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A continuation of EMTH118. Topics covered include methods and Engineering applications of calculus, differential equations, and linear algebra, along with an introduction to probability. This course is a prerequisite for many courses in engineering mathematics and other subjects at 200 level.
EMTH119 consolidates concepts from EMTH118 and introduces more advanced ideas in calculus and linear algebra. It includes applications of this mathematics to applied and engineering problems.It also incorporates some study of probability. It is a prerequisite for many courses in engineering mathematics and other subjects at the 200-level.Topics: First and second order ordinary differential equations with applications. Numerical solution using Euler's method.Determinants, eigenvalues and eigenvectors. Newton's method for nonlinear equations. Introduction to sequences and series. Approximation by Taylor polynomials. Probability. Sets and probability. Discrete random variables. Continuous random variables. Expectation, mean, and variance.Integration of rational functions using partial fractions. Application of integration to arc length. Numerical integration. Introduction to multivariable functions including partial differentiation and stationary points of surfaces.Python implementation of some of the introduced concepts and methods.Contact person for this course: Phillipa Gourdie
Students who have succeeded in this course will be able to• use calculus, algebra or probability to - solve first and second order differential equations - find Taylor approximations to functions - calculate determinants, eigenvalues and eigenvectors - calculate mean and variance of random variables and solve probability problems arising in engineering applications - evaluate integrals arising in mathematics and engineering - investigate the geometry of multivariable functions and classify critical points• demonstrate understanding of the mathematical topics in the course by - giving definitions of fundamental concepts - competent manipulation of functions, matrices, and random variables - choosing effective solution techniques for given problems - verifying correctness of mathematical calculations• describe and interpret the meaning of mathematical solutions to engineering problems (particularly differential equations and random variables)• synthesise material from different sections of course (for example, using integration techniques and limit evaluation to solve differential equation or probability problems)
EMTH118, COSC131
MATH103, MATH109, MATH199
Mingfeng Qiu
Jenny Harlow and Phillipa Gourdie
Stewart, James; Calculus : early transcendentals ; Eighth edition; Cengage Learning, 2016.
General information for students Library portal LEARN
Domestic fee $1,122.00
International fee $6,238.00
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
For further information see Mathematics and Statistics .