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Programme & Unit Catalogues

## PH10007: Mathematics for scientists 1

Owning Department/School: Department of Physics
Credits: 6
Level: Certificate (FHEQ level 4)
Period: Semester 1
Assessment: EX 100%
Supplementary Assessment: PH10007 - Mandatory Extra Work (where allowed by programme regulations)
Requisites: Students must have A-level Mathematics to undertake this unit.
Description: Aims:
The aim of this unit is to introduce basic mathematical techniques required by science students, both by providing a 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:
* sketch graphs of standard functions and their inverses;
* evaluate the derivative of a function and the partial derivative of a function of two or more variables;
* write down the Taylor series approximation to a function;
* represent complex numbers in Cartesian, polar and exponential forms, and convert between these forms;
* calculate the magnitude of a vector, and the scalar and vector products of two vectors;
* solve simple geometrical problems using vectors.

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

Content:
Functions of a real variable (3 hours): Graphs of standard functions (polynomial, exponential, logarithmic, trigonometric and hyperbolic). Domains and ranges. Composite functions. Inverse functions. Symmetries and transformations (reflections, rotation) of graphs.
Differentiation (9 hours): Limits and continuity, differentiability. Review of differentiation. Higher derivatives, meaning of derivatives. Graphical interpretation of derivatives. Logarithmic, parametric and implicit derivatives. Taylor and Maclaurin expansions, standard series. Convergence of series; ratio test, limits, L'Hopital's rule. Numerical differentiation. Functions of two variables. Partial differentiation. Taylor expansion in two variables. Chain rule. Small changes and differentials, total derivative.
Complex numbers (4 hours): Definition and algebra of complex numbers in x+iy form. Complex conjugate. Modulus and argument. Argand diagram, r exp(iθ) form. De Moivre's theorem. Solution of equations involving complex variables.
Vector algebra (6 hours): Introduction to vectors; physical examples of scalar and vector quantities. Magnitude of a vector, unit vector. Cartesian components. Scalar product; projections, components, physical examples. Vector product; determinantal form for Cartesian components, physical examples. Vector definitions of lines and planes. Triple product. Introduction to vector spaces.
Programme availability:

#### PH10007 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

#### PH10007 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

Notes:
* This unit catalogue is applicable for the 2013/4 academic year only. Students continuing their studies into 2014/15 and beyond should not assume that this unit will be available in future years in the format displayed here for 2013/14.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.