Course Descriptions - Undergraduate Calendar 2007-2008

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Note

See also Actuarial Science, Applied Mathematics, Combinatorics and Optimization, Computational Mathematics, Computer Science, Mathematics Electives, Pure Mathematics, Statistics.

MATH 00s


MATH 51 LEC 0.00Course ID: 010374
Pre-University Algebra and Geometry
Topics covered in the course include operations with vectors, scalar multiplications dot and cross products, projections, equations of lines and planes, systems of equations, Gaussian elimination, operations with matrices, determinants, binomial theorem, proof by mathematical induction, complex numbers.
Only offered by Distance Education

MATH 52 LEC 0.00Course ID: 010375
Pre-University Calculus
The concepts included are limits, derivatives, antiderivatives and definite integrals. These concepts will be applied to solve problems of rates of change, maximum and minimum, curve sketching and areas. The classes of functions used to develop these concepts and applications are: polynomial, rational, trigonometric, exponential and logarithmic.
Only offered by Distance Education

MATH 97 LEC 2.50Course ID: 010113
Study Abroad
For studies at other universities under approved exchange agreements.
Department Consent Required

MATH 100s


MATH 103 LEC,TUT 0.50Course ID: 006847
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. [Offered: F,W,S]
Prereq: Open only to students in the following Faculties: ARTS, AHS, ES.
Antireq: OAC Finite Mathematics, OAC Algebra & Geometry, 4U Geometry and Discrete Mathematics
Also offered by Distance Education

MATH 104 LEC,TUT 0.50Course ID: 006848
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. [Offered: F]
Prereq: Open only to students in the following Faculties: ARTS, AHS, ES.
Antireq: OAC Calculus, 4U Advanced Functions and Introductory Calculus
Also offered by Distance Education

MATH 109 LEC,TUT 0.50Course ID: 006853
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. Introduction to matrix algebra. [Offered: F,W]
Prereq: MATH 104 or OAC Calculus or 4U Advanced Functions and Introductory Calculus; Accounting and Financial Management, Science and Business, and Science Biotechnology/CA students only.
Antireq: MATH 116, 117, 127, 137/147

MATH 114 LEC,TUT 0.50Course ID: 011645
Linear Algebra for Science
Vectors in 2- and 3-space and their geometry. Linear equations, matrices and determinants. Introduction to vector spaces. Eigenvalues and diagonalization. Applications. Complex numbers. [Offered: F]
Prereq: OAC Algebra & Geometry or 4U Geometry and Discrete Mathematics or 4U Mathematics of Data Management or OAC Finite Mathematics; Open only to Science students.
Antireq: MATH 115, 125, 136/146

MATH 115 LEC,TUT 0.50Course ID: 006862
Linear Algebra for Engineering
Linear equations, matrices and determinants. Introduction to vector spaces. Eigenvalues and diagonalization. Applications. Complex numbers. [Offered: F]
Prereq: OAC Algebra & Geometry or 4U Geometry and Discrete Mathematics; Open only to Engineering students.
Antireq: MATH 114, 125, 136/146

MATH 116 LEC,TUT 0.50Course ID: 006865
Calculus 1 for Engineering
Functions: review of polynomials, exponential, logarithmic, trigonometric. Operations on functions, curve sketching. Trigonometric identities, inverse functions. Derivatives, rules of differentiation. Mean Value Theorem, Newton's Method. Indeterminate forms and L'Hopital's rule, applications. Integrals, approximations, Riemann definite integral, Fundamental Theorems. Applications of the integral. [Offered: F]
Prereq: OAC Calculus or 4U Advanced Functions and Intro Calculus; Open to students in Engineering excluding Electrical and Computer Eng, Nanotechnology Eng, Software Eng and Systems Design Eng.
Antireq: MATH 107, 117, 127, 137/147

MATH 117 LEC,TUT 0.50Course ID: 006866
Calculus 1 for Engineering
Functions of engineering importance; review of polynomial, exponential, and logarithmic functions; trigonometric functions and identities. Inverse functions (logarithmic and trigonometric). Limits and continuity. Derivatives, rules of differentiation; derivatives of elementary functions. Applications of the derivative, max-min problems, Mean Value Theorem. Antiderivatives, the Riemann definite integral, Fundamental Theorems. Methods of integration, approximation, applications, improper integrals. [Offered: F]
Prereq: OAC Calculus or 4U Advanced Functions and Introductory Calculus; Open only to students in Electrical and Computer Engineering or Software Engineering or Nanotechnology Engineering.
Antireq: MATH 107, 116, 127, 137/147

MATH 118 LEC,TUT 0.50Course ID: 006867
Calculus 2 for Engineering
Methods of integration: by parts, trigonometric substitutions, partial fractions; engineering applications, approximation of integrals, improper integrals. Linear and separable first order differential equations, applications. Parametric curves and polar coordinates, arc length and area. Infinite sequences and series, convergence tests, power series and applications. Taylor polynomials and series, Taylor's Remainder Theorem, applications. [Offered: W,S]
Prereq: MATH 107 or 116 or 117 or 127 or 137/147; Open only to students in Engineering excluding students in Electrical and Computer Eng, Nanotechology Eng, Software Eng and Systems Design Eng.
Antireq: MATH 108, 119, 128, 138/148

MATH 119 LEC,TUT 0.50Course ID: 006868
Calculus 2 for Engineering
Elementary approximation methods: interpolation; Taylor polynomials and remainder; Newton's method, Landau order symbol, applications. Infinite series: Taylor series and Taylor's Remainder Theorem, geometric series, convergence test, power series, applications. Functions of several variables: partial derivatives, linear approximation and differential, gradient and directional derivative, optimization and Lagrange multipliers. Vector-valued functions: parametric representation of curves, tangent and normal vectors, line integrals and applications. [Offered: W,S]
Prereq: MATH 107 or 116 or 117 or 127 or 137/147; Open only to students in Electrical and Computer Engineering or Software Engineering or Nanotechnology Engineering.
Antireq: MATH 108, 118, 128, 138/148

MATH 125 LEC,TUT 0.50Course ID: 006869
Applied Linear Algebra 1
Systems of linear equations. Matrix algebra. Determinants. Introduction to vector spaces. Applications. [Offered: F,W,S]
Prereq: MATH 103 or OAC Algebra & Geometry or 4U Geometry and Discrete Mathematics or 4U Mathematics of Data Management or OAC Finite Mathematics; Not open to Honours Mathematics students.
Antireq: MATH 114, 115, 136/146
Also offered by Distance Education

MATH 126 LEC,TUT 0.50Course ID: 006870
Applied Linear Algebra 2
Vector spaces. Linear transformations and matrices. Inner products. Eigenvalues and eigenvectors. Diagonalization. Applications. [Offered: W,S]
Prereq: MATH 125 or 136/146; Not open to Honours Mathematics students.
Antireq: MATH 235/245
Also offered by Distance Education

MATH 127 LEC,TUT 0.50Course ID: 006871
Calculus 1 for the Sciences
Functions of a real variable: powers, rational functions, trigonometric, exponential and logarithmic functions, their properties and inverses. Intuitive discussion of limits and continuity. Definition and interpretation of the derivative, derivatives of elementary functions, derivative rules and applications. Riemann sums and other approximations to the definite integral. Fundamental Theorems and antiderivatives; change of variable. Applications to area, rates, average value. [Offered: F,W,S]
Prereq: OAC Calculus or 4U Advanced Functions and Introductory Calculus; Not open to Honours Mathematics students.
Antireq: MATH 107, 109, 116, 117, 137/147
Also offered by Distance Education

MATH 128 LEC,TUT 0.50Course ID: 006872
Calculus 2 for the Sciences
Transforming and evaluating definite integrals; further applications to volumes, arc length, improper integrals. Separable and linear first order differential equations and applications. Convergence of series; Taylor polynomials, Taylor's Remainder Theorem, Taylor series and applications. Parametric/vector representation of curves, particle motion, arc length, line integrals and work. Polar coordinates in the plane. Functions of two variables, partial derivatives, the linear approximation/tangent plane, chain rule, directional derivative and the gradient. [Offered: F,W,S]
Prereq: MATH 107 or 117 or 127 or 137/147; Not open to Honours Mathematics students.
Antireq: MATH 108, 118, 119, 138/148
Also offered by Distance Education

MATH 135 LEC,TST,TUT 0.50Course ID: 006878
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.
[Note: Offered at St. Jerome's University in the Fall term. Offered: F,W,S]
Instructor Consent Required
Prereq: OAC Algebra and Geometry or 4U Geometry and Discrete Mathematics; Honours Mathematics or Mathematics/ELAS or Software Engineering students only.
Antireq: MATH 145
Also offered at St. Jerome's University

MATH 136 LAB,LEC,TST,TUT 0.50Course ID: 006879
Linear Algebra 1 For Honours Mathematics
Systems of linear equations, matrix algebra, elementary matrices, computational issues. Real and complex n-space, vector spaces and subspaces, basis and dimension, rank of a matrix, linear transformations and matrix representations. Inner products, angles and orthogonality, applications.
[Note: Offered at St. Jerome's University in the Winter term. Offered: F,W,S]
Prereq: MATH 135/145; Honours Mathematics or Mathematics/ELAS students only.
Antireq: MATH 114, 115, 125, 146
Also offered at St. Jerome's University

MATH 137 LAB,LEC,TST,TUT 0.50Course ID: 006880
Calculus 1 for Honours Mathematics
Rational, trigonometric, exponential, and power functions of a real variable; composites and inverses. Absolute values and inequalities. Limits and continuity. Derivatives and the linear approximation. Applications of the derivative, including curve sketching, optimization, related rates, and Newton's method. The Mean Value Theorem and error bounds. Introduction to the Riemann Integral and approximations. Antiderivatives and the Fundamental Theorem. Change of variable, areas and rate integrals. Suitable topics are illustrated using computer software.
[Note: Offered at St. Jerome's University in the Fall term. Offered: F,W,S]
Instructor Consent Required
Prereq: OAC Calculus or 4U Advanced Functions and Introductory Calculus; Honours Mathematics or Mathematics/ELAS students only.
Antireq: MATH 107, 116, 117, 127, 147
Also offered at St. Jerome's University

MATH 138 LEC,TST,TUT 0.50Course ID: 006881
Calculus 2 for Honours Mathematics
Riemann sums and the integral. Antiderivatives and the Fundamental Theorem of Calculus. Applications of the integral. Transforming and evaluating integrals. Improper integrals. Numerical approximation of integrals. Taylor's theorem and polynomial approximation. Convergence of series. Tests for convergence. Functions defined as power series. Taylor series.
[Note: Offered at St. Jerome's University in the Winter term. Offered: F,W,S]
Prereq: MATH 137/147; Honours Mathematics or Mathematics/ELAS students only.
Antireq: MATH 108, 118, 119, 128, 148
Also offered at St. Jerome's University

MATH 145 LEC,TST,TUT 0.50Course ID: 006886
Algebra (Advanced Level)
MATH 145 is an advanced-level version of MATH 135. [Offered: F]
Department Consent Required
Prereq: OAC Algebra & Geometry or 4U Geometry and Discrete Mathematics; Honours Mathematics students only.
Antireq: MATH 135

MATH 146 LAB,LEC,TST,TUT 0.50Course ID: 006887
Linear Algebra 1 (Advanced level)
MATH 146 is an advanced-level version of MATH 136. [Offered: W,S]
Prereq: MATH 145; Honours Mathematics students only.
Antireq: MATH 114, 115, 125, 136

MATH 147 LAB,LEC,TST,TUT 0.50Course ID: 006888
Calculus 1 (Advanced Level)
MATH 147 is an advanced-level version of MATH 137. [Offered: F]
Department Consent Required
Prereq: OAC Calculus or 4U Advanced Functions and Introductory Calculus; Honours Mathematics students only.
Antireq: MATH 107, 116, 117, 127, 137

MATH 148 LEC,TST,TUT 0.50Course ID: 006889
Calculus 2 (Advanced Level)
MATH 148 is an advanced-level version of MATH 138. [Offered: W,S]
Prereq: MATH 147; Honours Mathematics students only.
Antireq: MATH 108, 118, 119, 128, 138

MATH 200s


MATH 211 LEC,TUT 0.50Course ID: 006891
Advanced Calculus 1 for Electrical and Computer Engineers
Fourier series. Ordinary differential equations. Laplace transform. Applications to linear electrical systems. [Offered: F,W]
Prereq: MATH 119; Not open to Mathematics students.
Antireq: MATH 218, 228
(Cross-listed with ECE 205)

MATH 212 LEC,TUT 0.50Course ID: 006892
Advanced Calculus 2 for Electrical Engineers
Triple integrals, cylindrical and spherical polar coordinates. Divergence and curl, applications. Surface integrals, Green's, Gauss' and Stokes' theorems, applications. Complex functions, analytic functions, contour integrals, Cauchy's integral formula, Laurent series, residues. [Offered: F]
Prereq: MATH 211/ECE 205; Not open to Mathematics students.
Antireq: AMATH 231, MATH 217, 227/227P, 237/247
(Cross-listed with ECE 206)

MATH 213 LEC,TUT 0.50Course ID: 011849
Advanced Mathematics for Software Engineers
Fourier series. Differential equations. Laplace transforms. Applications to circuit analysis. [Offered: S]
Prereq: MATH 119; Software Engineering students only.
Antireq: AMATH 250, MATH 211/ECE 205, MATH 218, 228

MATH 217 LEC,TUT 0.50Course ID: 006897
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. [Offered: F,W]
Prereq: MATH 118; Not open to Mathematics students.
Antireq: AMATH 231, CIVE 221, ENVE 221, MATH 212/ECE 206, MATH 227/227P, 237/247, ME 201

MATH 218 LEC,TUT 0.50Course ID: 006898
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. [Offered: F,W,S]
Prereq: MATH 118 or SYDE 112; Engineering students only.
Antireq: AMATH 250, 251, 351, CIVE 222, ENVE 223, MATH 211/ECE 205, MATH 228, ME 203, SYDE 211

MATH 227 LEC,TUT 0.50Course ID: 006907
Calculus 3 for Honours Physics
Directional derivative and the chain rule for multivariable functions. Optimization, Lagrange multipliers. Double and triple integrals on simple domains; transformations and Jacobians; change of variable in multiple integrals. Vector fields, divergence and curl. Vector integral calculus: Line and surface integrals, Green's Theorem, Stokes' Theorem, Gauss' Theorem, conservative vector fields.
Prereq: MATH 128; Not open to Mathematics students.
Antireq: AMATH 231, MATH 212/ECE 206, MATH 217, 227P, 237/247

MATH 228 LEC,TUT 0.50Course ID: 006908
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. [Offered: F,W]
Prereq: MATH 128; Not open to Mathematics students.
Antireq: AMATH 250, MATH 218

MATH 235 LEC,TST,TUT 0.50Course ID: 006913
Linear Algebra 2 for Honours Mathematics
Orthogonal and unitary matrices and transformations. Orthogonal projections, Gram-Schmidt procedure, best approximations, least-squares. Determinants, eigenvalues and diagonalization, orthogonal diagonalization, singular value decomposition, applications.
[Note: Offered at St. Jerome's University in the Fall term. Offered: F,W,S]
Prereq: MATH 136/146; Honours Mathematics students only.
Coreq: MATH 138/148.
Antireq: MATH 126, 245
Also offered at St. Jerome's University

MATH 237 LEC,TST,TUT 0.50Course ID: 006914
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.
[Note: Offered at St. Jerome's University in the Fall term. Offered: F,W,S]
Prereq: MATH 136/146, 138/148; Honours Mathematics students only.
Antireq: MATH 212/ECE 206, MATH 217, 227/227P, 247
Also offered at St. Jerome's University

MATH 239 LEC,TST,TUT 0.50Course ID: 006915
Introduction to Combinatorics
Introduction to graph theory: colourings, matchings, connectivity, planarity. Introduction to combinatorial analysis: generating series, recurrence relations, binary strings, plane trees.
[Note: Offered at St. Jerome's University in the Fall term. Offered: F,W,S]
Prereq: (MATH 136/146, 138/148 and enrolled in Honours Mathematics) or level at least 2A Software Engineering.
Antireq: CO 220, MATH 249
Also offered at St. Jerome's University

MATH 245 LEC,TST 0.50Course ID: 006920
Linear Algebra 2 (Advanced Level)
MATH 245 is an advanced-level version of MATH 235. [Offered: F,W]
Prereq: MATH 146; Honours Mathematics students only.
Antireq: MATH 126, 235

MATH 247 LEC,TST 0.50Course ID: 006921
Calculus 3 (Advanced Level)
MATH 247 is an advanced-level version of MATH 237. [Offered: F,W]
Prereq: MATH 146, 148; Honours Mathematics students only.
Antireq: MATH 212/ECE 206, MATH 217, 227/227P, 237

MATH 249 LEC,TST 0.50Course ID: 006922
Introduction to Combinatorics (Advanced Level)
MATH 249 is an advanced-level version of MATH 239. [Offered: F,W]
Prereq: MATH 136/146, MATH 138/148; Honours Mathematics students only.
Antireq: CO 220, MATH 239


The Undergraduate Calendar is published by the Office of the Registrar, University of Waterloo, Waterloo, ON N2L 3G1 Canada

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