Teaching Responsibility
LJMU Schools involved in Delivery:
Computer Science and Mathematics
Learning Methods
Lecture
Practical
Tutorial
Module Offerings
4101MATHS-JAN-CTY
Aims
To provide a thorough grounding in the basic mathematical concepts and methods
needed to solve a range of problems with scientific, business and statistical
applications.
To develop a firm foundation for single variable calculus.
To provide a basic grounding in vector algebra.
To introduce the concepts of complex numbers and their application.
To introduce multivariable calculus.
To introduce methods for solving ordinary first and second order differential
equations.
Learning Outcomes
1.
Apply the theory of differentiation, integration, complex numbers, partial differentiation, differential equations and elementary vector algebra to solving problems.
2.
Formulate and solve problems using fundamental mathematical methods.
Module Content
Outline Syllabus:Differentiation: Limits, continuity, derivatives from first principles, differentiability.
Rules of Differentiation: Product, Quotient, Chain, Implicit, Parametric, Logarithmic.
Applications of Differentiation: maxima and minima, curve sketching, finding normals and tangents.
Series: Maclaurin series, Taylor series and regions of convergence.
L'Hopital's rule: derivation and application.
Integration: The Riemann Sum, the fundamental theorem of calculus, rules of integration, applications of integration.
Complex Numbers: Arithmetic of, conjugates, modulus and arguments, Argand diagram, Cartesian and polar form, Euler's formula.
Multivariable calculus: Introduction to Partial differentiation;
Ordinary differential equations: First order; variables separable, integrating factor.
Second order; constant coefficients, complementary function, particular integral.
Vectors: Vector algebra, equation of a line, scalar product, vector product, equation of a plane, volume of parallelepiped using determinants.
Module Overview:
This module will provide the basic mathematical concepts and methods needed to solve a range of problems with scientific, business and statistical applications. You will be introduced to concepts of complex numbers and their application and introduced to methods for solving ordinary first and second order differential equations.
This module will provide the basic mathematical concepts and methods needed to solve a range of problems with scientific, business and statistical applications. You will be introduced to concepts of complex numbers and their application and introduced to methods for solving ordinary first and second order differential equations.
Additional Information:The foundations of mathematics (concentrating particularly on calculus, complex numbers and vectors) are covered here using an online text and assessment software support as appropriate. The module provides an introduction to some of the mathematical methods required for the solution of problems in Applied Mathematics.