Undergraduate Calendar 2000-2001

Undergraduate Office
MC 5115, ext. 3905

Note

MATH000s

MATH 010 F,W,S 0.0
Non-Credit Year One Testing Slot
All students enrolled in one or more of MATH 135, 136, 137, 138, 145, 146, 147, 148, and CS 120, 130, 134 are automatically enrolled in a non-credit lab that is scheduled one evening each week from 7:00 to 9:00 p.m. This time slot appears as a MATH 010 entry on student timetables and is reserved for mid-term tests in the above courses. This time slot is used only on those evenings when mid-term tests are scheduled.


MATH 020 F,W,S 0.0
Non-Credit Year Two Testing Slot
All students enrolled in any second-year mathematics course offered by the Faculty of Mathematics, with the exception of various service courses designed for students in other faculties, are automatically enrolled in a non-credit lab that is scheduled from 4:30 to 6:30 p.m. Tuesday and Thursday each week. This time slot is used only on those days when mid-term tests are scheduled.


MATH100s

MATH 103 F,W,S 3C,1T 0.5
Introductory Algebra For Arts and Social Science
An introduction to applications of algebra to business, the behavioural sciences, and the social sciences. Topics will be chosen from set theory, permutations and combinations, binomial theorem, probability theory, systems of linear equations, vectors and matrices, mathematical induction.
Prereq: Grade 12 Mathematics or equivalent
Not open to students in the Faculties of Engineering, Mathematics or Science, or to other students who have credit in any one of OAC Algebra, OAC Finite Mathematics, or the equivalent.


MATH 104 W 3C,1T 0.5
Introductory Calculus For Arts and Social Science
An introduction to applications of calculus in business, the behavioural sciences, and the social sciences. The models studied will involve polynomial, rational, exponential and logarithmic functions. The major concepts introduced to solve problems are rate of change, optimization, growth and decay, and integration.
Prereq: Grade 12 Mathematics or equivalent
Not open to students in the Faculties of Engineering, Mathematics or Science, or to other students who have credit in OAC Calculus or the equivalent.


MATH 109 F 3C,2T 0.5
Mathematics For Accounting
Review and extension of differential calculus for functions of one variable. Multivariable differential calculus. Partial derivatives, the chain rule, maxima and minima and Lagrange multipliers. Mathematics of finance. Simple and compound interest, present value, annuities and continuous compounding.
Prereq: OAC Calculus, or MATH 104
Antireq: All Calculus courses labelled MATH 1x7, 1x8, 1x9
Open only to Arts students in the School of Accountancy.


MATH 111A
Algebra


MATH 115 F 3C,2T 0.5
Linear Algebra for Engineering
Linear equations, matrices and determinants. Introduction to vector spaces. Eigenvalues and diagonalization. Introduction to linear programming. Complex numbers.
Prereq: OAC Algebra or equivalent
Antireq: MATH 125, 136, 146
(Formerly MATH 114)
Not open to students registered in the Faculty of Mathematics.


MATH 117 F 3C,2L 0.5
Calculus 1 For Engineering
Limits, continuity, derivatives. Elementary funtions. Mean Value Theorem. Related rates, applications. Newton's method. Indeterminate forms and L'Hôpital's Rule. Indefinite and definite integrals. Fundamental Theorem. Applications of the integral. Improper integrals. Inverse functions. Methods of integration.
Prereq: OAC Calculus
Antireq: MATH 107, 127, 137, 147
Not open to students in the Faculty of Mathematics.


MATH 118 W,S 3C,2L 0.5
Calculus 2 For Engineering
Methods of integration (continued). Parametric and polar equations. Sequences and series, convergence tests. Power series, Taylor series. Functions of several variables, partial derivatives, chain rule. First-order and reducible second-order ordinary differential equations. Applications.
Prereq: MATH 117 or equivalent
Antireq: MATH 108, 119, 128, 138, and 148
Not open to students in Electrical & Computer Engineering or to students in the Faculty of Mathematics.


MATH 119 W,S 3C, 2L 0.5
Calculus 2 for Engineering
Methods of integration (continued). Parametric and polar equations. Sequences and series, convergence tests. Power series, Taylor series. Functions of several variables, partial derivatives, chain rule, implicit differentiation. Double integrals, iterated integrals, applications. Change of variables, Jacobians, polar coordinates. Triple integrals, cylindrical and spherical coordinates.
Prereq: MATH 117 or equivalent
Antireq: MATH 108, 118, 128, 138, and 148
Open only to students in Electrical and Computer Engineering.


MATH 125 F,W,S 3C,1T 0.5
Applied Linear Algebra 1
Vectors in 2- and 3-space and their geometry. Vectors in n-space. Scalar and vector products. Matrices. Systems of linear equations. Determinants. Complex numbers. Applications.
Prereq: One of OAC Algebra, OAC Finite Mathematics, MATH 103
Antireq: MATH 115, 136, 146
Not open to Honours Mathematics students.


MATH 126 F,W,S 3C 0.5
Applied Linear Algebra 2
Linear independence and bases. Linear transformations and matrices. Orthogonal transformations. Eigenvalues and eigenvectors. Diagonalization. Applications.
Prereq: MATH 125, or equivalent
Antireq: MATH 235, 245
Not open to Honours Mathematics students.


MATH 127 F,W,S 3C,2T 0.5
Calculus 1
Review of functions, limits, continuity and differentiation, including trigonometric, exponential, logarithmic, power and rational functions and their inverses. Interpretation and applications of the derivative. Riemann sums and the integral. Antiderivatives and the Fundamental Theorems of Calculus. Applications of the integral. Transforming and evaluating integrals. Improper integrals.
Prereq: OAC Calculus
Antireq: MATH 107, 109, 117, 137, 147
Not open to Honours Mathematics students.


MATH 128 F,W,S 3C,2T 0.5
Calculus 2
Separable and linear differential equations of first and second order. Convergence of power series. Taylor polynomials and Taylor series. Parametric representation of curves; applications to motion in R². and R³. Polar coordinates in R². Functions of two variables. Partial derivatives and the linear approximation. The Chain Rule. Directional derivatives. Maxima and minima; optimization problems.
Prereq: MATH 127 or equivalent
Antireq: MATH 108, 118, 119, 138, 148
Not open to Honours Mathematics students.


MATH 135 F,W 3C,1T 0.5
Algebra For Honours Mathematics
A study of the basic algebraic systems of mathematics: the integers, the integers modulo n, the rational numbers, the real numbers, the complex numbers and polynomials.
Prereq: OAC Algebra or equivalent
Antireq: MATH 145
Also offered at St. Jerome's College in the Fall term.


MATH 136 F,W,S 3C,1T 0.5
Linear Algebra 1 For Honours Mathematics
Vector spaces, linear independence and bases. Linear transformations, matrices and change of basis. Systems of linear equations, elementary operations and rank of a matrix. Applications.
Prereq: MATH 135
Antireq: MATH 115, 125, 146
Also offered at St. Jerome's College in the Winter term.


MATH 137 F,W,S 3C,2T 0.5
Calculus 1 For Honours Mathematics
Functions, limits, and continuity. Review of differentiation. Interpretation and applications of the derivative. The Mean Value Theorem. Inverse functions. Riemann sums and the integral. Antiderivatives and the Fundamental Theorem of Calculus. Applications of the integral. Transforming and evaluating integrals.
Prereq: OAC Calculus
Antireq: MATH 107, 117, 127, 147
Also offered at St. Jerome's College in the Fall term.


MATH 138 F,W,S 3C,1T 0.5
Calculus 2 For Honours Mathematics
Separable and linear differential equations. Taylor's theorem and polynomial approximations. L'Hopital's theorem and order symbols. Limits at infinity and improper integrals. Convergence of series. Functions defined as power series. Parametric representation of curves, arc length. Functions of two variables. Partial derivatives and the linear approximation.
Prereq: MATH 137
Antireq: MATH 108, 118, 119, 128, 148
Also offered at St. Jerome's College in the Winter term.


MATH 145 F 3C,1T 0.5
Algebra (Advanced Level)
MATH 145 is an advanced-level version of MATH 135.
Prereq: OAC Algebra (or equivalent). The students admitted are selected by the Faculty of Mathematics.
Antireq: MATH 135


MATH 146 W,S 3C,1T 0.5
Linear Algebra 1 (Advanced level)
MATH 146 is an advanced-level version of MATH 136.
Prereq: MATH 145 or consent of instructor
Antireq: MATH 115, 125, 136


MATH 147 F 3C,1T 0.5
Calculus 1 (Advanced Level)
MATH 147 is an advanced-level version of MATH 137.
Prereq: OAC Calculus (or equivalent). The students admitted are selected by the Faculty of Mathematics.
Antireq: MATH 107, 117, 127, 137


MATH 148 W,S 3C,1T 0.5
Calculus 2 (Advanced Level)
MATH 148 is an advanced-level version of MATH 138.
Prereq: MATH 147 or consent of instructor
Antireq: MATH 108, 118, 119, 128, 138


MATH200s

MATH 211 F,W 3C,1T 0.5
Advanced Calculus 1 For Electrical and Computer Engineers
Fourier series. Ordinary differential equations. Laplace transform. Applications to linear electrical systems.
Prereq: MATH 119
Antireq: MATH 218, 228
Cross-listed as E&CE 205
Not normally open to students in the Faculty of Mathematics.


MATH 212 F 3C,1T 0.5
Advanced Calculus 2 For Electrical Engineers
Gradient, directional derivative, divergence and curl; applications. Line and surface integrals. Green's, Gauss', and Stokes' theorems; applications. Complex functions, analytic functions, contour integrals, Cauchy's integral formula, Laurent series, residues.
Prereq: MATH 211
Antireq: AM 231, MATH 217, 227P
Cross-listed as E&CE 206
Not normally open to students in the Faculty of Mathematics.


MATH 217 F,W 3C, 1T 0.5
Calculus 3 for Chemical Engineering
Optimization problems including the method of Lagrange multipliers. Double and triple integrals, including transformations and change of variable. Vector fields, divergence and curl. Vector integral calculus, including Green's theorem, the divergence theorem and Stokes' theorem. Applications in engineering are emphasized.
Prereq: MATH 118
Antireq: AM 231, CIV E 221, E&CE 206, ENV E 221, M E 201, MATH 212, 227P, 237, 247
(Formerly MATH 210)
Not open to students in the Faculty of Mathematics.


MATH 218 F,W,S 3C, 1T 0.5
Differential Equations For Engineers
First order equations, second order linear equations with constant coefficients, series solutions, the Laplace transform method, systems of linear differential equations. Applications in engineering are emphasized.
Prereq: MATH 118 or SY DE 112
Antireq: AM 250, 251, 351, CIV E 222, E&CE 205, ENV E 223, M E 203, MATH 211, 228, SY DE 211
Cross-listed as SY DE 211
(Formerly MATH 216)
Not open to students in the Faculty of Mathematics.


MATH 227
Calculus 3


MATH 227P F 3C,1T 0.5
Calculus 3 for Honours Physics
Vector fields, divergence and curl. Double and triple integrals. Transformations and Jacobians. Change of variable in multiple integrals. Line and surface integrals. Vector integral calculus. Green's theorem, Stokes' theorem and Gauss' theorem. Conservative vector fields.
Prereq: MATH 128
Antireq: MATH 212, 217, 237, 247, AM 231
Not open to students registered in the Faculty of Mathematics.


MATH 228 F,W 3C 0.5
Differential Equations For Physics and Chemistry
First-order equations, second-order linear equations with constant coefficients, series solutions and special functions, the Laplace transform method. Applications in physics and chemistry are emphasized.
Prereq: MATH 128
Antireq: AM 250, MATH 218
(Formerly MATH 215, 216)
Not open to students in the Faculty of Mathematics.


MATH 235 F,W,S 3C 0.5
Linear Algebra 2 For Honours Mathematics
Determinants. Eigenvalues, diagonalization and the minimal polynomial. Inner products, orthonormal bases, orthogonal and unitary matrices, quadratic forms. Applications.
Prereq: MATH 136
Antireq: MATH 126, 245
Also offered at St. Jerome's College in the Fall term.


MATH 237 F,W,S 3C 0.5
Calculus 3 For Honours Mathematics
Calculus of functions of several variables. Limits, continuity, differentiability, the chain rule. The gradient vector and the directional derivative. Taylor's formula. Optimization problems. Mappings and the Jacobian. Multiple integrals.
Prereq: MATH 136, 138
Antireq: MATH 212, 217, 227P, 247
Also offered at St. Jerome's College in the Fall term.


MATH 239 F,W,S 3C 0.5
Introduction to Combinatorics
Introduction to graph theory: colourings, matchings, connectivity, planarity. Introduction to combinatorial analysis: generating series, recurrence relations, binary strings, plane trees.
Prereq: MATH 136, 138
Antireq: MATH 249, C&O 220 and C&O 230
Also offered at St. Jerome's College in the Fall term


MATH 245 F,W 3C 0.5
Linear Algebra 2 (Advanced Level)
MATH 245 is an advanced-level version of MATH 235.
Prereq: MATH 146 or consent of instructor
Antireq: MATH 126, 235


MATH 247 F,W 3C 0.5
Calculus 3 (Advanced Level)
MATH 247 is an advanced-level version of MATH 237.
Prereq: MATH 146 and 148 or consent of instructor
Coreq: MATH 136 or 146
Antireq: MATH 212, 217, 227P, 237


MATH 249 F,S 3C 0.5
Introduction to Combinatorics (Advanced Level)
MATH 249 is an advanced-level version of MATH 239.
Prereq: MATH 136, 138
Antireq: MATH 239, C&O 220, 230

The Undergraduate Calendar is published by the
Office of the Registrar, University of Waterloo, Waterloo, ON N2L 3G1 Canada
Inquiries: infoucal@www.adm.uwaterloo.ca
Revised February 2000