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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.
Due to the condensed nature of this course, this course requires a commitment of 20 hours per week of classes and study. You must be able to attend all in-person classes as these are essential to support your learningEMTH119 consolidates concepts from EMTH118 and introduces more advanced ideas in calculus, linear algebra and probability. It includes applications of this mathematics to applied and engineering problems, and uses python to implement numerical methods. It is a prerequisite for many courses in engineering mathematics and other subjects at the 200-level.Topics: First-order ordinary differential equations with applications. Direction Fields and Euler's method. Polar form of complex numbers. Second-order ordinary differential equations with applications.Newton-Raphson for root finding. Introduction to convergence of sequences and series. Applications of differentiation to approximation. Approximation by Taylor polynomials. Landau’s notation and order of magnitude.Determinants, eigenvalues and eigenvectors. Sets and probability. Discrete random variables. Continuous random variables. Expectation, mean, and variance.Integration of rational functions via partial fractions. Parametrised curves. Arc length. Numerical integration including the trapezium rule.Multivariate differentiation and classification of critical points.
Students who have succeeded in this course will be able touse calculus, algebra or probability to - evaluate integrals arising in mathematics and engineering - solve first and second order differential equations - find Taylor approximations to functions - calculate mean and variance of random variables and solve probability problems arising in engineering applications - calculate determinants, eigenvalues and eigenvectors - investigate the geometry of multivariable functions and classify critical pointsdemonstrate understanding of the mathematical topics in the course by - giving definitions of fundamental concepts - competent manipulation of functions, matrices, random variables and complex numbers - choosing effective solution techniques for given problems - verifying correctness of mathematical calculations - Knowing when and how to apply suitable numerical methodsdescribe 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
Phillipa Gourdie
Stewart, James; Calculus : early transcendentals ; Eighth edition; Cengage Learning, 2016.
General information for students Library portal LEARN
Domestic fee $986.00
International fee $5,500.00
* 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 .