hour workshops each week for 20 weeks
- Two 1-hour lectures each week for 20 weeks
- Two 1-hour computings each week for 10 weeks
In addition there will be a small group tutorial for 1-hour per week arranged at a mutually convenient time.
Assessment
- 5% Coursework 1: Maths Coursework 1
- 5% Coursework 2: Maths Coursework 2
- 5% Computing Coursework 1: Computing Coursework 1
- 5% Computing Coursework 2: Computing Coursework 2
- 5% Computing Coursework 3: Computing Coursework 3
- 25% Exam 1 (2-hour): In class test.
- 50% Exam 2 (3-hour): Written examination.
Assessed in both autumn & spring semest
Educational Aims
To consolidate pre-university mathematics;To develop familiarity and advanced use of differential and integral calculus;To give a firm foundation in linear mathematics and associated techniques;To introduce students to mathematical proof and limits of sequences and series;To provide confidence in core mathematical techniques for use in subsequent courses.Learning Outcomes
A student who completes this course successfully will be able to:
L1 - use and manipulate complex numbers;
L2 - apply manipulation of vectors and matrices to solve systems of linear equations and eigenvalue equations;
L3 - apply standard methods to solve first order ODEs and linear second order ODEs;
L4 - understand the basic concepts of multivariate calculus;
L5 - prove statements using logic and induction where appropriate;
L6 - apply tests for convergence of sequences and series;
L7 - use mathematical software to plot graphs and implement basic algorithms.