Module Code & Title: MATH1B Calculus of Several Variables
Availability: Semester 2
Academic Unit: 4 AU
Pre-requisite: MATH1A
Module Description: Lectures: 39 hours; Tutorials: 12 hours; Labs 6 hours
Content
Calculus of several variables: Parametric equations and polar coordinates. Vectors in R2 and R3. Vector functions. Partial derivatives, limits and continuity, chain rule, directional derivatives, gradients, Lagrange multipliers. Double integrals, area of a surface, triple integrals. Vector calculus, line integrals, Green’s Theorem, surface integrals, Gauss’s divergence theorem, Stokes’s Theorem.
Basics of Linear Algebra: Sets, operations on sets, properties of sets. Systems of linear equations, Gaussian elimination. Matrices, inverses, determinants. Vector spaces, subspaces, linear independence, basis, dimension, row and column spaces, rank.
Objectives
Intensive introduction to the calculus of several variables and linear algebra for Science and Engineering scholars.
Learning Outcomes
Upon successful completion of the course, the students will be able to:
a. Find critical points of a function of several variables an apply it to solve problems on optimization with or without constraints.
b. Understand concepts of continuity and differentiability of maps vector spaces.
c. Integrate functions of functions of several variables and apply these techniques in statistics and physics.
d. Know several forms of Stokes’ Theorem in R3.
e. Solve questions on matrices, systems of linear equations.
Course Outline
Topics Lecture hours Tutorial hours
1. Basics of differentiable maps 12 4
2. Basics of integration of functions 14 4
of several variables
3. Basics of linear algebra 13 4
Student Assessment
Students will be assessed by:
a. A final 2-hour written examination (60%)
b. Continuous assessment (40%)
Textbooks/References
J. Stewart, Calculus, 5th or 6th edition, Thomson Brook/Cole 2003
S.H. Freidberg, A.J. Insel, L.E. Spence. Linear Algebra, Prentice Hall, 4th edition, 2003