Mathematical Methods for Scientists 1a

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• Calculate the scalar and vector product of two vectors;
• Differentiate functions of several variables and manipulate then when changing variables
• Integrate various simple functions of one variable;
• Construct a Taylor series of a function and understand its relevance to local behaviour;
• Differentiate functions of one variable and use this to classify critical points
• Solve simple polynomial equations
• Understand the concept of a limit and be able to determine its value if it exists
• Sketch and manipulate exponential, trigonometric and hyperbolic functions

Basic vector algebra, cross and dot product, geometrical and physical applications.

Matrices and determinants, inverse of a matrix, using matrices to solve simultaneous equations.

Solving quadratic equations, factorising higher order polynomials. Specifying a function, its domain and range. Composition of functions. Graphs of functions. One-to-one functions, inverse functions and their graphs. Even and odd functions, periodic functions, trigonometric functions, inverse trigonometric functions.

Informal definition of a limit, rules for evaluating limits, infinite limits. Rules for differentiation, higher derivatives, critical points and applications to graph sketching. Method of least squares. Exponential and natural logarithm functions, power functions, hyperbolic functions, inverse hyperbolic functions and their derivatives. L'Hôpital's rule Rule, Taylor series expansions.

Integration, the Fundamental Theorem of Calculus, indefinite integrals, methods of integration, partial fractions, integration by parts.

Functions of two and more variables, partial derivatives of first and higher order. Chain rules. Transformations of second derivatives. Surfaces and critical points. Derivatives of vectors.

Teaching and learning methods

Resources & Reading list

Textbooks

ADAMS R A. Calculus - a Complete Course. Addison-Wesley.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.

Repeat Information

Repeat type: Internal & External