Lecturer: 
Dr. Alexander D. Rahm


Lectures: 
24 x 1 hour lectures plus 10 x 1 hour tutorials in Semester 2, plus 80 hours of self study.

Credit: 
5 ECTS for second year Bachelor students in courses 2BA1, 2BCS1, 2BCW1, 2BHR1, 2BIS1, 2BLS1, 2BTP1, 2BWM1, 1EM1, 1OA1, 2OA6, 2BPP1, 2BS1, 2EH1, 2MR1. Module code MA212.
Link
to the administrative sheet of the module.

Topics : 
 An introduction to the calculus of functions of two variables, and vector valued functions.
 The topics include: Vectors; Multivariate Calculus; Optimization of elementary multivariate functions; Integration of elementary multivariate functions over polygons.

What you will learn: 
You are going to acquire the following hard skills:
Apply vectors to describe lines and planes in 3d;
Solve 3d geometric problems using vectors;
Compute partial derivatives of chains of elementary multivariate functions;
Interpret gradient and tangent planes graphically;
Classify extreme values of elementary multivariate functions;
Solve a range of optimization problems modelled by multivariate functions;
Compute iterated integrals of multivariate functions over polygons;
Solve problems related to computing volumes in 3d.

Assessment: 
Exam (80%) and Continuous Assessment (20%). 
Texts: 
 James Stewart, Calculus, (Thomson Brooks/Cole). Available at Main Library Open Access (515 STE).
 G.B. Thomas & R.I. Finney, Calculus and Analytic Geometry, (Addison Wesley). Available at Main Library Open Access (515.15 THO)
 S.L. Salas, E. Hille & J.T. Anderson, Calculus, One and Several Variables, (Wiley). Available at Main Library Open Access (515 SAL).

Resources: 
Spheres_and_regular_tetrahedra__lecture_notes.
Planes_and_their_Hessian_Normal_Forms lecture notes.
Partial_derivatives_and_gradient lecture notes.
Calculus I exam paper.
Problem Sheet 1.
Last year's exam questions.
Problem sheet for exam preparation.


Link to the Electronic Continuous Assessment.
