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## PH10008: Mathematics for scientists 2

Credits: 6
Level: Certificate (FHEQ level 4)
Period: Semester 2
Assessment: EX 100%
Supplementary Assessment: PH10008 - Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this unit you must take PH10007
Description: Aims:
The aim of this unit is to introduce basic mathematical techniques required by science students, both by providing reinterpretation of material already covered at A-level in a more general and algebraic form and by introducing more advanced topics.

Learning Outcomes:
After taking this unit the student should be able to:
* integrate functions using a variety of standard techniques;
* find the general solution of first and second order ordinary differential equations and show how a particular solution may be found using boundary conditions;
* solve some first and second order partial differential equations by separation of variables;
* calculate the determinant and inverse of a matrix, and the product of two matrices;
* use matrix methods to solve simple linear systems.

Skills:
Numeracy T/F A, Problem Solving T/F A.

Content:
Integration (6 hours): Review of integration. Meaning of integration. Methods of integration. Multiple integral, change of order in integration. Applications of integration (area, volume, etc). Numerical integration methods.
Ordinary differential equations (8 hours): Origin of ODEs. Solution of first order ODEs by integrating factors and separation of variables. Solution of second order ODEs with constant coefficients. Complementary function and particular integral. Applications in the natural sciences. Numerical solution of ODEs; Euler method, Runge-Kutta methods.
Introduction to partial differential equations (2 hours): Origin of PDEs. Solution of PDEs by separation of variable. Wave equation in one dimension.
Matrices and determinants (6 hours): Introduction to matrices. Special matrices. Transpose of a matrix. Matrix multiplication. Linear transformations. Determinants. Inverse of a matrix. Simultaneous linear equations. Solution of simultaneous equations, Gaussian elimination.
Programme availability:

#### PH10008 is Compulsory on the following programmes:

Department of Physics
• USPH-AFB01 : BSc (hons) Physics (Full-time) - Year 1
• USPH-AFB05 : BSc (hons) Physics with Computing (Full-time) - Year 1
• USPH-AKB06 : BSc (hons) Physics with Computing (with Placement) (Full-time with Thick Sandwich Placement) - Year 1
• USPH-AAB06 : BSc (hons) Physics with Computing with Year Abroad (Full-time with Study Year Abroad) - Year 1
• USPH-AKB02 : BSc (hons) Physics (with Placement) (Full-time with Thick Sandwich Placement) - Year 1
• USPH-AAB02 : BSc (hons) Physics with Year Abroad (Full-time with Study Year Abroad) - Year 1
• USPH-AFM02 : MPhys Physics (Full-time) - Year 1
• USPH-AFM04 : MPhys Physics with Research Placement (Full-time) - Year 1
• USPH-AAM03 : MPhys Physics with Year Abroad (Full-time with Study Year Abroad) - Year 1

#### PH10008 is Optional on the following programmes:

Department of Chemistry
• USCH-AFB01 : BSc (hons) Chemistry (Full-time) - Year 1
• USCH-AKB02 : BSc (hons) Chemistry with Industrial Training (Full-time with Thick Sandwich Placement) - Year 1
• USCH-AAB02 : BSc (hons) Chemistry with Study Year abroad (Full-time with Study Year Abroad) - Year 1
• USCH-AFM02 : MChem (hons) Chemistry (Full-time) - Year 1
• USCH-AKM02 : MChem (hons) Chemistry with Industrial Training (Full-time with Thick Sandwich Placement) - Year 1
• USCH-AAM03 : MChem (hons) Chemistry with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
Programmes in Natural Sciences
• UXXX-AFB01 : BSc (hons) Natural Sciences (Full-time) - Year 1
• UXXX-AKB02 : BSc (hons) Natural Sciences with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 1
• UXXX-AAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 1
• UXXX-AFM01 : MSci (hons) Natural Sciences (Full-time) - Year 1
• UXXX-AKM02 : MSci (hons) Natural Sciences with Professional Placement (Full-time with Thick Sandwich Placement) - Year 1
• UXXX-AAM02 : MSci (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 1

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.