Advanced Calculus

Quick Info

The following courses are prerequisites:

This unit is offered as a part of the following awards:

Solve differential equations using different mathematical techniques and understanding their applications.
Investigate advanced topics in calculus - functions of two variables, multiple integrals, vector analysis and differential equations.
Examine partial derivatives, functions of two variables and Lagrange multipliers.
Acquire skills in working multiple integrals and vector analysis.
Examine the concepts of advanced calculus in context and the ability to use these concepts to make reasoned, logical answers with sound mathematical reasoning.

Introduction to multivariable calculus: Euclidean space, sets and function notation, open balls
Functions of two variables: Surfaces, Partial differentiation, Directional derivatives, The derivative, Differentials and chain rule, Limits – formal definition and polar coordinates, Continuity, Tangent plane and normal line, Critical points, Max and min values, Lagrange multipliers.
Multiple Integrals: Double and triple Integrals, Double integrals over rectangles, Integrating over a region, Change of variables, Inverse and Implicit function theorems.
Vector Analysis: Curves and paths, Vector fields, Laplace equation, Integrals over paths, Line integrals, Equivalent paths, Parameterised surfaces, Integrals over surfaces, Green’s theorem, Stoke’s theorem, Gauss’s theorem.
More Differential Equations: Refresher of linear and separable first order ODEs, Refresher of second order ODEs, Applications of ODEs, Variation of parameters, Laplace transforms.

Face to Face (on site)
E-Learning (online)
Intensive (2 hour seminar per week. The 10 hours total workload each week includes these 2 hours plus an additional 8 hours for personal study and assessments)

Please consult your course prospectus or enquire about how and when this course will be offered next at Alphacrucis University College.