Department of Mathematical Sciences, Unit Catalogue 2011/12
|Level:||Certificate (FHEQ level 4)|
|Assessment:||CW 15%, EX 85%|
|Supplementary Assessment:||MA10208 Mandatory extra work (where allowed by programme regulations)|
|Requisites:||Students must have A Level Mathematics: Grade A or equivalent in order to take this unit.|
To teach standard methods of differentiation, integration and solving particular classes of differential equations. To guarantee a solid foundation for the applications of calculus. To introduce the theory of three-dimensional vectors and their algebraic and geometrical properties. To introduce Newtonian mechanics by considering a selection of problems involving the dynamics of particles.
After taking this unit, the students should be able to:
* Demonstrate familiarity with methods of differentiation and integration and apply these methods in problems involving differential equations.
* Recognise the classical functions and know their derivatives and integrals.
* Demonstrate familiarity with the laws of vector algebra.
* Apply vector algebra in the solution of 3D algebraic and geometric problems.
* Apply vector algebra in the modelling of physical phenomena in kinematics and Newtonian mechanics.
* Apply Newton's second law of motion to derive, analyse and solve equations of motion for problems in particle dynamics.
Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials).
Revision of A level core material. Basic calculus: rules for differentiation (product, quotient, chain, trigonometric, logs, exponential). Exponentials and logs: rules and manipulation. Curve sketching. Trigonometric identities. Partial fractions. Applications in integration techniques. Hyperbolic functions: definitions, identities, derivatives, integrals. Integration by parts.
Integration techniques. Substitution techniques (trig and hyperbolic substitutions). Fundamental theorem of calculus in practice. Applications: volume and surface of revolution, arc length.
Differential equations. Order of a differential equation. Linear independence of solutions. Statement of theorem on number of linearly independent solutions. General Solutions. CF+PI. First order linear differential equations: integrating factors. Second order linear equations: characteristic equations; real and complex roots, general real solutions. Applications: simple harmonic motion, damped oscillations, radioactive decay, population growth. Nonlinear differential equations: separable equations, homogeneous equations, Bernoulli equations, exact equations.
Vectors. Vector Algebra: scalar and vector products, vector and scalar triple products and determinants from geometric viewpoint. Vector equations of lines and planes. Differentiation of vectors with respect to scalar variable.
Kinematics and Newtonian mechanics. Polar and spherical co-ordinates. Kinematics: description of particle motion in terms of vectors, velocity and acceleration in polar coordinates, angular velocity, relative velocity. Kepler's laws, Newton's laws: momentum, laws of motion, law of gravitation; Newtonian mechanics of particles: projectiles in a resisting medium, constrained particle motion; solution of the equations of motion for a variety of problems. Motion under a central force.
MA10208 is Compulsory on the following programmes:Department of Computer Science